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In this paper, we focus on non-conservative obstacle avoidance between robots with control affine dynamics with strictly convex and polytopic shapes. The core challenge for this obstacle avoidance problem is that the minimum distance between strictly convex regions or polytopes is generally implicit and non-smooth, such that distance constraints cannot be enforced directly in the optimization problem. To handle this challenge, we employ non-smooth control barrier functions to reformulate the avoidance problem in the dual space, with the positivity of the minimum distance between robots equivalently expressed using a quadratic program. Our approach is proven to guarantee system safety. We theoretically analyze the smoothness properties of the minimum distance quadratic program and its KKT conditions. We validate our approach by demonstrating computationally-efficient obstacle avoidance for multi-agent robotic systems with strictly convex and polytopic shapes. To our best knowledge, this is the first time a real-time QP problem can be formulated for general non-conservative avoidance between strictly convex shapes and polytopes.

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Bridging model-based safety and model-free reinforcement learning (RL) for dynamic robots is appealing since model-based methods are able to provide formal safety guarantees, while RL-based methods are able to exploit the robot agility by learning from the full-order system dynamics. However, current approaches to tackle this problem are mostly restricted to simple systems. In this paper, we propose a new method to combine model-based safety with model-free reinforcement learning by explicitly finding a low-dimensional model of the system controlled by a RL policy and applying stability and safety guarantees on that simple model. We use a complex bipedal robot Cassie, which is a high dimensional nonlinear system with hybrid dynamics and underactuation, and its RL-based walking controller as an example. We show that a low-dimensional dynamical model is sufficient to capture the dynamics of the closed-loop system. We demonstrate that this model is linear, asymptotically stable, and is decoupled across control input in all dimensions. We further exemplify that such linearity exists even when using different RL control policies. Such results point out an interesting direction to understand the relationship between RL and optimal control: whether RL tends to linearize the nonlinear system during training in some cases. Furthermore, we illustrate that the found linear model is able to provide guarantees by safety-critical optimal control framework, e.g., Model Predictive Control with Control Barrier Functions, on an example of autonomous navigation using Cassie while taking advantage of the agility provided by the RL-based controller.