Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

TL;DR

This paper extends a robotics modeling tool to automatically differentiate rigid body dynamics, enabling efficient gradient computations for control and estimation tasks, demonstrated through quadrupedal and robotic arm applications.

Contribution

It introduces an extension of RobCoGen compatible with automatic differentiation, allowing automatic derivative computation and efficient code generation for rigid body dynamics.

Findings

Successful trajectory optimization for HyQ robot using auto-differentiated dynamics.

Real-time obstacle avoidance demonstrated on a 6 DoF robotic arm.

Enhanced flexibility and performance in control algorithms.

Abstract

Many algorithms for control, optimization and estimation in robotics depend on derivatives of the underlying system dynamics, e.g. to compute linearizations, sensitivities or gradient directions. However, we show that when dealing with Rigid Body Dynamics, these derivatives are difficult to derive analytically and to implement efficiently. To overcome this issue, we extend the modelling tool `RobCoGen' to be compatible with Automatic Differentiation. Additionally, we propose how to automatically obtain the derivatives and generate highly efficient source code. We highlight the flexibility and performance of the approach in two application examples. First, we show a Trajectory Optimization example for the quadrupedal robot HyQ, which employs auto-differentiation on the dynamics including a contact model. Second, we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly moving obstacle in a go-to task by fast, dynamic replanning.