Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

Arkadiusz Mielczarek,Ignacy Dulęba

doi:10.3390/app112110245

Abstract

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

Highlights

A large number of contemporary and practically important robots can be described as nonholonomic systems
Using a linearization of a nonholonomic system along the trajectory corresponding to current controls, Tchon and coworkers [7] reformulated a nonholonomic motion planning task into an inverse task solved with classical methods
The paper is organized as follows: In Section 2 a model of nonholonomic systems is introduced supplemented with an output function, a motion planning task is defined and, a Lie algebraic algorithm to solve the task is presented

Summary

Introduction

A large number of contemporary and practically important robots can be described as nonholonomic systems. A vast majority of motion planning algorithms are based on discretization of control/configuration spaces to transform continuous tasks, described by differential equations and static output functions, into a graph domain. In this discrete space, graph-searching algorithms, like RRT or its numerous variants [13], can be used to solve the planning task. The paper is organized as follows: In Section 2 a model of nonholonomic systems is introduced supplemented with an output function, a motion planning task is defined and, a Lie algebraic algorithm to solve the task is presented.

Model and Algorithm

Simulations

Conclusions