Safe Online Dynamics Learning with Initially Unknown Models and Infeasible Safety Certificates

Safety-critical control tasks with high levels of uncertainty are becoming increasingly common. Typically, techniques that guarantee safety during learning and control utilize constraint-based safety certificates, which can be leveraged to compute safe control inputs. However, excessive model uncertainty can render robust safety certification methods or infeasible, meaning no control input satisfies the constraints imposed by the safety certificate. This paper considers a learning-based setting with a robust safety certificate based on a control barrier function (CBF) second-order cone program. If the control barrier function certificate is feasible, our approach leverages it to guarantee safety. Otherwise, our method explores the system dynamics to collect data and recover the feasibility of the control barrier function constraint. To this end, we employ a method inspired by well-established tools from Bayesian optimization. We show that if the sampling frequency is high enough, we recover the feasibility of the robust CBF certificate, guaranteeing safety. Our approach requires no prior model and corresponds, to the best of our knowledge, to the first algorithm that guarantees safety in settings with occasionally infeasible safety certificates without requiring a backup non-learning-based controller.

Online Constraint Tightening in Stochastic Model Predictive Control: A Regression Approach

Solving chance-constrained stochastic optimal control problems is a significant challenge in control. This is because no analytical solutions exist for up to a handful of special cases. A common and computationally efficient approach for tackling chance-constrained stochastic optimal control problems consists of reformulating the chance constraints as hard constraints with a constraint-tightening parameter. However, in such approaches, the choice of constraint-tightening parameter remains challenging, and guarantees can mostly be obtained assuming that the process noise distribution is known a priori. Moreover, the chance constraints are often not tightly satisfied, leading to unnecessarily high costs. This work proposes a data-driven approach for learning the constraint-tightening parameters online during control. To this end, we reformulate the choice of constraint-tightening parameter for the closed-loop as a binary regression problem. We then leverage a highly expressive \gls{gp} model for binary regression to approximate the smallest constraint-tightening parameters that satisfy the chance constraints. By tuning the algorithm parameters appropriately, we show that the resulting constraint-tightening parameters satisfy the chance constraints up to an arbitrarily small margin with high probability. Our approach yields constraint-tightening parameters that tightly satisfy the chance constraints in numerical experiments, resulting in a lower average cost than three other state-of-the-art approaches.

Sharp Calibrated Gaussian Processes

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees, and can be miscalibrated in practice. State-of-the-art approaches for designing calibrated models rely on inflating the Gaussian process posterior variance, which yields confidence intervals that are potentially too coarse. To remedy this, we present a calibration approach that generates predictive quantiles using a computation inspired by the vanilla Gaussian process posterior variance, but using a different set of hyperparameters, chosen to satisfy an empirical calibration constraint. This results in a calibration approach that is considerably more flexible than existing approaches. Our approach is shown to yield a calibrated model under reasonable assumptions. Furthermore, it outperforms existing approaches not only when employed for calibrated regression, but also to inform the design of Bayesian optimization algorithms.

Dext-Gen: Dexterous Grasping in Sparse Reward Environments with Full Orientation Control

Reinforcement learning is a promising method for robotic grasping as it can learn effective reaching and grasping policies in difficult scenarios. However, achieving human-like manipulation capabilities with sophisticated robotic hands is challenging because of the problem's high dimensionality. Although remedies such as reward shaping or expert demonstrations can be employed to overcome this issue, they often lead to oversimplified and biased policies. We present Dext-Gen, a reinforcement learning framework for Dexterous Grasping in sparse reward ENvironments that is applicable to a variety of grippers and learns unbiased and intricate policies. Full orientation control of the gripper and object is achieved through smooth orientation representation. Our approach has reasonable training durations and provides the option to include desired prior knowledge. The effectiveness and adaptability of the framework to different scenarios is demonstrated in simulated experiments.

Structure-Preserving Learning Using Gaussian Processes and Variational Integrators

Gaussian process regression is often applied for learning unknown systems and specifying the uncertainty of the learned model. When using Gaussian process regression to learn unknown systems, a commonly considered approach consists of learning the residual dynamics after applying some standard discretization, which might however not be appropriate for the system at hand. Variational integrators are a less common yet promising approach to discretization, as they retain physical properties of the underlying system, such as energy conservation or satisfaction of explicit constraints. In this work, we propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty. The simulative evaluation of the proposed method shows desirable energy conservation properties in accordance with the theoretical results and demonstrates the capability of treating constrained dynamical systems.

Gaussian Process Uniform Error Bounds with Unknown Hyperparameters for Safety-Critical Applications

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.

Gaussian Process-based Stochastic Model Predictive Control for Overtaking in Autonomous Racing

A fundamental aspect of racing is overtaking other race cars. Whereas previous research on autonomous racing has majorly focused on lap-time optimization, here, we propose a method to plan overtaking maneuvers in autonomous racing. A Gaussian process is used to learn the behavior of the leading vehicle. Based on the outputs of the Gaussian process, a stochastic Model Predictive Control algorithm plans optimistic trajectories, such that the controlled autonomous race car is able to overtake the leading vehicle. The proposed method is tested in a simple simulation scenario.

The Value of Data in Learning-Based Control for Training Subset Selection

Despite the existence of formal guarantees for learning-based control approaches, the relationship between data and control performance is still poorly understood. In this paper, we present a measure to quantify the value of data within the context of a predefined control task. Our approach is applicable to a wide variety of unknown nonlinear systems that are to be controlled by a generic learning-based control law. We model the unknown component of the system using Gaussian processes, which in turn allows us to directly assess the impact of model uncertainty on control. Results obtained in numerical simulations indicate the efficacy of the proposed measure.

Anticipating the Long-Term Effect of Online Learning in Control

Control schemes that learn using measurement data collected online are increasingly promising for the control of complex and uncertain systems. However, in most approaches of this kind, learning is viewed as a side effect that passively improves control performance, e.g., by updating a model of the system dynamics. Determining how improvements in control performance due to learning can be actively exploited in the control synthesis is still an open research question. In this paper, we present AntLer, a design algorithm for learning-based control laws that anticipates learning, i.e., that takes the impact of future learning in uncertain dynamic settings explicitly into account. AntLer expresses system uncertainty using a non-parametric probabilistic model. Given a cost function that measures control performance, AntLer chooses the control parameters such that the expected cost of the closed-loop system is minimized approximately. We show that AntLer approximates an optimal solution arbitrarily accurately with probability one. Furthermore, we apply AntLer to a nonlinear system, which yields better results compared to the case where learning is not anticipated.

Localized active learning of Gaussian process state space models

The performance of learning-based control techniques crucially depends on how effectively the system is explored. While most exploration techniques aim to achieve a globally accurate model, such approaches are generally unsuited for systems with unbounded state spaces. Furthermore, a globally accurate model is not required to achieve good performance in many common control applications, e.g., local stabilization tasks. In this paper, we propose an active learning strategy for Gaussian process state space models that aims to obtain an accurate model on a bounded subset of the state-action space. Our approach aims to maximize the mutual information of the exploration trajectories with respect to a discretization of the region of interest. By employing model predictive control, the proposed technique integrates information collected during exploration and adaptively improves its exploration strategy. To enable computational tractability, we decouple the choice of most informative data points from the model predictive control optimization step. This yields two optimization problems that can be solved in parallel. We apply the proposed method to explore the state space of various dynamical systems and compare our approach to a commonly used entropy-based exploration strategy. In all experiments, our method yields a better model within the region of interest than the entropy-based method.