Model Predictive Static Programming for Discrete-Time Optimal Control on Lie Groups
Avoids solving complex boundary value problems, delivering real-time control for quadrotors and helicopters.
Deep Dive
This paper extends Model Predictive Static Programming (MPSP) from Euclidean spaces to Lie groups, enabling real-time optimal control for mechanical systems. The method reformulates finite-horizon optimal control as a sequence of closed-form quadratic programs, avoiding nonlinear two-point boundary value problems. Demonstrated on variable-pitch quadrotor and single-main-rotor helicopter flipping maneuvers, and compared with iterative Linear Quadratic Regulator (iLQR).
Key Points
- Extends MPSP from Euclidean spaces to Lie groups, enabling optimal control for mechanical systems on curved configuration spaces.
- Reformulates optimal control as closed-form quadratic programs, avoiding computationally expensive TPBVPs.
- Demonstrated on quadrotor and helicopter flipping maneuvers; compared favorably with iLQR in numerical studies.
Why It Matters
Enables real-time optimal control for complex robotic systems like drones and helicopters, improving agility and efficiency.