Optimal Path Planning for Wheeled Robots

With Some Hints for Good Numerics

autonomous vehicles
robotics
optimal control
path planning
numerical methods
homotopy methods
Author

Willem Esterhuizen

Published

December 26, 2025

Abstract

Coming 1 February 2026

This article presents the steps involved in defining and solving an optimal path planning problem for a well-known car model. It examines common issues that arise when trying to solve the problem numerically and how to deal with them. Examples help to clarify the concepts. Get all the code here.

Keywords

autonomous vehicles, robotics, optimal control, path planning, numerical methods, homotopy methods