# Time-optimal Velocity Tracking Control for Differential Drive Robots

## TL;DR

This paper develops a control strategy for differential drive robots to achieve time-optimal velocity tracking, addressing both constant and smoothly varying velocity commands using optimal control principles and hybrid control structures.

## Contribution

It introduces a novel control approach for time-optimal velocity tracking in nonholonomic robots, combining Pontryagin's principle and hybrid control for dynamic velocities.

## Key findings

- Optimal control laws for constant velocity tracking
- Hybrid control structure for time-varying velocities
- Effective velocity tracking with minimal time

## Abstract

Nonholonomic wheeled mobile robots are often required to implement algorithms designed for holonomic kinematic systems. This creates a velocity tracking problem for the actual wheeled mobile robot. In this paper, we investigate the issue of tracking the desired velocity in the least amount of time, for a differential drive nonholonomic wheeled mobile robot. If the desired velocity is a constant, the Pontryagin Maximum Principle can be used to design a control. A control is designed for the cases when the wheel can be commanded speeds and torques. When the desired velocity is smoothly time-varying, we propose a hybrid structure and study its properties.