Evaluating Direct Transcription and Nonlinear Optimization Methods for Robot Motion Planning

This letter 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 nonminimal-phase ball-balancing robot with a 10-D state space and 3-D input space. Additionally, we validate the results on a simulated 3-D 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.