Optimization-based control for safe motion generation in mobile robotic systems

The deployment of robotic systems in human-centric environments demands the integration of motion generation with formal safety guarantees. As mobile robots and mobile manipulators increasingly operate in unstructured, dynamic, and crowded spaces, traditional collision avoidance methods prove insufficient. Ensuring safety, balance preservation, and robust task execution under dynamic uncertainty requires mathematically grounded, real-time control methodologies. This thesis addresses the problem of safe motion generation for wheeled mobile robots and mobile manipulators through optimization-based controller frameworks constrained by the CBF. The primary objective is to synthesize control strategies that guarantee forward invariance of a defined safe set while preserving task performance and computational tractability. The first part of the thesis develops theoretical advancements in CBF-based safety filtering. After establishing the mathematical foundations of continuous-time and discrete-time CBF, the work addresses a limitation of classical CBF formulations when applied to systems with varying relative degrees. The proposed methodology approximates safe sets by reformulating CBF design as a parameterized boundary-value problem, which is solved in real time using physics-informed neural networks, which provide a mechanism to approximate potentially non-convex safe sets while preserving differentiability and computational efficiency. This approach is validated both in simulation and experimentally on quadrotor platforms operating under strict spatial constraints. Subsequently, the thesis introduces a safe control architecture for mobile manipulators executing heavy-payload pick-up tasks. A novel preemptive balance constraint is formulated using the DT-CBF framework. This allows the robot to safely execute reaching motions and grasp heavy objects, even when subject to abrupt dynamic parameter changes. The approach avoids dynamic controller extension while maintaining the linearity of the optimization problem, ensuring real-time implementation. The second part focuses on safe motion generation in crowded human environments. A comprehensive pipeline for perception, estimation, and control is developed, integrating LiDAR, RGB-D data, and Kalman filter-based human state estimation. The motion generation module, designed to ensure safe navigation, is initially formulated as a QP incorporating CBF constraints for human avoidance. This is later extended to a MPC framework using DT-CBF constraints. To efficiently operate in multi-room environments, the framework decomposes complex, non-convex environmental maps into overlapping convex regions, enabling the local MPC to quickly find reliable solutions based on via points provided by a high-level planner. Finally, the thesis introduces an advanced hierarchical task motion generation architecture for mobile manipulators in crowded spaces. It enhances human modeling by accounting for their interactive nature through the optimal reciprocal collision avoidance formulation, moving beyond the assumption of humans as purely passive agents oblivious to the robot. This enables the generation of less conservative, more natural trajectories. The resulting bilevel optimization framework combines task prioritization, predictive control, and interactive safety modeling, demonstrating real-time feasibility in both simulated and experimental scenarios. Overall, this thesis contributes theoretical, algorithmic, and experimental advancements toward the realization of provably safe, optimization-based motion generation strategies for mobile robotic systems operating in dynamic and human-populated environments.