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This work presents and evaluates a novel input parameterization method whichimproves the tractability of model predictive control (MPC) for high degree offreedom (DoF) robots. Experimental results demonstrate that by parameterizingthe input trajectory more than three quarters of the optimization variablesused in traditional MPC can be eliminated with practically no effect on systemperformance. This parameterization also leads to trajectories which are moreconservative, producing less overshoot in underdamped systems with modelingerror. In this paper we present two MPC solution methods that make use of thisparameterization. The first uses a convex solver, and the second makes use ofparallel computing on a graphics processing unit (GPU). We show that bothapproaches drastically reduce solve times for large DoF, long horizon MPCproblems allowing solutions at real-time rates. Through simulation and hardwareexperiments, we show that the parameterized convex solver MPC has faster solvetimes than traditional MPC for high DoF cases while still achieving similarperformance. For the GPU-based MPC solution method, we use an evolutionaryalgorithm and that we call Evolutionary MPC (EMPC). EMPC is shown to have evenfaster solve times for high DoF systems. Solve times for EMPC are shown todecrease even further through the use of a more powerful GPU. This suggeststhat parallelized MPC methods will become even more advantageous with theimprovement and prevalence of GPU technology.

Parameterized and GPU-Parallelized Real-Time Model Predictive Control for High Degree of Freedom Robots