Trajectory Tracking with Reachability-Guided Quadratic Programming and Freeze-Resume

Many robotic systems must follow planned paths yet pause safely and resume when people or objects intervene. We present an output-space method for systems whose tracked output can be feedback-linearized to a double integrator (e.g., manipulators). The approach has two parts. Offline, we perform a pre-run reachability check to verify that the motion plan respects speed and acceleration magnitude limits. Online, we apply a quadratic program to track the motion plan under the same limits. We use a one-step reachability test to bound the maximum disturbance the system is capable of rejecting. When the state coincides with the reference path we recover perfect tracking in the deterministic case, and we correct errors using a KKT-inspired weight. We demonstrate that safety stops and unplanned deviations are handled efficiently, and the system returns to the motion plan without replanning. We demonstrate our system's improved performance over pure pursuit in simulation.