As robots increasingly operate in human environments, their controllers must ensure safe and reliable behavior under real-time constraints. Although optimization-based motion planners can enforce hard safety constraints, their computational demands limit their use on complex robotic platforms. Geometric motion planning offers a real-time alternative through optimization-free, closed-form control laws with reach–avoid guarantees. However, these guarantees rely on assumptions about obstacle representations that are often violated in realistic settings. When such assumptions fail, the planner’s dynamical system may preserve invariance of the safe set but lose global attractivity, jeopardizing goal reachability.

This thesis introduces a runtime verification algorithm, called Scenario-Shield, that adapts the geometric planner’s underlying dynamical system to expand its finite-time region of attraction. The method periodically samples nearby robot configurations and performs forward simulations to approximate this region. To accelerate this process, the approach is extended by incorporating statistical uncertainty quantification: conformal prediction is used to calibrate a fast membership test for candidate states, and the scenario approach provides a principled approximation of an uncountably infinite subset of the region of attraction.

To maintain computational efficiency, the algorithm is implemented using parallel computing and integrated into a geometric motion planning toolbox with ROS. The proposed method is validated in simulation on both a holonomic ground robot and a mobile manipulator, demonstrating improved reliability over baseline geometric fabrics controllers.
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Mobile manipulators, which integrate a robotic arm on a mobile base, are increasingly being explored and deployed in sectors such as healthcare, logistics, and aerospace. While motion planning for these systems has been studied in single-agent scenarios, the use of multiple robots to enhance efficiency and accelerate task completion in multi-agent settings remains largely unexplored, particularly in real-world environments. Extending motion planning to multi-mobile manipulators introduces challenges in real-time performance, collision avoidance, and coordination. To address these, this thesis proposes a decentralized Model Predictive Control (MPC) framework with a double integrator as dynamic model, denoted as MPC-d, tailored for multi-mobile manipulators operating in shared workspaces. It integrates optimization-based planning with robust state estimation, ensuring effective collision avoidance. Furthermore, a prioritized heuristic is introduced, leveraging the prediction horizon of MPC to resolve potential livelocks. The framework is validated through simulations and real-world experiments. Simulations compare MPC-d with MPC using a triple-integrator model (MPC-t) and a state-of-the-art geometric planner, called Geometric Fabrics (GF). Results demonstrate that MPC-d achieves comparable task success rates and collision avoidance compared to GF in pick-and-place scenarios while requiring less computation time than MPC-t. Real-world experiments confirm the framework’s viability, showcasing effective collision avoidance, enhanced efficiency from the prioritized heuristic, and consistency with simulation outcomes. Although MPC-d incurs higher computational costs than reactive geometric methods, it provides reliable performance and motion prediction of other agents in multi-agent settings. ... Read more