This paper presents a closed-form tracking and collision avoidance framework for multi-agent differential drive robots. Existing reactive methods often rely on purely geometric proximity, leading to conservative detours and local minima. A state-dependent adaptive avoidance strategy is developed to dynamically modulate repulsive forces using the time-derivative of fractional barrier risk functions, alleviating unnecessary evasive maneuvers. Within a convergence vector field (CVF) architecture, an active safety-corrected tracking mechanism orthogonally strips hazardous velocity projections from the spatial error. This mitigates the inherent conflict between target tracking and obstacle repulsion. A matrix projection-based Lyapunov approach demonstrates the finite-time convergence of the vehicle orientation, bounded tracking errors, and collision-free properties of the closed-loop system, with effectiveness further validated through simulations.
Zhang et al. (Mon,) studied this question.