  This paper proposes a solution to the problem of smooth path planning for
mobile robots in dynamic and unknown environments. A novel concept of
Time-Warped Grid is introduced to predict the pose of obstacles in the
environment and avoid collisions. The algorithm is implemented using C/C++ and
the CUDA programming environment, and combines stochastic estimation (Kalman
filter), harmonic potential fields and a rubber band model, and it translates
naturally into the parallel paradigm of GPU programming. In simple terms,
time-warped grids are progressively wider orbits around the mobile robot. Those
orbits represent the variable time intervals estimated by the robot to reach
detected obstacles. The proposed method was tested using several simulation
scenarios for the Pioneer P3-DX robot, which demonstrated the robustness of the
algorithm by finding the optimum path in terms of smoothness, distance, and
collision-free, in both static or dynamic environments, and with large number
of obstacles.
