| CPC G05D 1/0214 (2013.01) [B60W 60/0011 (2020.02); B60W 60/0027 (2020.02); G05D 1/0238 (2013.01); G05D 1/0253 (2013.01); G06V 20/58 (2022.01); B60W 2554/4042 (2020.02); B60W 2554/4043 (2020.02)] | 16 Claims | 

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               1. A computer-implemented method of planning a path for a mobile robot in a presence of a set of obstacles, the method comprising: 
            computing for each obstacle a probabilistic obstacle position distribution; 
                computing at least one path-independent function as a combination of the probabilistic obstacle position distributions; 
                for at least one candidate path, determining an upper bound on a total probability of obstacle collision along that path, by aggregating the path-independent function based on an area defined by the candidate path and a mobile robot shape, wherein the path-independent function is independent of the candidate path; 
                wherein the defined area is a surface of a spacetime tube defined by the candidate path and the mobile robot shape, and the path-independent function is integrated or otherwise aggregated over that surface; 
                  wherein the spacetime tube is determined as a set of spacetime voxels, wherein the path-independent function is determined by projecting faces of the voxels into a spacetime plane for each obstacle and integrating the probabilistic obstacle position distribution for that obstacle over each projection of the voxel face for that obstacle to compute a probability value for that voxel face, and wherein the path-independent function is aggregated over the surface of the spacetime tube by summing the probability values computed for the voxel faces; and 
                based on the at least one candidate path, planning a path for the mobile robot and maneuvering the mobile robot along the planned path. 
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