Evaluating direct transcription and nonlinear optimization methods for robot motion planning

TL;DR

This paper evaluates various direct transcription methods and optimization techniques for robot motion planning, analyzing their performance across different parameters and validating results through simulations and real robot experiments.

Contribution

It provides a comprehensive comparison of direct transcription alternatives and optimization methods for robot trajectory planning, including experimental validation on real robots.

Findings

Different parameters significantly affect computational time and accuracy.

Sequential Quadratic Programming outperforms Interior Point Method in certain scenarios.

Validated methods on real robot hardware for practical motion planning.

Abstract

This paper studies existing direct transcription methods for trajectory optimization applied to robot motion planning. There are diverse alternatives for the implementation of direct transcription. In this study we analyze the effects of such alternatives when solving a robotics problem. Different parameters such as integration scheme, number of discretization nodes, initialization strategies and complexity of the problem are evaluated. We measure the performance of the methods in terms of computational time, accuracy and quality of the solution. Additionally, we compare two optimization methodologies frequently used to solve the transcribed problem, namely Sequential Quadratic Programming (SQP) and Interior Point Method (IPM). As a benchmark, we solve different motion tasks on an underactuated and non-minimal-phase ball-balancing robot with a 10 dimensional state space and 3 dimensional input space. Additionally, we validate the results on a simulated 3D quadrotor. Finally, as a verification of using direct transcription methods for trajectory optimization on real robots, we present hardware experiments on a motion task including path constraints and actuation limits.