In various examples, a gradient-based motion planner evaluates a cost function corresponding to routes for a machine and an obstacle to jointly update the routes. The cost function may include terms to penalize deviation from an initial route predicted for the obstacle and acceleration or jerk for the obstacle. The routes for the machine and the obstacle that are updated may be selected using motion classes that characterize relative motion between a route for the machine and a route for the obstacle. A motion class may be based at least on an angular distance between the machine and the agent and free-end homotopy, where members of the class execute the same relative motion with respect to other agents while being continuously transformable to any other member of the class. The members of the class may have the same start point and different end points.