N-dimensional Convex Obstacle Avoidance using Hybrid Feedback Control (Extended version)

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.

A control framework is proposed for safe local navigation of mobile robots equipped with Ackermann steering in unmapped environments where a global goal is absent. Based on local obstacle detections, the safest heading angle is determined along the direction of the largest open space ahead of the vehicle. Guided by this direction, bounding lines are constructed on the left and right sides of the vehicle to achieve obstacle separation. These bounding lines are obtained by solving a convex quadratic optimization that maximizes vehicle-to-obstacle clearance. Optionally, conditions are imposed on the bounding lines to preserve parallelism and smooth abrupt changes from prior control steps. A feedback-linearizing controller is then used to regulate the vehicle's distance from one or both bounding lines, effectively enabling tracking of a local reference path that preserves safety through obstacle clearance maximization. Open-source code is included for the application of this control scheme. Experimental results demonstrate that the proposed method produces safer navigation paths with significantly shorter computation times, compared to some existing exploration-based planners.

This paper presents a unified control framework for robust trajectory tracking and moving obstacle avoidance applicable to a broad class of mobile robots. By formulating a generalized kinematic transformation, we convert diverse vehicle dynamics into a strict feedback form, facilitating the design of a Sliding Mode Control (SMC) strategy for precise and robust reference tracking. To ensure operational safety in dynamic environments, the tracking controller is integrated with a Collision Cone Control Barrier Function (C3BF) based safety filter. The proposed architecture guarantees asymptotic tracking in the presence of external disturbances while strictly enforcing collision avoidance constraints. The novelty of this work lies in designing a sliding mode controller for ground robots like the Ackermann drive, which has not been done before. The efficacy and versatility of the approach are validated through numerical simulations and extensive real-world experiments on three distinct platforms: an Ackermann-steered vehicle, a differential drive robot, and a quadrotor drone. Video of the experiments are available at https://youtu.be/dWcxwum96vk