Abstract: The invention provides a computer-implemented method of planning a path for a mobile robot such as an autonomous vehicle in the presence of K obstacles. The method uses, for each of the K obstacles, a shape Bk and a density function pk(x) representing the probabilistic position of the obstacle. The method repeats the following steps for at least two different paths A: —choosing a path A, where A is the swept area of the robot within a given time interval; and—calculating based on the density function of each obstacle and the swept path an upper bound on the total probability of at least one collision FD between the robot and the K obstacles. This allows a number of candidate paths to be ranked for safety. By precomputing factors of the computational steps over K obstacles, the computation per path is O(N), and not O(NK). A safety threshold can be used to filter out paths below that threshold.

Abstract: A computer-implemented method of planning a path for a mobile robot in the presence of a set of obstacles comprises: 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; and for at least one candidate path, determining an upper bound on the 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.

Abstract: The invention provides a computer-implemented method of planning a path for a mobile robot such as an autonomous vehicle in the presence of K obstacles. The method uses, for each of the K obstacles, a shape Bk and a density function pk(x) representing the probabilistic position of the obstacle. The method repeats the following steps for at least two different paths A:—choosing a path A, where A is the swept area of the robot within a given time interval; and—calculating based on the density function of each obstacle and the swept path an upper bound on the total probability of at least one collision FD between the robot and the K obstacles. This allows a number of candidate paths to be ranked for safety. By precomputing factors of the computational steps over K obstacles, the computation per path is O(N), and not O(NK). A safety threshold can be used to filter out paths below that threshold.