This dissertation address the computational challenges of whole-body, nonlinear model predictive control (MPC) by exposing, analyzing, and leveraging the structured sparsity and parallelism patterns found in the underlying numerical optimization and rigid body dynamics algorithms. Through careful algorithmic refactoring and re-design, this work exploits these patterns to enable real-time MPC performance through GPU-acceleration. It also validates the feasibility of this approach in the presence of model discrepancies and communication delays between the robot and GPU by deploying the resulting implementations onto a physical manipulator arm. Overall, this dissertation finds that GPU acceleration can provide nearly order-of-magnitude speedups, and open-sources its implementations to aid the wider robotics community in accelerating both robotics computations and application development timelines.
We introduce and release GRiD, an open-source, GPU-accelerated library for computing rigid body dynamics with analytical gradients. GRiD was designed to accelerate nonlinear trajectory optimization through optimized code generation, GRiD provides as much as a 7.2x speedup over a state-of-the-art, multi-threaded CPU implementation and maintains as much as a 2.5x speedup when accounting for I/O overhead.
In this paper, we detail the designs of three faster than state-of-the-art implementations of the gradient of rigid body dynamics on a CPU, GPU, and FPGA. Our optimized FPGA and GPU implementations provide as much as a 3.0x end-to-end speedup over our optimized CPU implementation by refactoring the algorithm to exploit its computational features, e.g., parallelism at different granularities.