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We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a trajectory tracking error bound for a contraction based controller that is subjected to this model error, and then learn a controller that optimizes this tracking bound. With a given probability, we verify the correctness of the controller and tracking error bound in the trusted domain. We then use the trajectory error bound together with the trusted domain to guide a sampling-based planner to return trajectories that can be robustly tracked in execution. We show results on a 4D car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our method plans safely with learned models of highdimensional underactuated systems, while baselines that plan without considering the tracking error bound or the trusted domain can fail to stabilize the system and become unsafe. 

We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. In addition, by leveraging a known parameterization of the constraint, we modify our method to learn parametric constraints in high dimensions. We also provide theoretical analysis on what subset of the constraint and safe set can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space. 

In this paper, we present a compositional condition for ensuring safety of a collection of interacting systems modeled by inter-triggering hybrid automata (ITHA). ITHA is a modeling formalism for representing multi-agent systems in which each agent is governed by individual dynamics but can also interact with other agents through triggering actions. These triggering actions result in a jump/reset in the state of other agents according to a global resolution function. A sufficient condition for safety of the collection, inspired by responsibility-sensitive safety, is developed in two parts: self-safety relating to the individual dynamics, and responsibility relating to the triggering actions. The condition relies on having an over-approximation method for the resolution function. We further show how such over-approximations can be obtained and improved via communication. We use two examples, a job scheduling task on parallel processors and a highway driving example, throughout the paper to illustrate the concepts. Finally, we provide a comprehensive evaluation on how the proposed condition can be leveraged for several multi-agent control and supervision examples.