Optimal Potential Shaping on SE(3) via Neural ODEs on Lie Groups
Yannik P. Wotte Federico Califano Stefano Stramigioli
This work presents a novel approach for the optimization of dynamic systems
on finite-dimensional Lie groups. We rephrase dynamic systems as so-called
neural ordinary differential equations (neural ODEs), and formulate the
optimization problem on Lie groups. A gradient descent optimization algorithm
is presented to tackle the optimization numerically. Our algorithm is scalable,
and applicable to any finite dimensional Lie group, including matrix Lie
groups. By representing the system at the Lie algebra level, we reduce the
computational cost of the gradient computation. In an extensive example,
optimal potential energy shaping for control of a rigid body is treated. The
optimal control problem is phrased as an optimization of a neural ODE on the
Lie group SE(3), and the controller is iteratively optimized. The final
controller is validated on a state-regulation task.