A novel second -order online local reactive motion planner, named 'Right-of-Way-based Acceleration Velocity Obstacle' (R-AVO), which also incorporates right-of-way rules established by regulatory authorities, is developed in this paper. Following the developed algorithm, each unmanned vehicle (a.k.a. agent) in a multi-agent, dynamic environment can generate a collision-free, dynamically feasible, and goal-oriented trajectory. Moreover, the considered right-of-way rules enable an implicit coordination between the agents and aid in preventing any reciprocal oscillation in the planned trajectories of the agents. Extensive simulation studies are performed to illustrate the performance of the proposed algorithm in terms of relevant measures of effectiveness, which also indicate real-time implementability of the developed motion planning algorithm. © 2022 IEEE.