Constant-time Motion Planning with Anytime Refinement for Manipulation

TL;DR

The paper addresses the challenge of reliable, real-time manipulation planning under time constraints by integrating an anytime refinement layer with Constant-Time Motion Planning (CTMP). It introduces a preprocessing phase that builds a local-RoI cover and attractor-based neighborhoods, an online phase that quickly emits an initial feasible plan, and an anytime refinement loop that progressively improves plan quality within a time budget, with theoretical guarantees of convergence to optimality given sufficient time. Empirical validation on a 6-DOF manipulator demonstrates fast initial queries and substantial improvements through refinement, including an extension to any-object manipulation and applications in sequential assembly tasks. The approach offers a practical pathway to fast yet progressively optimal motion planning for manipulation, with clear benefits for assembly-line autonomy and real-time robot control.

Abstract

Robotic manipulators are essential for future autonomous systems, yet limited trust in their autonomy has confined them to rigid, task-specific systems. The intricate configuration space of manipulators, coupled with the challenges of obstacle avoidance and constraint satisfaction, often makes motion planning the bottleneck for achieving reliable and adaptable autonomy. Recently, a class of constant-time motion planners (CTMP) was introduced. These planners employ a preprocessing phase to compute data structures that enable online planning provably guarantee the ability to generate motion plans, potentially sub-optimal, within a user defined time bound. This framework has been demonstrated to be effective in a number of time-critical tasks. However, robotic systems often have more time allotted for planning than the online portion of CTMP requires, time that can be used to improve the solution. To this end, we propose an anytime refinement approach that works in combination with CTMP algorithms. Our proposed framework, as it operates as a constant time algorithm, rapidly generates an initial solution within a user-defined time threshold. Furthermore, functioning as an anytime algorithm, it iteratively refines the solution's quality within the allocated time budget. This enables our approach to strike a balance between guaranteed fast plan generation and the pursuit of optimization over time. We support our approach by elucidating its analytical properties, showing the convergence of the anytime component towards optimal solutions. Additionally, we provide empirical validation through simulation and real-world demonstrations on a 6 degree-of-freedom robot manipulator, applied to an assembly domain.

Figures (3)

• Figure 1: An assembly cell, composed of three Yaskawa HC10DTP manipulators.
• Figure 2: Illustration of the preprocessing phase. For each local-RoI $\mathcal{G}_i$, we compute neighborhoods, distinguished by different colors, to finally form the cover of $\mathcal{G}$. Moreover, each neighborhood is associated with a path $\Pi_{ij}$ from $s_{home}$ to an attractor state, ensuring that every state within that neighborhood is constant-time feasible from the attractor state.
• Figure 3: Comparing CTMP with and without refinement. Fig. \ref{['fig:fig1']} and \ref{['fig:fig2']} show general and front views of the path from pick pose (green) to place pose (solid gray), without refinement, having to pass through $s_{home}$. The green line is the end-effector trajectory. Planning time: 38 msec, cost: 82 steps, suboptimallity: 20.4. Fig. \ref{['fig:fig3']} and \ref{['fig:fig4']} show general and front views with anytime refinement. Here, the path do not pass through $s_{home}$. Refining time: 1700 msec, cost: 32 steps, suboptimallity: 4.9.

Theorems & Definitions (11)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Proposition 1
• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 1