Model Predictive Control for Trajectory Tracking on Differentiable Manifolds
This work addresses the gap between geometric control theory and practical MPC implementation for robotics on manifolds, offering a symbolic framework that simplifies user input, though it is incremental in advancing existing MPC methods.
The authors tackled the problem of implementing model predictive control (MPC) for robotic systems on manifolds by proposing a generic on-manifold MPC formulation and a linearization-based solving method, achieving high tracking performance and computational efficiency in real-world experiments with quadrotors and ground vehicles.
We consider the problem of bridging the gap between geometric tracking control theory and implementation of model predictive control (MPC) for robotic systems operating on manifolds. We propose a generic on-manifold MPC formulation based on a canonical representation of the system evolving on manifolds. Then, we present a method that solves the on-manifold MPC formulation by linearizing the system along the trajectory under tracking. There are two main advantages of the proposed scheme. The first is that the linearized system leads to an equivalent error system represented by a set of minimal parameters without any singularity. Secondly, the process of system modeling, error-system derivation, linearization and control has the manifold constraints completely decoupled from the system descriptions, enabling the development of a symbolic MPC framework that naturally encapsulates the manifold constraints. In this framework, users need only to supply system-specific descriptions without dealing with the manifold constraints. We implement this framework and test it on a quadrotor unmanned aerial vehicle (UAV) operating on $SO(3) \times \mathbb{R}^n$ and an unmanned ground vehicle (UGV) moving on a curved surface. Real-world experiments show that the proposed framework and implementation achieve high tracking performance and computational efficiency even in highly aggressive aerobatic quadrotor maneuvers.