Ricardo Tapia | Searcharxiv

arXiv2026

RCOA Extension and Applications

The Relaxed Convex Obstacle Avoidance (RCOA) formulation is the first approach to enable a fully convex optimal control problem (OCP) for obstacle avoidance. Convergence analysis of RCOA yields an analytical framework that defines a unique characteristic: the ability to maintain obstacle avoidance (OA) efficacy even when obstacles reside beyond the controller's prediction horizon. In this paper, RCOA is extended to three-dimensional environments and apply it to Unmanned Aerial Vehicle (UAV) navigation. Furthermore, the formulation is enhanced to incorporate vehicle geometries, moving beyond point-mass representations to enable collision avoidance between 3D objects. Numerical simulations demonstrate that RCOA provides computational performance on par or exceeding state-of-the-art methods. Notably, RCOA is demonstrated to enable a Nonlinear Model Predictive Controller (NMPC) to execute aggressive maneuvers through narrow passages with reduced prediction horizons, ensuring real-time feasibility at frequencies exceeding 30~Hz.

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arXiv2025

A Convex Obstacle Avoidance Formulation

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.

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