Is Data All That Matters? The Role of Control Frequency for Learning-Based Sampled-Data Control of Uncertain Systems

Learning models or control policies from data has become a powerful tool to improve the performance of uncertain systems. While a strong focus has been placed on increasing the amount and quality of data to improve performance, data can never fully eliminate uncertainty, making feedback necessary to ensure stability and performance. We show that the control frequency at which the input is recalculated is a crucial design parameter, yet it has hardly been considered before. We address this gap by combining probabilistic model learning and sampled-data control. We use Gaussian processes (GPs) to learn a continuous-time model and compute a corresponding discrete-time controller. The result is an uncertain sampled-data control system, for which we derive robust stability conditions. We formulate semidefinite programs to compute the minimum control frequency required for stability and to optimize performance. As a result, our approach enables us to study the effect of both control frequency and data on stability and closed-loop performance. We show in numerical simulations of a quadrotor that performance can be improved by increasing either the amount of data or the control frequency, and that we can trade off one for the other. For example, by increasing the control frequency by 33%, we can reduce the number of data points by half while still achieving similar performance.

Optimized Control Invariance Conditions for Uncertain Input-Constrained Nonlinear Control Systems

Providing safety guarantees for learning-based controllers is important for real-world applications. One approach to realizing safety for arbitrary control policies is safety filtering. If necessary, the filter modifies control inputs to ensure that the trajectories of a closed-loop system stay within a given state constraint set for all future time, referred to as the set being positive invariant or the system being safe. Under the assumption of fully known dynamics, safety can be certified using control barrier functions (CBFs). However, the dynamics model is often either unknown or only partially known in practice. Learning-based methods have been proposed to approximate the CBF condition for unknown or uncertain systems from data; however, these techniques do not account for input constraints and, as a result, may not yield a valid CBF condition to render the safe set invariant. In this work, we study conditions that guarantee control invariance of the system under input constraints and propose an optimization problem to reduce the conservativeness of CBF-based safety filters. Building on these theoretical insights, we further develop a probabilistic learning approach that allows us to build a safety filter that guarantees safety for uncertain, input-constrained systems with high probability. We demonstrate the efficacy of our proposed approach in simulation and real-world experiments on a quadrotor and show that we can achieve safe closed-loop behavior for a learned system while satisfying state and input constraints.

Swarm-GPT: Combining Large Language Models with Safe Motion Planning for Robot Choreography Design

This paper presents Swarm-GPT, a system that integrates large language models (LLMs) with safe swarm motion planning - offering an automated and novel approach to deployable drone swarm choreography. Swarm-GPT enables users to automatically generate synchronized drone performances through natural language instructions. With an emphasis on safety and creativity, Swarm-GPT addresses a critical gap in the field of drone choreography by integrating the creative power of generative models with the effectiveness and safety of model-based planning algorithms. This goal is achieved by prompting the LLM to generate a unique set of waypoints based on extracted audio data. A trajectory planner processes these waypoints to guarantee collision-free and feasible motion. Results can be viewed in simulation prior to execution and modified through dynamic re-prompting. Sim-to-real transfer experiments demonstrate Swarm-GPT's ability to accurately replicate simulated drone trajectories, with a mean sim-to-real root mean square error (RMSE) of 28.7 mm. To date, Swarm-GPT has been successfully showcased at three live events, exemplifying safe real-world deployment of pre-trained models.

Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon

Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations.

A Remote Sim2real Aerial Competition: Fostering Reproducibility and Solutions' Diversity in Robotics Challenges

Shared benchmark problems have historically been a fundamental driver of progress for scientific communities. In the context of academic conferences, competitions offer the opportunity to researchers with different origins, backgrounds, and levels of seniority to quantitatively compare their ideas. In robotics, a hot and challenging topic is sim2real-porting approaches that work well in simulation to real robot hardware. In our case, creating a hybrid competition with both simulation and real robot components was also dictated by the uncertainties around travel and logistics in the post-COVID-19 world. Hence, this article motivates and describes an aerial sim2real robot competition that ran during the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems, from the specification of the competition task, to the details of the software infrastructure supporting simulation and real-life experiments, to the approaches of the top-placed teams and the lessons learned by participants and organizers.

What is the Impact of Releasing Code with Publications? Statistics from the Machine Learning, Robotics, and Control Communities

Open-sourcing research publications is a key enabler for the reproducibility of studies and the collective scientific progress of a research community. As all fields of science develop more advanced algorithms, we become more dependent on complex computational toolboxes -- sharing research ideas solely through equations and proofs is no longer sufficient to communicate scientific developments. Over the past years, several efforts have highlighted the importance and challenges of transparent and reproducible research; code sharing is one of the key necessities in such efforts. In this article, we study the impact of code release on scientific research and present statistics from three research communities: machine learning, robotics, and control. We found that, over a six-year period (2016-2021), the percentages of papers with code at major machine learning, robotics, and control conferences have at least doubled. Moreover, high-impact papers were generally supported by open-source codes. As an example, the top 1% of most cited papers at the Conference on Neural Information Processing Systems (NeurIPS) consistently included open-source codes. In addition, our analysis shows that popular code repositories generally come with high paper citations, which further highlights the coupling between code sharing and the impact of scientific research. While the trends are encouraging, we would like to continue to promote and increase our efforts toward transparent, reproducible research that accelerates innovation -- releasing code with our papers is a clear first step.

Barrier Bayesian Linear Regression: Online Learning of Control Barrier Conditions for Safety-Critical Control of Uncertain Systems

In this work, we consider the problem of designing a safety filter for a nonlinear uncertain control system. Our goal is to augment an arbitrary controller with a safety filter such that the overall closed-loop system is guaranteed to stay within a given state constraint set, referred to as being safe. For systems with known dynamics, control barrier functions (CBFs) provide a scalar condition for determining if a system is safe. For uncertain systems, robust or adaptive CBF certification approaches have been proposed. However, these approaches can be conservative or require the system to have a particular parametric structure. For more generic uncertain systems, machine learning approaches have been used to approximate the CBF condition. These works typically assume that the learning module is sufficiently trained prior to deployment. Safety during learning is not guaranteed. We propose a barrier Bayesian linear regression (BBLR) approach that guarantees safe online learning of the CBF condition for the true, uncertain system. We assume that the error between the nominal system and the true system is bounded and exploit the structure of the CBF condition. We show that our approach can safely expand the set of certifiable control inputs despite system and learning uncertainties. The effectiveness of our approach is demonstrated in simulation using a two-dimensional pendulum stabilization task.

RLO-MPC: Robust Learning-Based Output Feedback MPC for Improving the Performance of Uncertain Systems in Iterative Tasks

In this work we address the problem of performing a repetitive task when we have uncertain observations and dynamics. We formulate this problem as an iterative infinite horizon optimal control problem with output feedback. Previously, this problem was solved for linear time-invariant (LTI) system for the case when noisy full-state measurements are available using a robust iterative learning control framework, which we refer to as robust learning-based model predictive control (RL-MPC). However, this work does not apply to the case when only noisy observations of part of the state are available. This limits the applicability of current approaches in practice: First, in practical applications we typically do not have access to the full state. Second, uncertainties in the observations, when not accounted for, can lead to instability and constraint violations. To overcome these limitations, we propose a combination of RL-MPC with robust output feedback model predictive control, named robust learning-based output feedback model predictive control (RLO-MPC). We show recursive feasibility and stability, and prove theoretical guarantees on the performance over iterations. We validate the proposed approach with a numerical example in simulation and a quadrotor stabilization task in experiments.

safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning

In recent years, reinforcement learning and learning-based control -- as well as the study of their safety, crucial for deployment in real-world robots -- have gained significant traction. However, to adequately gauge the progress and applicability of new results, we need the tools to equitably compare the approaches proposed by the controls and reinforcement learning communities. Here, we propose a new open-source benchmark suite, called safe-control-gym. Our starting point is OpenAI's Gym API, which is one of the de facto standard in reinforcement learning research. Yet, we highlight the reasons for its limited appeal to control theory researchers -- and safe control, in particular. E.g., the lack of analytical models and constraint specifications. Thus, we propose to extend this API with (i) the ability to specify (and query) symbolic models and constraints and (ii) introduce simulated disturbances in the control inputs, measurements, and inertial properties. We provide implementations for three dynamic systems -- the cart-pole, 1D, and 2D quadrotor -- and two control tasks -- stabilization and trajectory tracking. To demonstrate our proposal -- and in an attempt to bring research communities closer together -- we show how to use safe-control-gym to quantitatively compare the control performance, data efficiency, and safety of multiple approaches from the areas of traditional control, learning-based control, and reinforcement learning.

Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning

The last half-decade has seen a steep rise in the number of contributions on safe learning methods for real-world robotic deployments from both the control and reinforcement learning communities. This article provides a concise but holistic review of the recent advances made in using machine learning to achieve safe decision making under uncertainties, with a focus on unifying the language and frameworks used in control theory and reinforcement learning research. Our review includes: learning-based control approaches that safely improve performance by learning the uncertain dynamics, reinforcement learning approaches that encourage safety or robustness, and methods that can formally certify the safety of a learned control policy. As data- and learning-based robot control methods continue to gain traction, researchers must understand when and how to best leverage them in real-world scenarios where safety is imperative, such as when operating in close proximity to humans. We highlight some of the open challenges that will drive the field of robot learning in the coming years, and emphasize the need for realistic physics-based benchmarks to facilitate fair comparisons between control and reinforcement learning approaches.