Constraint-Guided Online Data Selection for Scalable Data-Driven Safety Filters in Uncertain Robotic Systems

As the use of autonomous robotic systems expands in tasks that are complex and challenging to model, the demand for robust data-driven control methods that can certify safety and stability in uncertain conditions is increasing. However, the practical implementation of these methods often faces scalability issues due to the growing amount of data points with system complexity, and a significant reliance on high-quality training data. In response to these challenges, this study presents a scalable data-driven controller that efficiently identifies and infers from the most informative data points for implementing data-driven safety filters. Our approach is grounded in the integration of a model-based certificate function-based method and Gaussian Process (GP) regression, reinforced by a novel online data selection algorithm that reduces time complexity from quadratic to linear relative to dataset size. Empirical evidence, gathered from successful real-world cart-pole swing-up experiments and simulated locomotion of a five-link bipedal robot, demonstrates the efficacy of our approach. Our findings reveal that our efficient online data selection algorithm, which strategically selects key data points, enhances the practicality and efficiency of data-driven certifying filters in complex robotic systems, significantly mitigating scalability concerns inherent in nonparametric learning-based control methods.

In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States

Learning-based control approaches have shown great promise in performing complex tasks directly from high-dimensional perception data for real robotic systems. Nonetheless, the learned controllers can behave unexpectedly if the trajectories of the system divert from the training data distribution, which can compromise safety. In this work, we propose a control filter that wraps any reference policy and effectively encourages the system to stay in-distribution with respect to offline-collected safe demonstrations. Our methodology is inspired by Control Barrier Functions (CBFs), which are model-based tools from the nonlinear control literature that can be used to construct minimally invasive safe policy filters. While existing methods based on CBFs require a known low-dimensional state representation, our proposed approach is directly applicable to systems that rely solely on high-dimensional visual observations by learning in a latent state-space. We demonstrate that our method is effective for two different visuomotor control tasks in simulation environments, including both top-down and egocentric view settings.

Probabilistic Safe Online Learning with Control Barrier Functions

Learning-based control schemes have recently shown great efficacy performing complex tasks. However, in order to deploy them in real systems, it is of vital importance to guarantee that the system will remain safe during online training and execution. We therefore need safe online learning frameworks able to autonomously reason about whether the current information at their disposal is enough to ensure safety or, in contrast, new measurements are required. In this paper, we present a framework consisting of two parts: first, an out-of-distribution detection mechanism actively collecting measurements when needed to guarantee that at least one safety backup direction is always available for use; and second, a Gaussian Process-based probabilistic safety-critical controller that ensures the system stays safe at all times with high probability. Our method exploits model knowledge through the use of Control Barrier Functions, and collects measurements from the stream of online data in an event-triggered fashion to guarantee recursive feasibility of the learned safety-critical controller. This, in turn, allows us to provide formal results of forward invariance of a safe set with high probability, even in a priori unexplored regions. Finally, we validate the proposed framework in numerical simulations of an adaptive cruise control system.

Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty

Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are popular tools for enforcing safety and stability of a controlled system, respectively. They are commonly utilized to build constraints that can be incorporated in a min-norm quadratic program (CBF-CLF-QP) which solves for a safety-critical control input. However, since these constraints rely on a model of the system, when this model is inaccurate the guarantees of safety and stability can be easily lost. In this paper, we present a Gaussian Process (GP)-based approach to tackle the problem of model uncertainty in safety-critical controllers that use CBFs and CLFs. The considered model uncertainty is affected by both state and control input. We derive probabilistic bounds on the effects that such model uncertainty has on the dynamics of the CBF and CLF. Then, we use these bounds to build safety and stability chance constraints that can be incorporated in a min-norm convex optimization program, called GP-CBF-CLF-SOCP. As the main theoretical result of the paper, we present necessary and sufficient conditions for pointwise feasibility of the proposed optimization problem. We believe that these conditions could serve as a starting point towards understanding what are the minimal requirements on the distribution of data collected from the real system in order to guarantee safety. Finally, we validate the proposed framework with numerical simulations of an adaptive cruise controller for an automotive system.

Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects

This paper presents a method to design a min-norm Control Lyapunov Function (CLF)-based stabilizing controller for a control-affine system with uncertain dynamics using Gaussian Process (GP) regression. We propose a novel compound kernel that captures the control-affine nature of the problem, which permits the estimation of both state and input-dependent model uncertainty in a single GP regression problem. Furthermore, we provide probabilistic guarantees of convergence by the use of GP Upper Confidence Bound analysis and the formulation of a CLF-based stability chance constraint which can be incorporated in a min-norm optimization problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP). The data-collection process and the training of the GP regression model are carried out in an episodic learning fashion. We validate the proposed algorithm and controller in numerical simulations of an inverted pendulum and a kinematic bicycle model, resulting in stable trajectories which are very similar to the ones obtained if we actually knew the true plant dynamics.

Improving Input-Output Linearizing Controllers for Bipedal Robots via Reinforcement Learning

The main drawbacks of input-output linearizing controllers are the need for precise dynamics models and not being able to account for input constraints. Model uncertainty is common in almost every robotic application and input saturation is present in every real world system. In this paper, we address both challenges for the specific case of bipedal robot control by the use of reinforcement learning techniques. Taking the structure of a standard input-output linearizing controller, we use an additive learned term that compensates for model uncertainty. Moreover, by adding constraints to the learning problem we manage to boost the performance of the final controller when input limits are present. We demonstrate the effectiveness of the designed framework for different levels of uncertainty on the five-link planar walking robot RABBIT.

Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions

In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize a structure of an input-ouput linearization controller based on a nominal model, and Control Barrier Function (CBF) and Control Lyapunov Function (CLF)-based control methods. Specifically, a novel Reinforcement Learning framework which learns the model uncertainty in CBF and CLF constraints, as well as other dynamic constraints is proposed. The trained policy is combined with the nominal model-based CBF-CLF-QP, resulting in the Reinforcement Learning based CBF-CLF-QP (RL-CBF-CLF-QP), which now addresses the problem of uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview.