Optimal Constrained Trajectory Planning for Redundant Manipulators via Volumetric Obstacles Modeling and Analytical Gradient Fields

Abstract

Trajectory planning for redundant manipulators in precision manufacturing tasks, such as continuous dispensing or automated inspection, requires the simultaneous satisfaction of strict operational constraints and real-time obstacle avoidance. Traditional planning approaches struggle in these scenarios: dense meshes are computationally demanding, while spherical approximations are overly conservative for elongated tools in cluttered spaces. To overcome these limitations, this paper proposes a computationally efficient trajectory planning framework implemented in ROS 2. By dynamically modeling the workspace with 3D Oriented Bounding Boxes and the manipulator as a kinematic chain of spatial cylinders, the framework achieves a tight, non-conservative geometric approximation. This novel pairing enables a closed-form distance formulation, yielding exact and continuous gradients for realtime null-space redundancy resolution without numerical differentiation. Furthermore, to ensure feasibility in fully constrained scenarios, a Dynamic Task Relaxation mechanism is introduced to temporarily induce artificial redundancy. The planning strategy further separates free-space motion from a constrained Cartesian execution phase, ensuring strict compliance with process requirements. The effectiveness of the proposed framework is validated through a representative industrial case study featuring both natively redundant and non-redundant robotic platforms, demonstrating improved computational efficiency, enhanced task reliability, and robust performance in highly constrained environments.