Robot motion planning with uncertainty

This thesis concerns robot motion planning with uncertainty in control and sensing. The problem can be formulated, with some approximations, as path-planning in the extended space of poses × covariances. The reduction of uncertainty due to data acquired by exteroceptive sensors is modelled with the use of Fisher’s information matrix. Many optimization problems can be defined in this framework; this thesis considers two problems: minimizing the execution time, and minimizing the final covariance, with an upper bound on the execution time. Two approaches are discussed. The first is the straight extension of classical graph-search algorithms to the extended space. In the second approach, in place of the forward propagation of states, uncertainty constraints are propagated backward from the goal to the start state. Much attention is given to the definition of dominance relations that allow to discard useless nodes during the search. Simulations show that motion planning with uncertainty is much more expensive to solve than classical path-planning. The backward algorithms are slightly more computationally expensive, but their search tree can be reused for multiple queries.