# A Computationally Efficient Algorithm to Find Time-Optimal Trajectory of Redundantly Actuated Robots Moving on a Specified Path

## TL;DR

This paper introduces a computationally efficient algorithm for determining the time-optimal trajectory of redundantly actuated robots on a specified path, addressing unresolved issues in solution curve calculation.

## Contribution

It proposes a new method to efficiently establish solution curves and calculate maximum or minimum accelerations based on actuator saturation patterns.

## Key findings

- Reduced computational cost in trajectory planning
- Effective calculation of maximum velocity curves
- Validated with numerical examples

## Abstract

A time-optimal problem for redundantly actuated robots moving on a specified path is a challenging problem. Although the problem is well explored and there are proposed solutions based on phase plane analysis, there are still several unresolved issues regarding calculation of solution curves. In this paper, we explore the characteristics of the maximum velocity curve (MVC) and propose an efficient algorithm to establish the solution curve. Then we propose a straightforward method to calculate the maximum or minimum possible acceleration on the path based on the pattern of saturated actuators, which substantially reduces the computational cost. Two numerical examples are provided to illustrate the issues and the solutions.