Safety is one of the main challenges when applying learning-based motion controllers to practical robotic systems, especially when the dynamics of the robots and their surrounding dynamic environments are unknown. This issue is further exacerbated when the learned information is unreliable and inaccurate. In this paper, we aim to enhance the safety of learning-enabled mobile robots in dynamic environments from the perspective of distributionally robust optimization (DRO) and the unscented transform (UT). Our method infers the unknown dynamics of both the robot and the environment by adopting Gaussian process regression with an uncertainty propagation scheme based on UT to improve prediction accuracy. This leads to a novel learning-based model predictive control (MPC) method in which state information about both the robot and the environment is propagated via UT. The proposed method uses DRO to proactively limit the risk of collisions or other unsafe events in the presence of learning errors. However, the distributionally robust risk constraint is intractable because it involves a separate infinite-dimensional optimization problem. To overcome this challenge, we exploit UT with modern DRO techniques to replace the risk constraint with its simple upper bound. The performance and the utility of our method are demonstrated through simulations in autonomous driving scenarios, showing its capability to enhance safety and computational efficiency.

In this article, we propose a novel safety specification tool, called thedistributionally robust risk map(DR-risk map), for a mobile robot operating in a learning-enabled environment. Given the robot's position, the map aims to reliably assess the conditional value-at-risk (CVaR) of collision with obstacles whose movements are inferred by Gaussian process regression (GPR). Unfortunately, the inferred distribution is subject to errors, making it difficult to accurately evaluate the CVaR of collision. To overcome this challenge, our tool measures the risk under the worst-case distribution in a so-calledambiguity setthat characterizes allowable distribution errors. To resolve the infinite-dimensionality issue inherent in the construction of the DR-risk map, we derive a tractable semidefinite programming formulation that provides an upper bound of the risk, exploiting techniques from modern distributionally robust optimization. As a concrete application for motion planning, a distributionally robust RRT* algorithm is considered using the risk map that addresses distribution errors caused by GPR. Furthermore, a motion control method is devised using the DR-risk map in a learning-based model predictive control (MPC) formulation. In particular, a neural network approximation of the risk map is proposed to reduce the computational cost in solving the MPC problem. The performance and utility of the proposed risk map are demonstrated through simulation studies that show its ability to ensure the safety of mobile robots despite learning errors.

In this article, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model-predictive control (MPC) method for limiting the risk of unsafety even when the true distribution of the obstacles’ movements deviates, within anambiguity set, from the empirical distribution obtained using a limited amount of sample data. By choosing the ambiguity set as a statistical ball with its radius measured by theWasserstein metric, we achieve a probabilistic guarantee of theout-of-sample risk, evaluated using new sample data generated independently of the training data. To resolve the infinite-dimensionality issue inherent in the distributionally robust MPC problem, we reformulate it as a finite-dimensional nonlinear program using modern distributionally robust optimization techniques based on the Kantorovich duality principle. To find a globally optimal solution in the case of affine dynamics and output equations, a spatial branch-and-bound algorithm is designed using McCormick relaxation. The performance of the proposed method is demonstrated and analyzed through simulation studies using nonlinear dynamic and kinematic vehicle models and a linearized quadrotor model. The simulation results indicate that, even when the sample size is small, the proposed method can successfully avoid randomly moving obstacles with a guarantee of out-of-sample risk, while its sample average approximation counterpart fails to do so.

In this paper, we propose an optimization-based decision-making tool for safe motion planning and control in an environment with randomly moving obstacles. The unique feature of the proposed method is that it limits the risk of unsafety by a pre-specified threshold even when the true probability distribution of the obstacles' movements deviates, within a Wasserstein ball, from an available empirical distribution. Another advantage is that it provides a probabilistic out-of-sample performance guarantee of the risk constraint. To develop a computationally tractable method for solving the distributionally robust model predictive control problem, we propose a set of reformulation procedures using (i) the Kantorovich duality principle, (ii) the extremal representation of conditional value-at-risk, and (iii) a geometric expression of the distance to the union of halfspaces. The performance and utility of this distributionally robust method are demonstrated through simulations using a 12D quadrotor model in a 3D environment.

Safety is a critical issue in learning-based robotic and autonomous systems as learned information about their environments is often unreliable and inaccurate. In this paper, we propose a risk-aware motion control tool that is robust against errors in learned distributional information about obstacles moving with unknown dynamics. The salient feature of our model predictive control (MPC) method is its capability of limiting the risk of unsafety even when the true distribution deviates from the distribution estimated by Gaussian process (GP) regression, within an ambiguity set. Unfortunately, the distributionally robust MPC problem with GP is intractable because the worst-case risk constraint involves an infinite-dimensional optimization problem over the ambiguity set. To remove the infinite-dimensionality issue, we develop a systematic reformulation approach exploiting modern distributionally robust optimization techniques. The performance and utility of our method are demonstrated through simulations using a nonlinear car-like vehicle model for autonomous driving.