Optimal control of perturbed sweeping processes with applications to general robotics models

TL;DR

This paper develops optimal control methods for perturbed sweeping processes in robotics, formulating problems with constraints, deriving optimality conditions, and implementing numerical algorithms to simulate multi-robot systems using Python's GEKKO library.

Contribution

It introduces a novel framework for controlling perturbed sweeping processes in robotics, including new optimality conditions and numerical algorithms for simulation.

Findings

Successful simulation of multi-robot systems under various initial conditions

Development of numerical algorithms for optimal control of sweeping processes

Application of the GEKKO library for robotics control problems

Abstract

This paper primarily focuses on the practical applications of optimal control theory for perturbed sweeping processes within the realm of robotics dynamics. By describing these models as controlled sweeping processes with pointwise control and state constraints and by employing necessary optimality conditions for such systems, we formulate optimal control problems suitable to these models and develop numerical algorithms for their solving. Subsequently, we use the Python Dynamic Optimization library GEKKO to simulate solutions to the posed robotics problems in the case of any fixed number of robots under different initial conditions.