LQR and MPC on a Ball Bot

Code base for final project in ROB 498 Applied Optimal Control at Umich by Joseph Taylor and Connor Williams in Winter '23.

Code Layout

Main functions

• runLQR.m runs LQR on planar system. Generates output animation as LQR_2D.mp4.
• runLQR3D.m runs LQR on full system. Generates output animation as LQR_3D.mp4.
• runMPC.m runs MPC on planar system. Generates output animation as MPC_2D.mp4.
• runMPC3D.m runs MPC on full system. Generates output animation as MPC_3D.mp4.

Helper functions

• genfunctions.m generates dynamics functions and functions for running MPC.
• animate2D.m animates planar system and writes .mp4 of animation.
• animate3D.m animates full system and writes .mp4 of animation.
• transform_3D.m generates transformation matrix from translation vector and Euler angles. Used by animate3D.m.
• modelValidation.m simulates planar system from different initial conditions and plots output energies.
• modelValidation3D.m simulates full system from different initial conditions and plots output energies.
• calculateEnergies.m calculates energies of planar system.

Generated functions

• Hfunc.m generates matrix for quadratic term in QP cost.
• cfunc.m generates vector for linear term in QP cost.
• Afunc.m generates inequality constraint matrix for QP constraints.
• bfunc.m generates inequality constraint vector for QP constraints.
• Aeqfunc.m generates equality constraint matrix for QP constraints.
• beqfunc.m generates equality constraint vector for QP constraints.
• dynamfunc.m state space dynamics function for ball bot.