Exploiting visual constraints in the synthesis of uncertainty-tolerant motion plans. I. The directional backprojection

It is shown how the backprojection approach to fine-motion planning can be extended to exploit visual constraints. Specifically, by deriving a configuration space representation of visual constraint surfaces, visual constraint surfaces can be included as boundaries of the directional backprojection. An implemented backprojection planner for C=R² that is based on a plane-sweep algorithm for computing the directional backprojection is described. The effects of visual constraints on the asymptotic time complexity of the modified algorithm are discussed