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.
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Uncertainty-Aware Constraint Learning for Adaptive Safe Motion Planning from Demonstrations
We present a method for learning to satisfy uncertain constraints fromdemonstrations. Our method uses robust optimization to obtain a belief over thepotentially infinite set of possible constraints consistent with the demonstrations,and then uses this belief to plan trajectories that trade off performance with sat-isfying the possible constraints. We use these trajectories in a closed-loop policythat executes and replans using belief updates, which incorporate data gatheredduring execution. We derive guarantees on the accuracy of our constraint beliefand probabilistic guarantees on plan safety. We present results on a 7-DOF armand 12D quadrotor, showing our method can learn to satisfy high-dimensional (upto 30D) uncertain constraints, and outperforms baselines in safety and efficiency.
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- Award ID(s):
- 1553873
- NSF-PAR ID:
- 10211345
- Date Published:
- Journal Name:
- Conference on Robot Learning
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation’s parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.more » « less
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Creating a domain model, even for classical, domain-independent planning, is a notoriously hard knowledge-engineering task. A natural approach to solve this problem is to learn a domain model from observations. However, model learning approaches frequently do not provide safety guarantees: the learned model may assume actions are applicable when they are not, and may incorrectly capture actions' effects. This may result in generating plans that will fail when executed. In some domains such failures are not acceptable, due to the cost of failure or inability to replan online after failure. In such settings, all learning must be done offline, based on some observations collected, e.g., by some other agents or a human. Through this learning, the task is to generate a plan that is guaranteed to be successful. This is called the model-free planning problem. Prior work proposed an algorithm for solving the model-free planning problem in classical planning. However, they were limited to learning grounded domains, and thus they could not scale. We generalize this prior work and propose the first safe model-free planning algorithm for lifted domains. We prove the correctness of our approach, and provide a statistical analysis showing that the number of trajectories needed to solve future problems with high probability is linear in the potential size of the domain model. We also present experiments on twelve IPC domains showing that our approach is able to learn the real action model in all cases with at most two trajectories.
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Accepted Manuscript1.0
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