Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
This work addresses a bottleneck in robotics for control, optimization, and estimation by automating derivative computation, though it is incremental as it builds on existing tools like RobCoGen.
The authors tackled the difficulty of deriving and implementing analytical derivatives for rigid body dynamics in robotics by extending RobCoGen to be compatible with automatic differentiation, enabling efficient source code generation. They demonstrated the approach's flexibility and performance in trajectory optimization for a quadrupedal robot and dynamic replanning for a robotic arm, achieving practical results in hardware experiments.
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.