Contact-Rich Manipulation and Contact Planning

1. Introduction

Robotic manipulation in unstructured environments demands sustained, purposeful contact between the robot and objects in its workspace. Unlike pick-and-place in structured settings, where contact is confined to brief grasping events, tasks such as in-hand reorientation, tool use, assembly, and object rearrangement among clutter involve sequences of contacts that must be planned, established, maintained, and broken in a coordinated fashion. The difficulty of this problem stems from a confluence of challenges that are individually hard and collectively formidable. Contact dynamics are hybrid, switching between continuous motion phases and discrete mode transitions. The space of possible contact sequences is combinatorially vast. Contact forces are governed by nonsmooth complementarity conditions. Real-world deployment demands robustness to geometric, material, and state-estimation uncertainty.

The past few years have seen a convergence of advances that make a comprehensive review timely. Trajectory optimization has matured from methods requiring pre-specified contact schedules [101] to contact-implicit formulations that discover contact sequences as part of the optimization [7, 58, 59, 75], with recent work achieving real-time model predictive control rates [32, 34, 39, 43, 45, 47]. Concurrently, deep reinforcement learning has progressed from learning simple contact tasks in simulation [50, 51] to zero-shot sim-to-real transfer of dexterous in-hand manipulation [69], while tactile sensing technology has advanced from laboratory prototypes to low-cost, open-source designs that can be retrofitted to commercial grippers [76, 110]. These developments have been accompanied by a conceptual shift. Contact is increasingly framed not as an obstacle to be avoided or a constraint to be satisfied, but as a resource to be deliberately exploited [16, 53, 93].

This review addresses the following research question. What are the current approaches, representations, and algorithms for contact-rich manipulation and contact planning in robotics, and how do they address the challenges of hybrid dynamics, contact sequencing, and real-world deployment? We adopt a scoping review of the period 2018 to 2026, with selected foundational works from earlier years where they are essential for contextualizing recent advances. The review spans trajectory optimization, discrete planning, machine learning, and tactile sensing, unified by their shared concern with the physics and computation of contact.

The remainder of this survey is organized as follows. Section 2 establishes background definitions and delineates scope. Section 3 reviews contact models and representations that underpin planning and control. Section 4 analyzes contact-implicit trajectory optimization. Section 5 covers contact mode and sequence planning. Section 6 examines learning-based approaches, including reinforcement learning, imitation learning, and their hybrids. Section 7 discusses tactile sensing and feedback integration. Section 8 treats dexterous multi-finger manipulation as an integrative application. Section 9 surveys sim-to-real transfer as a cross-cutting deployment concern. Section 10 offers a cross-cutting analysis, Section 11 identifies open problems with concrete methodological directions, and Section 12 concludes.

2. Background and Definitions

2.1 Contact-Rich Manipulation

We define contact-rich manipulation as robotic manipulation in which the task objective requires establishing, maintaining, modulating, or transitioning through multiple contacts between the robot, the manipulated object, and the environment. This definition encompasses both tasks that inherently require force-controlled contact (assembly, polishing, massage) and tasks that opportunistically leverage environmental contact to reduce uncertainty or extend capability (using a table edge to reorient an object) [93]. The distinction matters. In the former category, contact control is the task. In the latter, contact is an intentional robustness strategy.

2.2 Hybrid Dynamics and Contact Modes

Contact induces hybrid dynamics. The system alternates between continuous motion phases governed by differential equations and discrete transitions at contact events (impacts, mode switches). A contact mode specifies, for each potential contact point, whether it is in separation, sticking, or sliding, and if sliding, in which direction. The number of contact modes grows combinatorially with the number of contact points, which renders exhaustive enumeration intractable for all but the simplest systems. The mathematical encoding of unilateral contact requires a non-negative normal force (\(\lambda_n \ge 0\)), a non-negative separation gap (\(\phi_n \ge 0\)), and their complementarity so that at least one is zero at any instant. This gives rise to complementarity constraints that are inherently nonsmooth [2, 75].

The first relation is the normal complementarity condition. The second is the Coulomb friction cone, where (\(\lambda_t\)) is the tangential force and (\(\mu\)) the friction coefficient. The entire nonsmooth apparatus of contact mechanics flows from these two simple inequalities, and most of the methodological variety in this review is a response to their awkwardness for standard optimization and learning.

2.3 Quasistatic Versus Dynamic Formulations

A recurring modeling choice across the literature is whether to adopt quasistatic (force-balance) dynamics, which neglect inertial effects and assume instantaneous force equilibrium, or full dynamic models that include acceleration and impact phenomena. Quasistatic models dramatically reduce computational complexity and have proven sufficient for slow manipulation tasks [15, 38, 71], but they exclude tasks involving throwing, catching, dynamic regrasping, or fast locomotion maneuvers where inertial effects are dominant.

2.4 Implicit Versus Explicit Contact Reasoning

The literature reveals a fundamental methodological dichotomy. Contact-implicit methods encode contact physics through complementarity constraints or smooth approximations and allow contact sequences to emerge from optimization [75]. Contact-explicit methods enumerate, search over, or learn discrete contact mode sequences, then plan continuous motions within each mode [16, 23]. The dichotomy is not absolute. Hybrid approaches combine elements of both, but it provides a useful organizing axis throughout this survey.

2.5 Scope Boundaries

This review focuses on manipulation tasks involving planned or emergent multi-contact interactions. We exclude pure grasp synthesis (extensively surveyed elsewhere), locomotion without manipulation, soft material design, and industrial assembly in fully structured settings. We include loco-manipulation, the combined locomotion and manipulation setting, where contact planning for the manipulation component is central.

3. Contact Models and Representations

The choice of contact model is not merely a modeling convenience. It fundamentally constrains what planning and optimization algorithms can achieve, because the mathematical properties of the contact representation determine which solvers are applicable and what guarantees they can provide. The dominant paradigm for rigid-body contact has been the linear complementarity problem (LCP) formulation, which encodes Coulomb friction and unilateral constraints as complementarity conditions between contact forces and velocities [2]. This formulation is physically principled and admits efficient solution for forward simulation, as implemented in physics engines such as MuJoCo [95] and in analyses of rigid-body dynamics with friction and impact [89]. Its nonsmoothness, however, creates difficulties for gradient-based optimization and learning. The LCP structure means that contact forces are piecewise-linear functions of state with discontinuous derivatives at mode boundaries, and gradient-based methods receive uninformative or misleading gradient information precisely at the contact transitions that matter most.

Recent work has pursued complementarity-free formulations that replace the LCP structure with smooth, differentiable representations amenable to gradient-based optimization [4, 35]. The motivation is pragmatic. If contact models are to be embedded within trajectory optimization or differentiable simulation for learning, they must provide useful gradients everywhere in state space, not just within contact modes. Jin and colleagues [35] proposed a complementarity-free multi-contact model for dexterous manipulation that handles simultaneous heterogeneous contact modes (fingertip, edge, and face contacts) within a unified smooth framework. Beker [4] developed algorithms for smoothly differentiable contact manifold construction that are additionally vectorizable, targeting the computational throughput needed for GPU-accelerated simulation and optimization. These complementarity-free approaches represent a significant departure from the classical formulation. Their physical fidelity relative to LCP models, particularly for impacts and Coulomb friction corners, requires further empirical validation.

An alternative representational strategy uses signed distance functions (SDFs) to encode both collision detection and contact force computation within a unified geometric framework. ContactSDF [100] approximates multi-contact models using SDFs derived from the supporting-plane representation of objects, achieving smooth contact transitions without explicit mode enumeration. This geometric approach offers natural compatibility with modern shape representations (neural implicit surfaces, point clouds) but introduces approximation errors whose magnitude depends on object geometry complexity. A complementary line of work develops convex, smooth, and invertible contact models for trajectory optimization, as well as convex quasistatic time-stepping schemes for rigid multibody systems [72, 95]. These contributions blur the line between simulation and planning by providing contact representations whose solution structure is amenable to both.

The experimental validation of contact models against real physical interactions remains limited. Kolbert and colleagues [42] conducted one of the few systematic comparisons, evaluating state-of-the-art contact models against measured motions and forces for primitive in-hand manipulation actions (sliding, pivoting, rolling). Their findings revealed significant discrepancies between predicted and observed contact behavior, particularly for pivoting, a cautionary result that underscores the gap between contact modeling theory and physical reality. Comparative analyses of contact models in trajectory optimization for manipulation [18, 68] confirm that no single model dominates across tasks, and that the relevant fidelity criteria depend on whether the model is used for simulation, planning, or policy learning. Taken together, these results motivate the recent turn toward model-agnostic formulations that absorb contact uncertainty through learning or robust planning rather than through a single carefully tuned model.

The conceptual framing of contact itself has also evolved. A comprehensive survey by Suomalainen [93] proposed a taxonomy that distinguishes tasks inherently requiring contact (force-controlled operations such as polishing, massage, and insertion) from those that opportunistically leverage environmental contact to reduce uncertainty or extend manipulation capability. This distinction reframes contact as an intentional planning resource rather than solely a physical constraint, and has influenced subsequent work on extrinsic contact exploitation [53, 64], whole-body contact manipulation [49, 62], and multi-contact loco-manipulation [52, 86, 87].

4. Contact-Implicit Trajectory Optimization

4.1 From Mode Pre-Specification to Implicit Discovery

Contact-implicit trajectory optimization eliminates the need to pre-specify contact sequences by encoding contact physics directly within the optimization constraints, allowing the solver to discover when and where contacts occur as part of the solution. The foundational formulation by Posa and colleagues [75] cast multi-contact dynamics as a mathematical program with complementarity constraints (MPCC) and demonstrated that rigid-body trajectories involving impacts and friction could be optimized directly without enumerating contact modes. This built on earlier work treating MPCCs as nonlinear programs [24, 89] and explorations of trajectory optimization for structure-variant mechanical systems [106]. The approach was transformative. It converted a combinatorial problem (which mode sequence?) into a continuous optimization problem (what forces and motions satisfy complementarity?), though the resulting nonlinear programs are nonconvex, nonsmooth, and notoriously difficult to solve reliably.

Early demonstrations showed the promise and limitations of this paradigm. Mordatch and colleagues [61] and Tassa and colleagues [94] applied contact-invariant optimization to synthesize complex humanoid behaviors (getting up from the ground, climbing, recovering from disturbances), demonstrating that contact-implicit methods could discover behaviors that would be extremely difficult to specify manually. Xi [103] used the framework to discover optimal gaits for legged robots, while Mastalli [60] extended it to hierarchical planning of dynamic movements with rich contact interactions. Schultz [82] independently applied optimal-control formulations to human-like running on articulated robots. These early methods required careful initialization, extensive parameter tuning, and were far from real-time execution.

4.2 Numerical Conditioning and Physical Fidelity

A central challenge for contact-implicit optimization is the tension between physical fidelity and numerical tractability. Complementarity constraints introduce non-differentiable points into the feasible set, causing standard NLP solvers to struggle with convergence. Two principal strategies have emerged. The first improves the underlying discretization to produce better-conditioned optimization problems. The second develops smooth approximations that preserve essential contact physics while enabling reliable gradient-based solution.

Grounding contact-implicit optimization in discrete mechanics, by discretizing the Lagrangian rather than the equations of motion, yields variational integrators that inherently conserve momentum maps and exhibit superior long-horizon energy behavior [58, 59]. The variational approach improves trajectory quality and optimization conditioning independently of contact mode handling, because the symplectic structure of the integrator prevents the artificial energy drift that plagues standard discretizations and confounds the optimizer. Building on this foundation, Patel and colleagues [73] demonstrated that higher-order orthogonal collocation polynomials can be integrated into contact-implicit optimization to substantially improve trajectory accuracy, with the key insight that impacts can be assumed localized within a single finite element, decoupling accuracy gains from the combinatorial complexity of contact modes.

The alternative strategy of smooth contact models has yielded several practical advances. Onol [66] proposed a variable smooth contact model (VSCM) combined with successive convexification that facilitates gradient-based convergence without compromising physical fidelity at the solution. To address parameter sensitivity, Onol [67] developed a tuning-free framework using a relaxed contact model with automatic parameter scheduling, which enables planning across different robot architectures and tasks from trivial initial guesses. Chatzinikolaidis [8] introduced an analytically solvable contact model that permits closed-form computation while satisfying friction cone constraints, enabling planning on variable ground surfaces (hard, soft, slippery). Kurtz [44] combined hydroelastic contact modeling with iLQR, leveraging the compliance-based contact formulation from Drake and MuJoCo to provide smooth gradients while maintaining physical realism.

4.3 Bilevel and Structured Formulations

Rather than smoothing complementarity constraints, an alternative line of work preserves hard contact physics through bilevel optimization structures that separate the contact force computation from trajectory optimization. Carius and colleagues [7] treated the contact force solve as an inner problem and computed gradients through implicit differentiation, enabling unconstrained gradient-based optimizers such as iLQR to perform contact-implicit optimization with physically correct hard contacts. This approach avoids the approximation errors introduced by relaxation and the convergence difficulties of direct MPCC solution, at the cost of requiring the inner contact problem to be solved to sufficient accuracy at each iteration. Chatzinikolaidis and colleagues [9] extended the implicit-dynamics approach using sensitivity analysis within a Differential Dynamic Programming framework, demonstrating compatibility with inverse-dynamics, variational, and implicit integrators. Related work has explored relaxed complementarity within contact-implicit DDP for model predictive control [40], and trajectory optimization with optimization-based dynamics that treats the equations of motion themselves as an implicit layer [117].

Computational efficiency has been addressed through structural exploitation. Sleiman [85] reformulated contact-implicit optimization as a multi-staged multiple-shooting program whose sparse block structure can be exploited by structure-aware solvers, yielding efficiency gains without relaxing complementarity constraints. Neunert [65] demonstrated that whole-body trajectory optimization through contacts could discover diverse gaits for quadruped robots without pre-specifying contact schedules, though computational cost limited the approach to offline planning.

4.4 Trust Regions and Local Approximation Quality

A recent and conceptually important contribution addresses the quality of local approximations in contact-implicit optimization. Suh [90] argued that standard ellipsoidal trust regions, inherited from unconstrained optimization, are structurally inconsistent with unilateral contact constraints. Because contact constraints are inherently one-sided (a foot can push the ground but not pull it), symmetric trust regions include infeasible directions that corrupt the local model. The proposed Contact Trust Region (CTR) is asymmetric, respects the one-sided nature of contact, and yields more faithful local approximations of contact dynamics. This represents a rare instance of the optimization methodology being adapted to the specific structure of contact physics, rather than applying generic optimization tools unchanged. The CTR framework demonstrates improved convergence and solution quality on dexterous manipulation benchmarks, though its computational overhead relative to standard trust regions remains to be characterized at scale.

4.5 Real-Time and Model Predictive Control

The progression from offline optimization to real-time model predictive control (MPC) represents a major practical advance. Kong and colleagues [43] proposed hybrid iLQR-MPC for contact-implicit stabilization of legged robots, combining the mode-discovery capability of contact-implicit optimization with the feedback properties of MPC. Kurtz and colleagues [45] achieved real-time contact-implicit MPC through a surprisingly simple approach. Inverse-dynamics trajectory optimization avoids explicitly computing forward dynamics and contact forces. A concurrent line of work has delivered fast contact-implicit MPC through careful solver design [47], adaptive contact-implicit MPC with online residual learning to correct model error during deployment [32], and linear contact-implicit MPC that exploits LQR-like structure for extremely high control rates [48]. Kim and colleagues [39] extended contact-implicit MPC to diverse quadruped motions without pre-planned contact modes or trajectories, demonstrating that the paradigm is now mature enough for deployed locomotion. Jiang and colleagues [34] demonstrated long-horizon contact-implicit MPC for dexterous in-hand manipulation, showing that real-time operation is achievable even for the high-dimensional state spaces of multi-finger hands.

4.6 Global Planning and Mode Coverage

Global planning, finding trajectories that traverse multiple local optima separated by contact mode boundaries, remains significantly more challenging than local optimization. Pang and colleagues [71] addressed this through local smoothing of quasi-dynamic contact models, drawing connections between the empirical success of reinforcement learning and the structure of smoothed contact dynamics landscapes. A related global quasi-dynamic model for contact-trajectory optimization [14] pre-computes a manipulation-specific reachability representation that frames local planners as refinements within a globally consistent envelope. Suh and colleagues [91] proposed composing local contact-implicit MPC plans into a global manipulation policy by stitching them together in a roadmap structure, enabling efficient dexterous manipulation without full re-optimization from scratch. Turski [98] developed a staged approach that combines the mode-discovery capability of contact-implicit optimization with the trajectory quality of multi-phase hybrid optimization, using the former to initialize the latter.

4.7 Whole-Body and Loco-Manipulation Applications

Contact-implicit optimization has increasingly been applied beyond point-contact locomotion to whole-body manipulation, where the robot exploits contacts across its entire body surface. Leve and colleagues [49] parameterized the robot body surface as a continuous explicit representation, converting the combinatorially intractable contact-location enumeration problem into a smooth continuous optimization. This hierarchical co-optimization of contact location and motion achieved dramatic reductions in planning time compared to discrete contact search approaches. Salagame and colleagues [80, 81] and Gangaraju [26] applied non-impulsive contact-implicit planning to snake-robot loco-manipulation, demonstrating the generality of the framework beyond legged and manipulator systems. Doshi and colleagues [21] pushed the approach to microrobotics, optimizing locomotion trajectories for a quadrupedal microrobot where high-frequency passive dynamics and discontinuous contacts make analytical modeling particularly challenging. Winkler [101], while not strictly contact-implicit, demonstrated that gait sequence, step timings, footholds, swing-leg motions, and body motion could be simultaneously optimized within a single trajectory optimization formulation, evidence that the boundaries between contact-implicit and contact-explicit methods are increasingly blurred.

5. Contact Mode and Sequence Planning

5.1 The Case for Explicit Mode Reasoning

While contact-implicit methods sidestep mode enumeration by embedding contact physics in continuous optimization, an alternative tradition explicitly reasons about discrete contact mode switches and plans contact sequences before or alongside continuous trajectory generation. Explicit mode reasoning remains valuable when the task structure permits it, because discrete search can exploit combinatorial structure (pruning, heuristics, symmetries) that continuous optimization cannot. The key tradeoff is between the generality of implicit methods and the structural efficiency of explicit search on problems where mode transitions are sparse and well-characterized.

5.2 Mixed-Integer Convex Programming

Mixed-integer convex programming (MICP) provides a principled framework for simultaneous optimization of discrete contact decisions and continuous trajectories by encoding contact mode selection as integer variables within a convex relaxation. Aceituno-Cabezas and colleagues [1] demonstrated this for multi-legged locomotion, jointly optimizing contact sequence, gait, and motion without pre-specified gait patterns or flat-terrain assumptions. The MICP framework guarantees global optimality within the convex relaxation and naturally handles combinatorial constraints (at most (\(k\)) contacts active simultaneously), but computational cost grows exponentially with the number of integer variables, limiting scalability to moderate numbers of candidate contact locations and short planning horizons. Escande and colleagues [23] applied a related formulation to humanoid contact-point planning, combining integer programming with kinematic reachability analysis. More recently, Dhedin and colleagues [19] extended MICP-style reasoning within a pipeline that uses Monte Carlo tree search (MCTS) to handle the combinatorial explosion, a hybrid between pure integer programming and heuristic search.

5.3 Graph Search and Heuristic Methods

Heuristic graph-search methods offer a computationally cheaper alternative to MICP by exploring candidate contact configurations through problem-specific feasibility checks rather than solving an integer program. Escande and colleagues [23] proposed a search over candidate contact locations on environmental surfaces with per-stance kinematic reachability and static-equilibrium checks, a combinatorial search at the planning layer that avoids the computational burden of integer programming. Zhu [111] extended contact-point search to deformable linear objects, introducing a contact mobility index, a scalar metric quantifying how effectively an environmental contact can reshape a cable. This metric guides contact location selection for cable manipulation, extending contact-point feasibility reasoning from rigid-body systems to deformable objects, a domain where MICP formulations become particularly unwieldy due to the high-dimensional deformation state. Murooka and colleagues [63] developed a graph-search loco-manipulation planner for humanoid robots using reachability maps, achieving efficient planning for object-transport tasks.

5.4 Sampling-Based and Mode-Guided Planning

Sampling-based methods provide a third route to contact mode discovery, one that neither solves integer programs nor requires problem-specific heuristics but instead relies on randomized exploration to uncover feasible contact sequences. Nakatsuru and colleagues [64] proposed a probabilistic roadmap-based method that uses an expanded object mesh model to plan manipulation motions with environment support. Contact modes and transitions emerge from the sampling process itself rather than from explicit enumeration or complementarity constraints, offering a planning-side route to implicit contact mode determination.

A conceptually distinct approach uses explicit contact mode enumeration not to directly plan motions but to guide sampling-based tree expansion. Cheng and colleagues [15, 16] developed Contact Mode Guided Manipulation Planning (CMGMP), which automatically enumerates all feasible contact modes of environment-object contacts and uses them to bias RRT-style tree expansion. Contact modes serve as automatically synthesized manipulation primitives that the planner sequences into hybrid plans combining discrete mode switches and continuous trajectories. CMGMP was demonstrated for both 2D quasistatic [15] and 3D quasidynamic dexterous manipulation [16], showing that mode guidance substantially improves planning efficiency compared to naive sampling. The reliance on quasistatic or quasidynamic models restricts applicability to slow manipulation tasks, but the framework requires no pre-designed motion primitives, a significant advance over earlier template-based approaches. Related ideas appear in planar in-hand motion cones [11], where analytical cone constructions serve as mode-aware primitives, and in reactive planar non-prehensile manipulation with hybrid MPC [113], where mode selection becomes part of an online control law.

5.5 Hybrid Discrete-Continuous Planning

Several recent methods explicitly combine discrete search over contact sequences with continuous trajectory optimization, capturing the strengths of both paradigms. Dhedin and colleagues [19] paired MCTS with whole-body trajectory optimization for simultaneous contact sequence and contact patch (area) selection in dynamic locomotion. MCTS drives combinatorial search using trajectory-optimization-evaluated rollouts, enabling acyclic multi-contact locomotion planning with full rigid-body dynamics. This approach is distinguished from MICP (no integer program), heuristic graph search (uses learned rollout value rather than static feasibility), and point-contact planners (explicitly selects contact patch geometry). Chen and colleagues [12] proposed TrajectoTree, which augments contact-implicit trajectory optimization with a high-level tree search for multi-contact dexterous manipulation, using tree search to provide initialization diversity that helps the local optimizer escape poor local minima. Tsikelis and colleagues [97] presented a bi-level optimization framework integrating contact sequence discovery with SE(3)-tangent-space trajectory optimization for agile whole-body motion planning.

5.6 Complementarity-Based Implicit Mode Determination

Bridging the implicit-explicit divide, several contact mode planning methods encode mode transitions through complementarity constraints while retaining an explicit planning structure. Katayama and colleagues [38] proposed a Linear Complementarity Quadratic Program (LCQP) that determines contact modes implicitly as part of a quadratic programming solution, achieving real-time contact-rich manipulation control without mode enumeration. The quasistatic dynamics assumption is central to tractability. Li and colleagues [52] developed multi-contact MPC for humanoid loco-manipulation capable of capturing various contact modes, while Sleiman and colleagues [86] proposed a versatile multi-contact planning and control framework for legged loco-manipulation that coordinates complex holistic movements with multiple contact interactions.

5.7 Task-Level Integration

The integration of contact mode planning with higher-level task planning represents an emerging frontier. Ciebielski and colleagues [17] presented a task and motion planning (TAMP) framework that unifies locomotion and manipulation through a shared representation of contact modes, defining symbolic actions as contact mode changes and grounding high-level planning in low-level motion feasibility. Le and colleagues [46] developed SPONGE, a sequence planning pipeline for deformable-on-rigid contact prediction, using deep learning to predict contact outcomes and guide manipulation sequence generation. Arreguit and colleagues [3] proposed a fast multi-contact planning method based on a five-mass model formulated in Cartesian space rather than joint angles, achieving efficient encoding of internal dynamics without full-model computation. Chavan-Dafle [10] and Sahin [78] demonstrated contact mode planning for specialized in-hand manipulation primitives, namely stable prehensile pushing and within-hand manipulation via variable-friction fingers with extrinsic contacts, showing that targeted mode reasoning remains effective for well-characterized task classes.

6. Learning-Based Contact-Rich Manipulation

6.1 Guided Policy Search and End-to-End Visuomotor Learning

Learning-based approaches to contact-rich manipulation offer an alternative to model-based optimization. Rather than explicitly modeling contact physics, the robot learns control policies from data that implicitly encode contact behavior. The foundational work by Levine and colleagues [50] demonstrated that Guided Policy Search (GPS) with iteratively refitted time-varying linear-Gaussian models could learn contact-rich manipulation skills directly on real robots without demonstrations or known dynamics. By fitting local linear approximations to dynamics around each trajectory rather than learning a global model, GPS achieved the sample efficiency needed for real-robot learning of precision tasks (peg insertion, bottle-cap screwing) in minutes of interaction. Levine [51] extended this to end-to-end training of deep visuomotor policies, integrating perception and control into a single learned system. These early results established the feasibility of learning contact-rich skills, but left open questions of safety, generalization, and scaling.

6.2 Structured Action Spaces and Variable Impedance

A critical insight from the learning-for-contact literature is that the action space in which the policy operates profoundly affects learning efficiency, safety, and transferability. Embedding traditional force control schemes as the structured action space of an RL agent provides inherent compliance and safety guarantees that end-to-end learning in joint-position or joint-torque space does not. Beltran-Hernandez and colleagues [5] demonstrated that combining RL with an admittance control interface enables contact-rich manipulation learning on rigid position-controlled industrial robots, hardware that would otherwise be unsuitable for contact tasks due to lack of inherent compliance. This approach was subsequently adopted and extended across multiple studies [22, 83, 104], establishing force-control-structured action spaces as a design pattern for safe contact-rich RL.

The progression from fixed to variable impedance parameters represents a significant advance in expressiveness. Yang and colleagues [104] proposed learning variable impedance (stiffness and damping) as part of the RL policy's action output, initialized from impedance-space information extracted from suboptimal demonstrations. This enables adaptive compliance that modulates throughout task execution (stiff during free-space motion, compliant during contact transitions), going beyond the fixed compliance of admittance or parallel force/position control. Shaw and colleagues [83] integrated Riemannian Motion Policies as a geometric safety layer within a variable-impedance RL framework, replacing reward-penalty-based safety with structural constraint enforcement. Gao and colleagues [27] and Zhang and colleagues [108] further explored compliance adaptation, with Zhang specifically addressing efficient sim-to-real transfer through online admittance residual learning. Adjacent lines of work learn variable impedance control via inverse reinforcement learning for force-related tasks [115] and propose deep-RL variable-compliance controllers for peg-in-hole assembly [116], showing that compliance-as-action is a broadly effective inductive bias.

6.3 Learning from Demonstrations and Residual Policies

Pure reinforcement learning from scratch is sample-inefficient for contact-rich tasks because contact interactions are sparse in the exploration space. The probability of randomly discovering a useful contact sequence decreases rapidly with task complexity. Demonstration data provides a strong prior that concentrates learning on the relevant regions of state-action space. Rajeswaran and colleagues [77] showed that augmenting deep RL with demonstrations dramatically accelerates learning of complex dexterous manipulation. Vecerik and colleagues [99] proposed using both demonstrations and actual interactions to fill a replay buffer for DDPG, enabling learning on real robotic tasks with sparse rewards.

A particularly effective paradigm combines demonstration-extracted motor primitives with residual learning. Davchev and colleagues [18] used Dynamic Movement Primitives extracted via behavior cloning as a base policy, then trained a residual RL policy in task space to correct DMP failures at contact. This residual learning from demonstration enables few-shot transfer to new geometries and friction conditions. Si and colleagues [84] extended this with a human-in-the-loop component, using teleoperation correction of pre-trained DMP models to handle tasks with complex or unpredictable physical properties. The human serves as an active update mechanism rather than a one-time demonstrator. Stepputtis and colleagues [88] developed a bimanual manipulation imitation system combining admittance control with human demonstrations, addressing coordination of two arms during contact-rich tasks. TossingBot [107] independently illustrated residual physics in a dynamic non-prehensile setting, learning a correction atop a nominal projectile model to throw arbitrary objects.

6.4 Exploration, Reward, and Safety

The exploration-exploitation tradeoff is particularly acute in contact-rich domains because the reward landscape is typically sparse and discontinuous. The robot receives no useful signal until it achieves contact, and the transition from no-contact to successful-contact is abrupt. Hoppe and colleagues [31] addressed this with UCB-based trajectory optimization as a global exploration strategy, planning approximate trajectories by optimizing over an upper confidence bound of the advantage function with ensemble-based uncertainty estimation. This principled exploration generates informative data that accelerates discovery of contact-exploiting solutions independently of demonstrations. Wu and colleagues [102] tackled the reward-design problem directly, learning dense reward functions for contact-rich manipulation to replace hand-crafted sparse rewards.

Safety during learning is a growing concern as contact-rich RL moves toward real-robot deployment. Zhu and colleagues [112] proposed a contact-safe RL framework that explicitly manages collision risks during training and in unseen scenarios. Liang and colleagues [54] learned preconditions of hybrid force-velocity controllers, enabling the robot to determine when contact-rich strategies are applicable and when to fall back to safer behaviors. The trend is toward structural safety, building safety into the policy architecture, action space, or dynamics model, rather than relying solely on reward penalties, which sufficiently expressive policies can circumvent.

6.5 Dexterous Policies and Sim-to-Real

Deep RL has achieved impressive results on dexterous in-hand manipulation, but these results depend critically on simulation fidelity and transfer mechanisms. The landmark OpenAI result [69] demonstrated that domain randomization over physical parameters during simulated training is sufficient for zero-shot sim-to-real transfer of block reorientation on a Shadow Hand. Extending this approach to more complex tasks has proven difficult. Domain randomization provides robustness through diversity but does not guarantee that the simulation distribution covers real-world conditions [36]. Liu and colleagues [55] proposed contact-coverage-guided exploration for general-purpose dexterous manipulation, using contact pattern diversity as an intrinsic motivation signal that does not require task-specific reward design.

Saito and colleagues [79] decomposed in-hand tool manipulation into action primitives based on contact-state transitions (APriCoT), using contact mode structure to guide RL rather than learning end-to-end. Kannan and colleagues [37] addressed the gap between simulated and real dexterous manipulation through fine-tuning, enabling transfer to soft, deformable objects and long-horizon tasks. Sleiman [87] proposed guided RL for multi-contact loco-manipulation, using model-based trajectory optimization to systematically shape the RL exploration, bridging the optimization-learning divide. Portela [74] addressed force-control learning for legged manipulation, proposing explicit force regulation within an RL framework rather than relying on implicit force control through position tracking. Elguea-Aguinaco and colleagues [22] provided a comprehensive review noting that RL for contact-rich manipulation extends beyond rigid objects to deformable-object manipulation (cloth, cables, soft materials), requiring distinct reward formulations, state representations, and sim-to-real strategies that rigid-body domain randomization does not address.

7. Tactile Sensing and Feedback for Contact Planning

7.1 Tactile Sensing as Compensation for Occlusion

Contact-rich manipulation inherently involves occlusion. The robot's own body and the grasped object block visual observation of the contact state that is most relevant for control. Tactile sensing provides a complementary modality that directly observes contact information unavailable to vision. Ichiwara and colleagues [33] demonstrated this concretely in a flexible-object (zipper) manipulation task, where the gripper hides the bag deformation state from cameras. Adding tactile feedback to an end-to-end deep-predictive-learning model improved task success from 56.7% to 93.3%, with the tactile signal recovering the hidden contact information that vision could not access. This result illustrates a general principle. For contact-rich tasks involving deformable objects or occluded contact geometry, tactile sensing is not merely beneficial but may be necessary for reliable closed-loop control [33, 57, 110].

7.2 Low-Cost and Accessible Contact Feedback

Contact feedback for manipulation has historically relied on expensive six-axis force/torque (F/T) sensors, creating a cost barrier that has limited adoption in research and industry. A promising recent finding is that relative force changes, rather than precise absolute force magnitudes, are sufficient for many contact-rich manipulation tasks. Zhu and colleagues [110] demonstrated this with ShapeForce, a low-cost compliant wrist sensor using soft-body deformation and marker tracking that matches six-axis F/T sensor performance for contact-rich tasks. Proesmans [76] developed open-source tactile fingertip designs that augment off-the-shelf industrial grippers, providing readily interpretable tactile outputs without custom hardware development. Han [30] introduced low-cost, lightweight compliant force-sensing gripping pads for humanoid robots measuring normal forces and center of pressure. Ford [25] demonstrated shear-based grasp control using miniature biomimetic tactile sensors on an anthropomorphic soft hand, showing that shear information (not just normal force) enables delicate object manipulation. These contributions collectively lower the instrumentation barrier for contact-rich manipulation research, though the diversity of sensing modalities (resistive, capacitive, optical, magnetic) highlights the fragmentation problem discussed below.

7.3 Tactile Sensing in Reinforcement Learning

Tactile sensing can serve a dual role in RL for dexterous manipulation. As a reward-shaping signal it explicitly incentivizes desired contact patterns. As an observation it provides the policy with contact-state information. Kim and colleagues [41] proposed Tac2Motion, which uses tactile sensing for both reward shaping (incentivizing firm grasping and smooth finger gaiting) and observation embedding, demonstrating improved data efficiency and robustness for in-hand manipulation across varying object geometries. Chen and colleagues [13] developed a general-purpose sim-to-real protocol for marker-based visuotactile sensors, showing that FEM-based elastic deformation simulation, not rigid-body physics, is required for accurate tactile simulation during RL training. Yin and colleagues [105] proposed a complementary approach, signal discretization as a sim-to-real bridging strategy. Representing tactile feedback as low-resolution categorical values (ternary shear, binary normal) restricts the signal space to what both simulator and real sensor reliably agree on, enabling zero-shot transfer without accurate physics simulation. George and colleagues [29] demonstrated that visuotactile pretraining improves both tactile and non-tactile manipulation policies, suggesting that tactile experience provides transferable representations of contact physics.

7.4 Sim-to-Real Transfer for Tactile Manipulation

The sim-to-real gap for tactile sensing presents unique challenges distinct from visual or proprioceptive transfer, because tactile signals depend on contact mechanics (material deformation, friction, surface texture) that are difficult to simulate accurately. Three strategies have emerged. First, high-fidelity simulation. Chen and colleagues [13] showed that FEM-based elastic deformation modeling combined with self-supervised pre-training of marker-coordinate features bridges the gap for visuotactile sensors, enabling generalization across contact-rich tasks. Second, signal discretization. Yin and colleagues [105] demonstrated that restricting tactile signals to categorical values eliminates the need for accurate continuous simulation, achieving zero-shot transfer for in-hand manipulation. Third, domain randomization over approximate simulation. Ding and colleagues [20] showed that randomizing physical parameters during approximate soft-body simulation enables zero-shot sim-to-real transfer for optical tactile sensors, achieving sub-millimeter edge-detection accuracy without real-world training data. These three strategies represent complementary points on the simulation accuracy-cost tradeoff, and the field has not yet converged on which is most effective for which task classes.

7.5 Temporal Models and Whole-Body Sensing

The temporal structure of tactile signals carries information that instantaneous measurements do not. Bhattacharjee and colleagues [6] demonstrated that temporal sequence models (HMMs, LSTMs) over tactile time series generalize to novel robot motion parameters where instance-based methods fail, because the temporal shape of a contact event, not its peak magnitude, encodes transferable contact properties. This result suggests that tactile representations for contact planning should be fundamentally sequential, not frame-based. The same work showed that whole-arm (forearm) tactile sensing enables mechanical-property inference (compliance, mobility) from incidental contact during reaching motions, extending contact-based perception beyond end-effectors to the full arm surface. Ma and colleagues [57] demonstrated extrinsic contact sensing, localizing contacts between a grasped object and the environment from distributed tactile measurements on the robot hand, using relative-motion tracking rather than absolute force measurement. Tactile intrinsic motivation [114] leverages tactile signatures to drive exploration in RL, completing the loop between sensing, planning, and learning.

7.6 The Standardization Challenge

Hardware fragmentation across tactile sensing systems presents a significant barrier to cumulative progress. Each research group tends to design custom sensors with incompatible outputs, physical form factors, and measurement modalities, preventing cross-system benchmarking and hindering reproducibility [76]. Unlike computer vision, where standardized cameras and datasets enabled rapid algorithmic progress, tactile manipulation research lacks both standardized hardware and shared evaluation benchmarks. The open-source designs proposed by Proesmans [76] and the low-cost approaches of Zhu [110] and Han [30] represent steps toward accessibility, but a community-wide standardization effort comparable to the YCB object set for grasping has not yet materialized.

8. Dexterous and Multi-Finger Contact Manipulation

Dexterous manipulation with multi-fingered hands represents an integrative challenge that draws on contact modeling, planning, learning, and sensing simultaneously. The high dimensionality of the joint space, the multiplicity of simultaneous contact points, and the need for coordinated finger motions make this domain a stringent test for all the approaches surveyed in preceding sections. Explicit multi-finger analyses trace back to classic kinematic and force-closure frameworks [96], and subsequent deep-RL systems have catalyzed a shift toward learned policies [69, 70].

Deliberate exploitation of sliding contacts as a manipulation primitive, rather than treating slip as a failure mode, has a long history. Trinkle [96] developed quasi-static contact kinematics models for planning sequences in which controlled sliding transitions the hand from an initial grasp to a more secure enveloping grasp. This work introduced liftability regions, geometric characterizations of which initial grasps permit successful object liftoff given contact and force constraints, providing a principled basis for decomposing in-hand manipulation into grasp selection and continuous grasp alteration phases. While the quasi-static assumption and 2D restriction limit direct applicability, the conceptual framework (contact transitions as deliberate primitives rather than disturbances) has influenced subsequent work on extrinsic contact exploitation [10, 53, 78].

The landmark result of OpenAI [69] demonstrated that domain randomization during simulated RL training is sufficient for zero-shot sim-to-real transfer of dexterous in-hand object reorientation on a physical Shadow Hand, without any real-world data or human demonstrations. This result shifted the field's focus from analytical contact modeling toward learned policies, though it relied on extensive domain randomization over physical parameters (friction, object appearance, dynamics) and a carefully designed observation space. The gap between this demonstration and general-purpose dexterous manipulation remains substantial. The task was single-object reorientation with a fixed initial grasp, and extensions to diverse objects, multi-step manipulation, and tool use have proven significantly more difficult [37, 55].

Hand morphology itself is a design variable that affects manipulation capability. Sun [92] demonstrated that non-anthropomorphic hand configurations (specifically dual symmetric thumb-index designs) can outperform human-mimicking single-thumb designs for dexterous manipulation of deformable objects (cables). This suggests that hand topology should be derived from task-specific coordination requirements rather than anatomical analogy, a finding that challenges the predominant design philosophy of anthropomorphic robotic hands. Sun additionally showed that long-horizon dexterous manipulation of deformable objects can be systematically decomposed into short-horizon action primitives via a task taxonomy, with thumb-index coordination identified as the critical structural bottleneck.

Real-time collision-free motion planning for multi-fingered hands presents a specific computational challenge, as the configuration space of multiple fingers plus a manipulated object is high-dimensional and the collision geometry is complex. Gao and colleagues [28] addressed this by learning a neural network representation of the collision-free configuration space that is efficiently queryable at runtime, then integrating it with closed-loop dynamical system control and sampling-based planning. This learned C-space representation decouples expensive geometric collision computation from online replanning, enabling dynamic obstacle avoidance among fingers in real time. Lundell and colleagues [56] proposed Multi-FinGAN, a generative adversarial network trained on a grasp taxonomy that synthesizes diverse multi-finger grasp poses directly from RGB-D images in approximately one second, replacing slow analytical grasp sampling with learned approximation and enabling feedback-based online grasp re-planning.

Robustness to parametric uncertainty in contact-rich in-hand manipulation has received increasing attention. Liang and colleagues [53] proposed a two-stage motion-cone framework for robust in-hand manipulation with extrinsic contacts. Compute a nominal motion cone assuming precise parameters, then refine it to the largest subset of motions that guarantee the desired contact mode across the full range of parametric errors. This principled approach to robustness decouples nominal mechanics from robust constraint tightening and provides stronger guarantees than domain randomization, which offers statistical robustness but no worst-case bounds. The work additionally demonstrates that extrinsic contacts can be deliberately incorporated as a planning resource for simultaneous in-hand pose adjustment and environmental contact maintenance.

9. Sim-to-Real Transfer for Contact-Rich Manipulation

Sim-to-real transfer is not a standalone subfield so much as a cross-cutting deployment concern that shapes every preceding theme. Contact-rich tasks are particularly unforgiving here because three sources of reality gap compound. Contact geometry (the fingertip-object normal and gap functions) is sensitive to small model errors. Friction and compliance are routinely miscalibrated. Soft sensor deformations and their dependence on surface texture are difficult to simulate accurately. The dominant strategies in the literature can be read as different theories of what aspect of this gap matters most.

Domain randomization treats the gap as a distributional shift and responds with policy robustness. OpenAI's in-hand reorientation result [69] established this as the canonical approach. Randomize friction, masses, object appearance, and actuator noise broadly enough, and a policy trained only in simulation will generalize to the real Shadow Hand. Kaidanov and colleagues [36] revisited the approach for diffusion policies in whole-body humanoid control, emphasizing that randomization is not a free lunch and that its benefit depends on the distribution covering plausible real-world conditions. Follow-up work on pre- and post-contact policy decomposition for non-prehensile manipulation [109] further exposes when randomization suffices and when sub-task decomposition is required.

Residual and adaptive correction treats the gap as a model residual and tackles it by learning or online-estimating the difference between simulation and reality. Zhang and colleagues [108] learned an online admittance residual that corrects a nominal compliance model during deployment. Davchev and colleagues [18] used a residual policy atop DMPs to handle contact-specific corrections. Adaptive contact-implicit MPC with online residual learning [32] extends the idea to model-based control, merging planning and learning for a single deployed controller. TossingBot [107] is a historically influential example of residual physics applied to a dynamic non-prehensile task.

Structure-preserving transfer uses model-based substructure that is known to generalize, and limits learning to the components that do not. Sleiman [87] guides RL exploration with a model-based trajectory optimizer so that the learned component has a narrow, physically sensible search space. Portela [74] imposes explicit force regulation on top of RL for legged manipulation, ensuring that the low-level contact interaction respects a physically principled force law. Saito [79] decomposes dexterous manipulation into action primitives indexed by contact-state transitions, which transfer more readily than end-to-end trajectories because the discrete structure is invariant across domains.

Tactile sim-to-real stands apart because tactile observations depend on soft material deformation that is expensive to simulate. The three strategies identified in Section 7 (FEM-based high-fidelity simulation [13], signal discretization [105], and domain randomization over approximate soft-body simulation [20]) each attack a different link of the tactile pipeline. The field has not converged on a dominant approach, and the right choice appears to depend on whether the task is dominated by fine normal force discrimination, by shear direction, or by coarse contact presence.

Finally, real-to-sim is beginning to complement sim-to-real. Model-predictive contact controllers that learn online residuals from real data [32] and pre- and post-contact policy decompositions that bootstrap from a small number of real rollouts [109] narrow the gap from the real side. Roadmap-based policy composition in dexterous manipulation [91] offers a related route, since stitching local real-transferable plans can reduce reliance on any single accurate global simulation. The cumulative picture is that the sim-to-real gap for contact-rich manipulation is not one gap but several, and effective deployment usually requires more than one of the above strategies applied in combination.

10. Cross-Cutting Analysis

10.1 The Implicit-Explicit Continuum

The dichotomy between contact-implicit and contact-explicit methods, while useful for organization, obscures a more nuanced reality. Most successful recent methods occupy intermediate positions on a continuum. Staged optimization [98] uses contact-implicit methods for mode discovery and contact-explicit methods for trajectory refinement. Mode-guided sampling [15, 16] explicitly enumerates modes but uses them to guide continuous sampling rather than solving an integer program. MCTS with trajectory optimization [19] searches discrete contact sequences but evaluates them through continuous optimization. Complementarity-based planning [38] uses implicit complementarity within an explicit MPC structure. The convergence suggests that the field is moving toward hybrid methods that match the level of discrete-continuous reasoning to the problem structure, rather than committing a priori to either pure paradigm.

10.2 The Optimization-Learning Convergence

A parallel convergence is occurring between optimization-based and learning-based approaches. On the optimization side, contact-implicit MPC has achieved real-time rates [34, 39, 45, 47] that approach the control frequencies at which learned policies operate. On the learning side, structured action spaces [5, 104], residual policies [18, 108], and guided RL [87] increasingly incorporate model-based structure. Pang and colleagues [71] explicitly connected the success of RL in contact-rich manipulation to the smoothing properties of stochastic policies on discontinuous contact dynamics, suggesting a theoretical link between the two paradigms. The emerging pattern is that model-based methods provide structure and sample efficiency while learning provides robustness and adaptability, and the most effective systems combine both.

10.3 The Quasistatic Simplification

The quasistatic assumption (neglecting inertial effects and assuming instantaneous force equilibrium) appears as a recurring enabler across themes. In contact-implicit optimization for global planning [71], in mode-guided sampling for dexterous manipulation [15, 16, 38], and implicitly in many learning-based approaches that operate at low control frequencies. This assumption is powerful because it eliminates impact dynamics and reduces the hybrid character of the system, but it fundamentally limits the tasks that can be addressed. Dynamic manipulation (throwing, catching, fast regrasping, impact-based assembly) requires inertial reasoning that quasistatic models cannot provide. The field would benefit from principled criteria for when quasistatic approximations are valid and when dynamic models are necessary, rather than the current practice of choosing based on tractability preferences.

10.4 Sim-to-Real as a Universal Challenge

Simulation-to-reality transfer, discussed as its own theme in Section 9, is simultaneously a cross-cutting concern that affects optimization (model accuracy), learning (training environment fidelity), and sensing (tactile simulation). For optimization the gap manifests as model mismatch between the contact dynamics used for planning and real contact physics [42]. For learning, domain randomization [36, 69] and residual adaptation [18, 108] dominate. For tactile sensing, three distinct approaches (high-fidelity FEM simulation [13], signal discretization [105], and domain randomization over approximate simulation [20]) have emerged without consensus. The multiplicity of transfer strategies, each effective in its own domain, suggests that no single approach will suffice. The appropriate transfer mechanism depends on which aspects of contact physics are most task-critical.

10.5 From Point Contact to Whole-Body and Deformable Contact

A clear trend in the literature is the expansion of contact reasoning from idealized point contacts to richer contact representations. Whole-body manipulation [49, 62] exploits contact across the robot's entire surface. Contact patch selection [19] reasons about contact area geometry rather than points. Deformable object manipulation [33, 46, 92, 111] requires contact models that handle material deformation. This expansion creates opportunities, richer contact capabilities, but also challenges, higher-dimensional contact state spaces that stress all existing computational methods.

11. Open Problems and Future Directions

Scalable long-horizon multi-contact planning. Current methods either plan short horizons in real time (MPC) or long horizons offline (global optimization). Tasks requiring dozens of contact transitions (furniture assembly, cooking, dressing) demand planning methods that scale gracefully with horizon length. Future work should investigate hierarchical decomposition approaches that combine task-level discrete search with local contact-implicit optimization, building on staged [98] and roadmap-stitching [91] approaches while extending to much longer task horizons.

Unified optimization-learning frameworks. The convergence of optimization and learning (Section 10.2) suggests that principled integration, not ad hoc combination, should be a priority. Specifically, differentiable contact-implicit optimization embedded within policy gradient computation would allow end-to-end training of systems that combine the physical reasoning of optimization with the adaptability of learning. Complementarity-free contact models [4, 35] may be essential enablers for this direction.

Contact-rich manipulation of deformable objects. Deformable objects remain under-addressed relative to rigid-body manipulation, despite their prevalence in human environments (clothing, food, cables, packaging). The contact mobility index [111] and SPONGE [46] represent initial steps, but systematic contact planning for deformable objects requires new representations that capture the coupling between contact forces, material deformation, and object configuration. Combining learned deformation models with contact-implicit optimization is a promising but largely unexplored direction.

Standardized tactile benchmarks and hardware. The hardware fragmentation identified in Section 7.6 can only be resolved through community coordination. A concrete next step would be developing a standardized benchmark suite (analogous to the YCB grasping benchmarks) that specifies tasks, metrics, and reference implementations for tactile manipulation, designed to be sensor-agnostic while requiring contact feedback for successful completion. The open-source designs of Proesmans [76] provide a starting point.

Multi-modal sensing integration in planning loops. Current methods typically use vision for state estimation and tactile feedback for reactive control, with limited integration between the two in the planning loop itself. Future planning algorithms should jointly reason about visual predictions (what will happen) and tactile observations (what is happening at contact), using tactile information not only for feedback but for online plan adaptation and contact model refinement.

Formal safety and robustness guarantees. Structural safety approaches [53, 83, 112] represent progress, but formal guarantees for contact-rich manipulation policies remain elusive. The robust motion cone framework [53] provides worst-case bounds for specific contact modes, but extending such guarantees to learned policies operating across multiple contact transitions is an open theoretical challenge with significant practical implications for human-robot interaction.

Real-time performance for complex multi-contact systems. Despite progress toward real-time contact-implicit MPC [34, 39, 45, 47, 48, 32], performance degrades with the number of contact points and the complexity of the contact geometry. Complementarity-free models [35] and GPU-accelerated contact manifold computation [4] offer promising computational substrates, but achieving reliable real-time planning for whole-body multi-contact manipulation remains an engineering and algorithmic challenge.

12. Conclusion

Contact-rich manipulation has progressed from a niche concern of dexterous hand research to a central challenge spanning trajectory optimization, discrete planning, machine learning, and tactile sensing. The period 2018 to 2026 has seen three transformative developments. Contact-implicit trajectory optimization has matured from offline planning tools to real-time MPC controllers capable of discovering contact sequences online. Reinforcement learning has progressed from simple contact tasks to dexterous in-hand manipulation with sim-to-real transfer, with structured action spaces and variable impedance control emerging as essential design patterns. Tactile sensing has moved from expensive laboratory instruments to low-cost, accessible designs that demonstrably improve contact-rich task performance.

The most important insight from this survey is that the implicit-explicit and optimization-learning dichotomies that have historically organized the field are dissolving. The most effective recent methods are hybrids. Staged optimizers combine implicit mode discovery with explicit trajectory refinement. Guided RL uses model-based optimization to shape learned policies. Mode-guided samplers use discrete contact structure to direct continuous planning. The future of contact-rich manipulation lies not in resolving these dichotomies in favor of one side, but in developing principled frameworks for integrating discrete contact reasoning, continuous optimization, data-driven learning, and multi-modal sensing into unified systems capable of robust, real-time, long-horizon manipulation in unstructured environments.