Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation

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.

References in corpus (4)

• The Stan Math Library: Reverse-Mode Automatic Differentiation in C++
• The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control
• Evaluating direct transcription and nonlinear optimization methods for robot motion planning
• Efficient Kinematic Planning for Mobile Manipulators with Non-holonomic Constraints Using Optimal Control

Cited by in corpus (12)

• Whole-Body Nonlinear Model Predictive Control Through Contacts for Quadrupeds
• Whole-Body MPC for a Dynamically Stable Mobile Manipulator
• The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control
• DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation
• Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification
• Efficient Analytical Derivatives of Rigid-Body Dynamics using Spatial Vector Algebra
• An $O(n$)-Algorithm for the Higher-Order Kinematics and Inverse Dynamics of Serial Manipulators using Spatial Representation of Twists
• Augmenting Differentiable Simulators with Neural Networks to Close the Sim2Real Gap
• Differentiable model-based adaptive optics for two-photon microscopy
• Structured Neural Network Dynamics for Model-based Control
• Differentiable model-based adaptive optics with transmitted and reflected light
• Adapting Rigid-Body Dynamics Derivatives for Constraint Embedding Closed-Chain Models