ernestds/robust_ccm_tube

Tube-certified nonlinear tracking with robust control contraction metrics

Tube-Certified Trajectory Tracking With Robust Control Contraction Metrics (CCM)

Codes for the paper

P. Zhao, A. Lakshmanan, K. Ackerman, A. Gahlawat, M. Pavone, and N. Hovakimyan, “Tube-certified trajectory tracking for nonlinear systems with robust control contraction metrics,” IEEE Robotics and Automation Letter, 2022. arXiv:2109.04453.

Dependencies

• YALMIP + Mosek solver for search of CCM or robust CCM (RCCM) using sum of squares (SOS) relaxation.
• SPOTLESS also needed for CCM/RCCM synthesis for the 3D quadrotor example
• OptimTraj for planning trajectories.
• OPTI + Matlab fmincon slover for solving the nonlinear programming (NLP) problem associated with geodesic computation.

Usage

For each example,

• Run main.m under the metric folder to design the CCM/RCCM controller.
• Run main.m under the sim folder to simulate the behavior of the system under a CCM/RCCM controller.
• Accelerate the geodesic and control law computation by generating C codes with generate_code_for_geodesic_cal.m.

Suggestions

SOS programming seems not reliable for CCM/RCCM synthesis for high dimensional systems (e.g., a 3D quadrotor). If you struggle in getting a CCM/RCCM for your system using SOS programming, you can try gridding the state space and solving an LMI problem instead, as I did for the quadrotor example.