Contact Mode Guided Sampling-Based Planning for Quasistatic Dexterous Manipulation in 2D

Robotic manipulation involving contact-rich interactions has evolved from simple pick-and-place tasks to complex multi-contact operations. Early methods relied on predefined motion primitives, such as grasping and pushing, often embedded within hierarchical or task-and-motion planning frameworks like STRIPS or PDDL-based planners. While effective in structured environments, these approaches lack flexibility and require extensive manual engineering. Recent advances incorporate sampling-based algorithms like RRT and RRT*, which explore high-dimensional configuration spaces but struggle with multi-modal contact states due to the combinatorial explosion of contact modes. Contact formation enumeration and constrained sampling have been explored to some extent, but fully automatic, scalable solutions remain elusive. This work builds on these foundations, aiming to automate contact transition generation and improve exploration efficiency in multi-contact scenarios.

The core challenge in dexterous manipulation planning lies in efficiently exploring the vast, multi-modal configuration space characterized by discrete contact modes and continuous motions. Existing methods either depend heavily on pre-designed motion primitives, limiting adaptability, or rely on computationally expensive optimization that lacks guarantees of completeness. The discrete nature of contact mode transitions introduces combinatorial complexity, making it difficult to find feasible trajectories that satisfy physical constraints, force limits, and stability requirements. This bottleneck hampers the development of autonomous systems capable of handling unstructured environments and complex tasks, especially in 2D where contact states are numerous and transitions are abrupt.

The main innovation is the integration of contact mode enumeration with a sampling-based planning framework, enabling automatic exploration of multi-modal contact states. Key components include:

• �� Contact Mode Enumeration: Systematically listing all feasible contact modes based on relative motions.
• �� Contact Mode Projection: Developing a projection operator that maps random samples onto the low-dimensional manifolds defined by contact modes, ensuring samples are physically feasible.
• �� Forward Integration: Exploring continuous trajectories along these manifolds via Euler-based integration constrained by contact mechanics.
• �� Probabilistic Completeness: Theoretical proof that the method will find a solution if one exists, given sufficient sampling.
• �� Stability Margin Filtering: Incorporating robustness evaluation to select stable motions for execution.

This approach reduces manual effort, enhances scalability, and allows the generation of task-specific, complex manipulation strategies automatically.

• �� Enumerate all feasible contact modes for the current configuration, forming a discrete set M.
• �� Randomly sample a configuration point qrand in the configuration space.
• �� For each mode m ∈ M, project qrand onto the corresponding contact mode manifold using the projection operator P(·), which iteratively moves towards the closest feasible configuration via forward integration.
• �� Solve a quadratic programming problem to find the closest feasible velocity v that aligns with the desired contact mode, ensuring system constraints are satisfied.
• �� Use Euler integration to propagate the configuration along v, updating contact states based on collision detection.
• �� If the new configuration qnew is valid and reachable, add it to the exploration tree, connecting it with the parent node.
• �� Repeat the process, systematically exploring different contact modes and configurations, until the goal region is reached or time runs out.
• �� Incorporate stability margin evaluation to filter out unstable trajectories, improving robustness during execution.

The experimental setup involves multiple 2D manipulation tasks, including pushing objects to targets, pivoting, navigating narrow passages, and in-hand reorientations. Each scenario is tested with 10 random seeds, measuring planning time, node count, and success rate. The planner is compared against baseline sampling methods, demonstrating significant improvements in efficiency and success probability. The parameters are kept minimal to showcase robustness. Robot experiments with ABB IRB-120 validate the real-world applicability, where the generated trajectories are executed using a hybrid force-velocity controller. Success is measured by task completion, trajectory smoothness, and stability, confirming the method's practicality in physical systems.

The planner consistently produces feasible trajectories within seconds, with success rates of 100% across all tested scenarios. For example, in a push-and-pivot task, it completes planning in approximately 0.3 seconds with only 7 nodes. In complex tasks like navigating narrow corridors, it achieves solutions in under 4 seconds with around 480 nodes. Robot experiments demonstrate successful execution of strategies such as pushing objects onto cliffs and maneuvering through obstacle courses, confirming the approach's robustness and real-world viability. The generated motions often resemble human strategies, like sliding objects or creating gaps for finger insertion, highlighting the method’s ability to produce task-specific, dexterous behaviors.

This framework is suitable for autonomous manipulation in manufacturing, service robots, and assistive devices, especially in unstructured or cluttered environments. Its ability to automatically generate complex contact-rich trajectories reduces manual programming effort and enhances adaptability. The approach can be integrated into robotic systems requiring high dexterity, such as assembly lines, logistics, or medical robotics. Long-term, combining this method with learning-based models could enable robots to improve their manipulation skills through experience, leading to more autonomous, versatile, and intelligent robotic systems capable of handling diverse tasks with minimal human intervention.

The current approach assumes quasistatic conditions, ignoring dynamic effects like inertia and impacts, which limits its use in fast or dynamic tasks. Dependence on accurate geometric and frictional models makes it sensitive to perception errors and environmental uncertainties. The computational cost grows with the number of contacts and environmental complexity, potentially hindering real-time applications in high-dimensional spaces. Extending the framework to 3D and dynamic scenarios remains a challenge, requiring further algorithmic optimization and integration with learning methods to improve scalability and robustness in real-world settings.