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Robot motion is a field of continuing and active research that has recorded a number of achievements in the last decade, but research appears to be becoming stagnant in key areas. Current researchers limit the success of their work by using sensors with limited features capable of operating in static environments with known static obstacles and not considering implementation on non-holonomic vehicles. These simplifications of the task of dynamic obstacle avoidance greatly reduce the possible applications of current robot motion algorithms in areas such as autonomous driving. This paper deals with algorithms for on-the-fly avoidance of dynamic obstacle by presenting a new approach, the time-varying dynamic window algorithm capable of operating at high speeds on a non-holonomic vehicle in an environment that changes over time.