The invariant-set motion planner uses a collection of safe sets to find a collision-free path through an obstacle-filled environment [1]-[4]. This article extends the invariant-set motion planner to systems with persistently varying disturbances and parametric model uncertainty. This is accomplished by replacing the previously used positive invariant sets with robust positive invariant sets. Since the model uncertainty obfuscates the relationship between the invariant sets in the state space, and the references and obstacles in the output space, we reformulate the dynamics in velocity form so that the system output appears directly in the modified system state. Since the persistently varying disturbances will prevent the closed-loop system from converging to the desired reference, we introduce a new robust connection rule where references are connected when the invariant set of one reference contains the minimal volume robust invariant-set of another. In addition, we bound the time required to transition between invariant sets to ensure safety when the obstacles are moving. By parameterizing the invariant sets using a precomputed input-to-state Lyapunov function, we reduce the real-time computational complexity of our motion planner. The robust invariant-set motion planner is demonstrated for an automated highway driving case study.