ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control (2311.18056v1)

Abstract: We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of Multipliers (ADMM) algorithm for solving QPs as a deep, weight-tied neural network with rectified linear unit (ReLU) activations. This reformulation enables the deployment of ReLU-QP on GPUs using standard machine-learning toolboxes. We evaluate the performance of ReLU-QP across three model-predictive control (MPC) benchmarks: stabilizing random linear dynamical systems with control limits, balancing an Atlas humanoid robot on a single foot, and tracking whole-body reference trajectories on a quadruped equipped with a six-degree-of-freedom arm. These benchmarks indicate that ReLU-QP is competitive with state-of-the-art CPU-based solvers for small-to-medium-scale problems and offers order-of-magnitude speed improvements for larger-scale problems.

• The paper introduces ReLU-QP, a GPU-accelerated quadratic programming solver that maps ADMM into a neural network architecture for real-time MPC applications.
• It leverages ReLU activations for efficient matrix-vector multiplications and projections on GPUs, accelerating high-dimensional control computations.
• Experiments with Atlas humanoid and quadruped robots validate its superior speed compared to state-of-the-art CPU-based solvers in demanding control tasks.

Overview

The paper introduces ReLU-QP, a novel GPU-accelerated quadratic programming solver that enhances the speed at which high-dimensional control problems can be addressed in real-time. This solver transforms the alternating direction method of multipliers (ADMM) algorithm into the architecture of a neural network, which efficiently operates on GPUs. The key advantage of ReLU-QP lies in its fast computation abilities, which make it valuable for real-time model-predictive control (MPC) applications in robotics.

The Challenge in Control Problems

MPC is an advanced method utilized in robotic control systems to predict and optimize future states and inputs of a system. It involves solving quadratic programs that can become computationally intensive as the number of variables increases. Traditional CPU-based solvers can struggle with the real-time demands of high-dimensional MPC problems.

ReLU-QP's Approach

The unique approach of ReLU-QP involves the mapping of a specific optimization algorithm (ADMM) to a neural network format. This transformation leverages rectified linear unit (ReLU) activations within the neural network to execute matrix-vector multiplications and projections onto the positive orthant, which aligns seamlessly with GPU capabilities.

Performance and Validation

Experiments were conducted across various control scenarios, including random linear systems and tasks involving an Atlas humanoid robot and a quadruped robot with an arm. These tasks were chosen to test the solver's performance under real-world conditions involving control limits and disturbances. ReLU-QP achieved significant speed improvements over state-of-the-art CPU-based solvers, validating its efficacy in real-time MPC applications.

Conclusion and Future Directions

ReLU-QP is an innovative solver that can work effectively with standard machine-learning toolboxes, allowing detailed modeling and reasoning in complex control scenarios. Despite potential for further enhancements, such as better handling of matrix sparsity and real-time updates, ReLU-QP already represents a substantial advancement in the ability to solve MPC problems in real-time, carrying implications for the future of robotic control systems.