Topological and spatial analysis of self-motion manifolds for global redundancy resolution in kinematically redundant robots

Abstract

This paper introduces a novel framework for global redundancy resolution in kinematically redundant robots, which have more degrees of freedom than the dimensions required to complete their task. The method is based on the concept of self-motion manifolds (SMMs), which are subsets of the joint space where the robot can move without affecting the task. Given a task trajectory, a sequence of SMMs is generated by building a graph where each node represents a c-bundle, which are sets of SMMs that share the same topology. The graph is then explored to establish feasible paths, from which preliminary joint trajectories are derived. The joint trajectories undergo an iterative optimization process that moves each joint trajectory point along the SMM of the associated task instant. The method is capable of handling kinematic constraints, such as joint limits and collisions, and it is designed to be adaptable to the kinematic complexity of the robot, real-time requirements, or optimality. The effectiveness and global optimality of the method in solving redundancy is validated through simulations with different robots and degrees of redundancy.