In path planning, we do not have any information about the motion of the robot with respect to time (i.e., do not confuse path planning with trajectory planning). So the only cost functions that I can think of is the shortest path, smooth path, or obstacle-free path. Can you suggest any other cost function?
Dear Dr. Ishan Chawla,
The cost functions which you have mentioned are correct in their own forms. However, the cost function related with obstacle-free path inherently encompasses several other cost functions. For instance, obstacle could be static or dynamic in nature. The mechanical structure of obstacles could be non-rigid and deformable like curtains, plants etc.
Moreover, I think by saying shortest path, you mean the optimal one.
Regards
Jyotindra Narayan
For parallel robots, if the path is done and the robot admits several solutions to its inverse kinematic problem, we have to select in which working mode, the trajectory is done. We have to stay in the same aspect, ie to stay in a singularity free region in WxQ. After that, the cost functions for serial robots can be used.
Dear Ishan Chawla
One important cost functional to be minimized is the energy or fuel consumption. In mechanical and aerospace realm, particularly in macro-scale machines and air-vehicles (not UAVs), we may usually penalize energy consumption, for fuel-efficient motion. However, in the case of a robot as you are concerned with, I guess battery usage should be minimized, since these robots are usually remotely-operated, and optimum battery usage is naturally a binding restriction, for high sustainability and also for endurance in some critical missions.
Please also see:
https://www.researchgate.net/post/How_to_compare_performance_between_obstacle_avoidance_algorithms_of_a_mobile_robot
Dear Saeb AmirAhmadi Chomachar
For energy optimal motion planning, we have to obtain the energy consumed during the motion. This will depend on the actuator's torque as well as actuator velocity. In path planning, we do not have information regarding velocity.
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