Robust and Efficient Embedded Convex Optimization through First-Order Adaptive Caching

2025-07-03

AI Summary

To address the poor adaptability and real-time performance limitations of embedded Model Predictive Control (MPC) arising from fixed hyperparameters, this paper proposes an efficient and robust convex optimization framework. The method integrates Alternating Direction Method of Multipliers (ADMM)-based first-order optimization, offline precomputation, and cache reuse. Its key contribution is the first introduction of hyperparameter sensitivity precomputation coupled with an adaptive cache update mechanism—enabling dynamic hyperparameter adjustment without full recomputation. This reduces computational complexity from $O(n^3)$ to $O(n^2)$. Experimental validation on a micro quadrotor demonstrates that, during wind-disturbance-rejection figure-eight flight, the required ADMM iterations decrease by up to 63.4%, while achieving 70% of the performance of a full-cache recomputation baseline. The framework significantly enhances both real-time capability and robustness in resource-constrained embedded MPC applications.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Hardware-aware ML
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Recent advances in Model Predictive Control (MPC) leveraging a combination of first-order methods, such as the Alternating Direction Method of Multipliers (ADMM), and offline precomputation and caching of select operations, have excitingly enabled real-time MPC on microcontrollers. Unfortunately, these approaches require the use of fixed hyperparameters, limiting their adaptability and overall performance. In this work, we introduce First-Order Adaptive Caching, which precomputes not only select matrix operations but also their sensitivities to hyperparameter variations, enabling online hyperparameter updates without full recomputation of the cache. We demonstrate the effectiveness of our approach on a number of dynamic quadrotor tasks, achieving up to a 63.4% reduction in ADMM iterations over the use of optimized fixed hyperparameters and approaching 70% of the performance of a full cache recomputation, while reducing the computational cost from O(n^3) to O(n^2) complexity. This performance enables us to perform figure-eight trajectories on a 27g tiny quadrotor under wind disturbances. We release our implementation open-source for the benefit of the wider robotics community.

Problem

• Enables real-time MPC on microcontrollers with adaptive hyperparameters
• Reduces computational complexity from O(n^3) to O(n^2) for embedded systems
• Improves quadrotor performance under dynamic conditions like wind disturbances

Innovation

• First-Order Adaptive Caching for hyperparameter updates
• Precomputes matrix operations and their sensitivities
• Reduces computational cost from O(n^3) to O(n^2)