Parallel Computing

Optimizing at All Scales: Edge (Non)linear Model Predictive Control from MCUs to GPUs

In our recent works, by leveraging a combination of parallelism, approximation, and structure exploitation, we have enabled and accelerated (nonlinear) trajectory optimization solvers for real-time performance on non-standard computational hardware, ranging from microcontrollers (MCUs) to graphical processing units (GPUs). This has led to real-time MPC onboard an MCU powered 27g quadrotor for dynamic obstacle avoidance, as well as simulated whole-body nonlinear MPC at kHz rates for a GPU powered manipulator for high speed trajectory tracking.

Parallel Optimization for Robotics: An Undergraduate Introduction to GPU Parallel Programming and Numerical Optimization Research

While parallel programming, particularly on graphics processing units (GPUs), and numerical optimization hold immense potential to tackle real-world computational challenges across disciplines, their inherent complexity and technical demands often act as daunting barriers to entry. This, unfortunately, limits accessibility and diversity within these crucial areas of computer science. To combat this challenge and ignite excitement among undergraduate learners, we developed an application-driven course, harnessing robotics as a lens to demystify the intricacies of these topics making them tangible and engaging. Our course's prerequisites are limited to the required undergraduate introductory core curriculum, opening doors for a wider range of students. Our course also features a large final-project component to connect theoretical learning to applied practice. In our first offering of the course we attracted 27 students without prior experience in these topics and found that an overwhelming majority of the students felt that they learned both technical and soft skills such that they felt prepared for future study in these fields.

MPCGPU: Real-Time Nonlinear Model Predictive Control through Preconditioned Conjugate Gradient on the GPU

We introduce MPCGPU, a GPU-accelerated, real-time NMPC solver that leverages an accelerated preconditioned conjugate gradient (PCG) linear system solver at its core. We show that MPCGPU increases the scalability and real-time performance of NMPC, solving larger problems, at faster rates. In particular, for tracking tasks using the Kuka IIWA manipulator, MPCGPU is able to scale to kilohertz control rates with trajectories as long as 512 knot points. This is driven by a custom PCG solver which outperforms state-of-the-art, CPU-based, linear system solvers by at least 10x for a majority of solves and 3.6x on average.

GPU Acceleration for Real-time, Whole-body, Nonlinear Model Predictive Control

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.

GRiD: GPU-Accelerated Rigid Body Dynamics with Analytical Gradients

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.

Accelerating Robot Dynamics Gradients on a CPU, GPU, and FPGA

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.

Realtime Model Predictive Control using Parallel DDP on a GPU

In this extended abstract we extend our [previous work](/publication/parallelddp) by using our Parallel DDP implementation for MPC on a physical Kuka arm. We demonstrated the feasibility of this approach in the presence of model discrepancies and communication delays between the robot and GPU and found that higher control rates generally lead to better tracking performance across a range of parallelization options.

A Performance Analysis of Parallel Differential Dynamic Programming on a GPU

We analyze the benefits and tradeoffs of higher degrees of parallelization using a multiple-shooting variant of DDP implemented on a GPU. We describe our implementation strategy and present results demonstrating its performance compared to an equivalent multi-threaded CPU implementation using several benchmark control tasks. Our results suggest that GPU-based solvers can offer increased per-iteration computation time and faster convergence in some cases, but in general tradeoffs exist between convergence behavior and degree of algorithm-level parallelism. This work was [extended](/publication/parallelddp_icra) and used for MPC on a physical Kuka arm.

Parallel and Constrained Differential Dynamic Programming for Model Predictive Control

This thesis builds on recent work on Unscented Dynamic Programming (UDP)—which eliminates dynamics derivative computations in DDP—to support general nonlinear state and input constraints to high precision using an augmented Lagrangian. It then leverages parallel computations for increased throughput and systematically analyzes the insights, challenges, tradeoffs, and benefits of implementing a parallelized variant of DDP on both a multi-core CPU and a graphics processing unit (GPU).