1. The planner updates the current best path to be executed by the system every ∆t seconds. During each cycle, the current state is updated (line 4) and propagated to the end of the planning cycle (line 5), yielding x(t+∆t). The tree root is set to the node whose trajectory the propagated state is following; this node’s trajectory is committed and must be followed. The remaining time in the cycle is used to expand the tree (lines 6-8). Following this tree growth, the cost estimates are used5to select the best feasibleapath in the tree (line 9); the nature of these cost estimates is discussed further in Section IV.D. Assuming at least one such feasible path existsb, it is selected and executed by the vehicle (line 10).