We present a mobile robot exploration strategy that computes trajectories that minimize both path and map entropies. The method evaluates joint entropy reduction and computes a potential ¿eld in robot con¿guration space using these joint entropy reduction estimates. The exploration trajectory is computed descending on the gradient of these ¿eld. The technique uses Pose SLAM as its estimation backbone. Very ef¿cient kernel convolution mechanisms are used to evaluate entropy reduction for each sensor ray, and for each possible robot orientation, taking frontiers and obstacles into account. In the end, the computation of this ¿eld on the entire C-space is shown to be very efficient computationally. The approach is tested in simulations in a common publicly available dataset comparing favorably both in quality of estimates and execution time against another entropy reduction strategy that uses occupancy maps

Peer Reviewed