Path Planning for Continuum Rods Using Bernstein Surfaces

TL;DR

This paper introduces a novel approach for optimal motion planning of continuum robots using Bernstein surfaces to discretize complex continuous problems, enabling efficient solutions with standard optimization tools.

Contribution

It extends previous Bernstein polynomial methods by employing Bernstein surfaces for better approximation of continuum robot dynamics and constraints.

Findings

Effective discretization of infinite-dimensional problems

Successful numerical validations in various scenarios

Potential for advanced soft robotics control

Abstract

This paper presents a method for optimal motion planning of continuum robots by employing Bernstein surfaces to approximate the system's dynamics and impose complex constraints, including collision avoidance. The main contribution is the approximation of infinite-dimensional continuous problems into their discrete counterparts, facilitating their solution using standard optimization solvers. This discretization leverages the unique properties of Bernstein surface, providing a framework that extends previous works which focused on ODEs approximated by Bernstein polynomials. Numerical validations are conducted through several numerical scenarios. The presented methodology offers a promising direction for solving complex optimal control problems in the realm of soft robotics.