A Formal gatekeeper Framework for Safe Dual Control with Active Exploration
Kaleb Ben Naveed, Devansh R. Agrawal, Dimitra Panagou
TL;DR
The paper tackles safe trajectory planning under bounded parametric uncertainty by integrating a gatekeeper-inspired dual-control framework with robust tube MPC. It constructs a safe backup tube to guarantee constraint satisfaction and concurrently generates informative trajectories aimed at shrinking the parameter-set width $w_d(\Theta)$ without exceeding a mission budget $B$. A candidate-formation, validity test, and a scoring mechanism ensure exploration occurs only when safe and beneficial, with a budget-aware commitment that updates the backup iteratively. The authors provide theoretical guarantees that the planned and committed tubes are safe and budget-feasible, and they demonstrate online uncertainty reduction and cost savings on quadrotor case studies with drag and vector-drag dynamics. The approach advances practical dual control by coupling safety guarantees with principled, budget-conscious exploration, supported by simulations and concrete implementation details in Julia.
Abstract
Planning safe trajectories under model uncertainty is a fundamental challenge. Robust planning ensures safety by considering worst-case realizations, yet ignores uncertainty reduction and leads to overly conservative behavior. Actively reducing uncertainty on-the-fly during a nominal mission defines the dual control problem. Most approaches address this by adding a weighted exploration term to the cost, tuned to trade off the nominal objective and uncertainty reduction, but without formal consideration of when exploration is beneficial. Moreover, safety is enforced in some methods but not in others. We propose a framework that integrates robust planning with active exploration under formal guarantees as follows: The key innovation and contribution is that exploration is pursued only when it provides a verifiable improvement without compromising safety. To achieve this, we utilize our earlier work on gatekeeper as an architecture for safety verification, and extend it so that it generates both safe and informative trajectories that reduce uncertainty and the cost of the mission, or keep it within a user-defined budget. The methodology is evaluated via simulation case studies on the online dual control of a quadrotor under parametric uncertainty.