Figure 5: An illustration of the velocity selection problem for robot 𝑖 . 𝑢 𝛼 is the set of all vectors in the same half plane as 𝜕 𝜙 𝑖 g o a l / 𝜕 𝑞 𝑖 (labeled as Goal). Similarly, the range and line of sight constraints define cones in the tangent space. The set of feasible directions lies at the intersection of these sets.