Nonlinear model predictive control with discrete control barrier functions for mobile manipulator navigation in narrow environments

Safe motion planning for mobile manipulators in cluttered and constrained environments is a challenging problem due to the coupling between the mobile base and manipulator, which creates a high-dimensional configuration space where collision avoidance must be enforced in real time. The problem becomes particularly challenging in narrow environments, where obstacles are in close proximity and conservative geometric approximations can severely limit feasible motion. This thesis presents a safety–critical control framework that integrates Discrete-Time Control Barrier Functions (DCBFs) within a Nonlinear Model Predictive Control (NMPC) architecture. The robot and obstacles are represented as convex polytopes, enabling collision-avoidance constraints to be formulated via a dual representation of minimum-distance problems. This formulation embeds safety guarantees directly into the predictive control problem while maintaining computational tractability. To improve scalability, an adaptive constraint activation strategy is introduced, dynamically enforcing only constraints associated with spatially relevant obstacles. A height-based obstacle classification further distinguishes obstacles affecting the mobile base, the manipulator arm, or both subsystems, enabling subsystem-specific constraint enforcement. Moreover, planar projection is applied to base-relevant obstacles to reduce the dimensionality of the associated distance computations. The resulting DCBF–NMPC framework enables safe whole-body motion of mobile manipulators in narrow and cluttered environments while maintaining a reduced number of optimization variables and constraints. Experimental validation on a real robot confirms the effectiveness of the proposed approach in achieving safe and computationally efficient navigation in constrained and narrow spaces.