Lie Theory Based Optimization for Unified State Planning of Mobile Manipulators

TL;DR

This paper introduces a Lie theory-based optimization method for unified motion planning of mobile manipulators, enabling smooth and accurate joint state computation by considering the entire system holistically.

Contribution

It presents a novel approach using Lie theory to unify the motion planning of mobile bases and manipulators, improving over existing methods that treat them separately.

Findings

Validated on simulated mobile manipulators with positive results.

Achieved smooth and accurate motion plans in experiments.

Provides an open-source solver with derivations and results.

Abstract

Mobile manipulators are finding use in numerous practical applications. The current issues with mobile manipulation are the large state space owing to the mobile base and the challenge of modeling high degree of freedom systems. It is critical to devise fast and accurate algorithms that generate smooth motion plans for such mobile manipulators. Existing techniques attempt to solve this problem but focus on separating the motion of the base and manipulator. We propose an approach using Lie theory to find the inverse kinematic constraints by converting the kinematic model, created using screw coordinates, between its Lie group and vector representation. An optimization function is devised to solve for the desired joint states of the entire mobile manipulator. This allows the motion of the mobile base and manipulator to be planned and applied in unison resulting in a smooth and accurate motion plan. The performance of the proposed state planner is validated on simulated mobile manipulators in an analytical experiment. Our solver is available with further derivations and results at https://github.com/peleito/slithers.