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Bridging Discrete Planning and Continuous Execution for Redundant Robot

Teng Yan, Yue Yu, Yihan Liu, Bingzhuo Zhong

Abstract

Voxel-grid reinforcement learning is widely adopted for path planning in redundant manipulators due to its simplicity and reproducibility. However, direct execution through point-wise numerical inverse kinematics on 7-DoF arms often yields step-size jitter, abrupt joint transitions, and instability near singular configurations. This work proposes a bridging framework between discrete planning and continuous execution without modifying the discrete planner itself. On the planning side, step-normalized 26-neighbor Cartesian actions and a geometric tie-breaking mechanism are introduced to suppress unnecessary turns and eliminate step-size oscillations. On the execution side, a task-priority damped least-squares (TP-DLS) inverse kinematics layer is implemented. This layer treats end-effector position as a primary task, while posture and joint centering are handled as subordinate tasks projected into the null space, combined with trust-region clipping and joint velocity constraints. On a 7-DoF manipulator in random sparse, medium, and dense environments, this bridge raises planning success in dense scenes from about 0.58 to 1.00, shortens representative path length from roughly 1.53 m to 1.10 m, and while keeping end-effector error below 1 mm, reduces peak joint accelerations by over an order of magnitude, substantially improving the continuous execution quality of voxel-based RL paths on redundant manipulators.

Bridging Discrete Planning and Continuous Execution for Redundant Robot

Abstract

Voxel-grid reinforcement learning is widely adopted for path planning in redundant manipulators due to its simplicity and reproducibility. However, direct execution through point-wise numerical inverse kinematics on 7-DoF arms often yields step-size jitter, abrupt joint transitions, and instability near singular configurations. This work proposes a bridging framework between discrete planning and continuous execution without modifying the discrete planner itself. On the planning side, step-normalized 26-neighbor Cartesian actions and a geometric tie-breaking mechanism are introduced to suppress unnecessary turns and eliminate step-size oscillations. On the execution side, a task-priority damped least-squares (TP-DLS) inverse kinematics layer is implemented. This layer treats end-effector position as a primary task, while posture and joint centering are handled as subordinate tasks projected into the null space, combined with trust-region clipping and joint velocity constraints. On a 7-DoF manipulator in random sparse, medium, and dense environments, this bridge raises planning success in dense scenes from about 0.58 to 1.00, shortens representative path length from roughly 1.53 m to 1.10 m, and while keeping end-effector error below 1 mm, reduces peak joint accelerations by over an order of magnitude, substantially improving the continuous execution quality of voxel-based RL paths on redundant manipulators.

Paper Structure

This paper contains 24 sections, 28 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. RL-Based Motion Planning and Voxel Policies
  4. Redundancy Resolution and Task-Priority Control
  5. Trajectory Smoothing and Optimization
  6. Methodology: bridging discrete geometry and continuous physics
  7. Geometry layer: voxel-based Q-learning and action regularisation
  8. Q-learning planner on a 3-D voxel grid
  9. Normalized 26-Connected Actions with Geometric Tie-Break
  10. Task-space spline smoothing and micro-step control
  11. Physics Layer: Task-Priority Damped Least-Squares Execution
  12. Primary Task: Damped Least-Squares Position Control
  13. Null-space joint-centering objective
  14. Step-Length and Velocity Clipping
  15. Experimental Setup: From Simulation to Data
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Conceptual motivation. Left: classical planning - feasible collision-free path (Q1); Right: practical deployment - high-quality path (Q2). The proposed method meets the second requirement by bridging a voxel RL planner with a continuous execution layer on a redundant manipulator.
  • Figure 2: Overall architecture of the proposed bridging framework combining discrete Q-learning planning, geometric regularization, and continuous TP-DLS execution.
  • Figure 3: Qualitative comparison on a 7-DoF arm. (a) Baseline (unnormalised actions + Num-IK) shows irregular steps and joint-limit configurations. (b) Proposed bridge (normalised 26-neighbour + TP–DLS) equalises step size and keeps joints away from limits.