Symmetric Stair Preconditioning of Linear Systems for Parallel Trajectory Optimization

There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems. Iterative methods are particularly well-suited for parallel solves of such systems. However, fast and stable convergence of iterative methods is reliant on the application of a high-quality preconditioner that reduces the spread and increase the clustering of the eigenvalues of the target matrix. To improve the performance of these approaches, we present a new parallel-friendly symmetric stair preconditioner. We prove that our preconditioner has advantageous theoretical properties when used in conjunction with iterative methods for trajectory optimization such as a more clustered eigenvalue spectrum. Numerical experiments with typical trajectory optimization problems reveal that as compared to the best alternative parallel preconditioner from the literature, our symmetric stair preconditioner provides up to a 34% reduction in condition number and up to a 25% reduction in the number of resulting linear system solver iterations.Comment: Accepted to ICRA 2024, 8 pages, 3 figure

Just Round: Quantized Observation Spaces Enable Memory Efficient Learning of Dynamic Locomotion

Deep reinforcement learning (DRL) is one of the most powerful tools for synthesizing complex robotic behaviors. But training DRL models is incredibly compute and memory intensive, requiring large training datasets and replay buffers to achieve performant results. This poses a challenge for the next generation of field robots that will need to learn on the edge to adapt to their environment. In this paper, we begin to address this issue through observation space quantization. We evaluate our approach using four simulated robot locomotion tasks and two state-of-the-art DRL algorithms, the on-policy Proximal Policy Optimization (PPO) and off-policy Soft Actor-Critic (SAC) and find that observation space quantization reduces overall memory costs by as much as 4.2x without impacting learning performance.Comment: Accepted to ICRA 202

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

Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded, implementations of direct trajectory optimization that use iterative methods to solve the underlying moderately-large and sparse linear systems, are a natural fit for parallel hardware acceleration. In this work, 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.Comment: Accepted to ICRA 2024, 8 pages, 6 figure

Code Generation for Conic Model-Predictive Control on Microcontrollers with TinyMPC

Conic constraints appear in many important control applications like legged locomotion, robotic manipulation, and autonomous rocket landing. However, current solvers for conic optimization problems have relatively heavy computational demands in terms of both floating-point operations and memory footprint, making them impractical for use on small embedded devices. We extend TinyMPC, an open-source, high-speed solver targeting low-power embedded control applications, to handle second-order cone constraints. We also present code-generation software to enable deployment of TinyMPC on a variety of microcontrollers. We benchmark our generated code against state-of-the-art embedded QP and SOCP solvers, demonstrating a two-order-of-magnitude speed increase over ECOS while consuming less memory. Finally, we demonstrate TinyMPC's efficacy on the Crazyflie, a lightweight, resource-constrained quadrotor with fast dynamics. TinyMPC and its code-generation tools are publicly available at https://tinympc.org.Comment: Submitted to CDC, 2024. First two authors contributed equall

TinyMPC: Model-Predictive Control on Resource-Constrained Microcontrollers

Model-predictive control (MPC) is a powerful tool for controlling highly dynamic robotic systems subject to complex constraints. However, MPC is computationally demanding, and is often impractical to implement on small, resource-constrained robotic platforms. We present TinyMPC, a high-speed MPC solver with a low memory footprint targeting the microcontrollers common on small robots. Our approach is based on the alternating direction method of multipliers (ADMM) and leverages the structure of the MPC problem for efficiency. We demonstrate TinyMPC both by benchmarking against the state-of-the-art solver OSQP, achieving nearly an order of magnitude speed increase, as well as through hardware experiments on a 27 g quadrotor, demonstrating high-speed trajectory tracking and dynamic obstacle avoidance.Comment: First three authors contributed equally and are ordered alphabeticall

Datasheets for Machine Learning Sensors

Machine learning (ML) sensors offer a new paradigm for sensing that enables intelligence at the edge while empowering end-users with greater control of their data. As these ML sensors play a crucial role in the development of intelligent devices, clear documentation of their specifications, functionalities, and limitations is pivotal. This paper introduces a standard datasheet template for ML sensors and discusses its essential components including: the system's hardware, ML model and dataset attributes, end-to-end performance metrics, and environmental impact. We provide an example datasheet for our own ML sensor and discuss each section in detail. We highlight how these datasheets can facilitate better understanding and utilization of sensor data in ML applications, and we provide objective measures upon which system performance can be evaluated and compared. Together, ML sensors and their datasheets provide greater privacy, security, transparency, explainability, auditability, and user-friendliness for ML-enabled embedded systems. We conclude by emphasizing the need for standardization of datasheets across the broader ML community to ensure the responsible and effective use of sensor data

Project-based, collaborative, algorithmic robotics for high school students: Programming self-driving race cars at MIT

We describe the pedagogy behind the MIT Beaver Works Summer Institute Robotics Program, a new high-school STEM program in robotics. The program utilizes state-of-the-art sensors and embedded computers for mobile robotics. These components are carried on an exciting 1/10-scale race-car platform. The program has three salient, distinguishing features: (i) it focuses on robotics software systems: the students design and build robotics software towards real-world applications, without being distracted by hardware issues; (ii) it champions project-based learning: the students learn through weekly project assignments and a final course challenge; (iii) the learning is implemented in a collaborative fashion: the students learn the basics of collaboration and technical communication in lectures, and they work in teams to design and implement their software systems. The program was offered as a four-week residential program at MIT in the summer of 2016. In this paper, we provide the details of this new program, its teaching objectives, and its results. We also briefly discuss future directions and opportunities

RobotPerf: An Open-Source, Vendor-Agnostic, Benchmarking Suite for Evaluating Robotics Computing System Performance

We introduce RobotPerf, a vendor-agnostic benchmarking suite designed to evaluate robotics computing performance across a diverse range of hardware platforms using ROS 2 as its common baseline. The suite encompasses ROS 2 packages covering the full robotics pipeline and integrates two distinct benchmarking approaches: black-box testing, which measures performance by eliminating upper layers and replacing them with a test application, and grey-box testing, an application-specific measure that observes internal system states with minimal interference. Our benchmarking framework provides ready-to-use tools and is easily adaptable for the assessment of custom ROS 2 computational graphs. Drawing from the knowledge of leading robot architects and system architecture experts, RobotPerf establishes a standardized approach to robotics benchmarking. As an open-source initiative, RobotPerf remains committed to evolving with community input to advance the future of hardware-accelerated robotics

Widening Access to Applied Machine Learning with TinyML

Broadening access to both computational and educational resources is critical to diffusing machine-learning (ML) innovation. However, today, most ML resources and experts are siloed in a few countries and organizations. In this paper, we describe our pedagogical approach to increasing access to applied ML through a massive open online course (MOOC) on Tiny Machine Learning (TinyML). We suggest that TinyML, ML on resource-constrained embedded devices, is an attractive means to widen access because TinyML both leverages low-cost and globally accessible hardware, and encourages the development of complete, self-contained applications, from data collection to deployment. To this end, a collaboration between academia (Harvard University) and industry (Google) produced a four-part MOOC that provides application-oriented instruction on how to develop solutions using TinyML. The series is openly available on the edX MOOC platform, has no prerequisites beyond basic programming, and is designed for learners from a global variety of backgrounds. It introduces pupils to real-world applications, ML algorithms, data-set engineering, and the ethical considerations of these technologies via hands-on programming and deployment of TinyML applications in both the cloud and their own microcontrollers. To facilitate continued learning, community building, and collaboration beyond the courses, we launched a standalone website, a forum, a chat, and an optional course-project competition. We also released the course materials publicly, hoping they will inspire the next generation of ML practitioners and educators and further broaden access to cutting-edge ML technologies.Comment: Understanding the underpinnings of the TinyML edX course series: https://www.edx.org/professional-certificate/harvardx-tiny-machine-learnin

Widening Access to Applied Machine Learning With TinyML

Broadening access to both computational and educational resources is crit- ical to diffusing machine learning (ML) innovation. However, today, most ML resources and experts are siloed in a few countries and organizations. In this article, we describe our pedagogical approach to increasing access to applied ML through a massive open online course (MOOC) on Tiny Machine Learning (TinyML). We suggest that TinyML, applied ML on resource-constrained embedded devices, is an attractive means to widen access because TinyML leverages low-cost and globally accessible hardware and encourages the development of complete, self-contained applications, from data collection to deployment. To this end, a collaboration between academia and industry produced a four part MOOC that provides application-oriented instruction on how to develop solutions using TinyML. The series is openly available on the edX MOOC platform, has no prerequisites beyond basic programming, and is designed for global learners from a variety of backgrounds. It introduces real-world applications, ML algorithms, data-set engineering, and the ethi- cal considerations of these technologies through hands-on programming and deployment of TinyML applications in both the cloud and on their own microcontrollers. To facili- tate continued learning, community building, and collaboration beyond the courses, we launched a standalone website, a forum, a chat, and an optional course-project com- petition. We also open-sourced the course materials, hoping they will inspire the next generation of ML practitioners and educators and further broaden access to cutting-edge ML technologies