This paper addresses the issue of collision avoidance using lane-change maneuvers. Of particular interest is to determine the minimum distance beyond which an obstacle cannot be avoided at a given initial speed. Using a planar bicycle model, we first compute the sharpest dynamically feasible maneuver by minimizing the longitudinal distance of a lane transition, assuming given initial and free final speeds. The minimum distance to an obstacle is then determined from the path traced by the optimal maneuver. Plotting the minimum distance in the phase plane establishes the clearance curve, a valuable tool for planning emergency maneuvers. For the bicycle model, the clearance curve is shown to closely correlate with the straight line produced by a point mass model. Examples demonstrate the use of the clearance curve for planning safe avoidance maneuvers.
This paper solves the on-line obstacle avoidance problem using the Hamilton-Jacobi-Bellman (HJB) theory. Formulating the shortest path problem as a time optimal control problem, the shortest paths are generated by following the negative gradient of the return function, which is the solution of the HJB equation. To account for multiple obstacles, we avoid obstacles optimally one at a time. This is equivalent to following the pseudoreturn function, which is an approximation of the true return function for the multi-obstacle problem. Paths generated by this method are near-optimal and guaranteed to reach the goal, at which the pseudoreturn function is shown to have a unique minimum. The proposed method is computationally very efficient, and applicable for on-line applications. Examples for circular obstacles demonstrate the advantages of the proposed approach over traditional path planning methods.
This paper presents a method for generating neartime optimal trajectories in cluttered environments for manipulators wath invariant inertia matrices. For one obsdacle, the .methop generates the time-optimal trajectory b y manamatang the fame-deravatave of the return (cost) function for this problem, satisfying the Hamilton-Jacobi-Bellman (HJB) equation. For multiple obstacles, the trajectory i s generated using the pseudo return function whzch is an approximation o the return function for the multi-obstacle problem. Jhe pseudo return function avoids one obstacle at a time, producing near-o timal trajectories that are guaranteed to avoid the oistacles and satisfy the actuator constraints. An exam le wath circular obstacles demonstrates close correit ion between the nearoptimal and optimal aths, re uiring computational efforts that are suitabz for on-!ine implementations.
Design methods of robotic manipulators to select the link lengths and actuator sizes for minimum-time motions along specified paths are presented. An exact method is based on a parameter optimization, using the motion time along the path as the cost function. This method serves as a bench mark for a more efficient approximation which selects system parameters so as to maximize the acceleration along the path. Examples of the design of a two link manipulator are presented, demonstrating close correlation between the exact and the approximate methods.
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