Constraint Learning in Multi-Agent Dynamic Games from Demonstrations of Local Nash Interactions

We present an inverse dynamic game-based algorithm to learn parametric constraints from a given dataset of local generalized Nash equilibrium interactions between multiple agents. Specifically, we introduce mixed-integer linear programs (MILP) encoding the Karush-Kuhn-Tucker (KKT) conditions of the interacting agents, which recover constraints consistent with the Nash stationarity of the interaction demonstrations. We establish theoretical guarantees that our method learns inner approximations of the true safe and unsafe sets, as well as limitations of constraint learnability from demonstrations of Nash equilibrium interactions. We also use the interaction constraints recovered by our method to design motion plans that robustly satisfy the underlying constraints. Across simulations and hardware experiments, our methods proved capable of inferring constraints and designing interactive motion plans for various classes of constraints, both convex and non-convex, from interaction demonstrations of agents with nonlinear dynamics.

Toward Extending Concentric Tube Robot Kinematics for Large Clearance and Impulse Curvature

Concentric Tube Robots (CTRs) have been proposed to operate within the unstructured environment for minimally invasive surgeries. In this letter, we consider the operation scenario where the tubes travel inside the channels with a large clearance or large curvature, such as aortas or industrial pipes. Accurate kinematic modeling of CTRs is required for the development of advanced control and sensing algorithms. To this end, we extended the conventional CTR kinematics model to a more general case with large tube-to-tube clearance and large centerline curvature. Numerical simulations and experimental validations are conducted to compare our model with respect to the conventional CTR kinematic model. In the physical experiments, our proposed model achieved a tip position error of 1.53 mm in the 2D planer case and 4.36 mm in 3D case, outperforming the state-of-the-art model by 71% and 66%, respectively.