Safe Navigation of Multi-Agent Quadrupedal Robots: A Hierarchical Control Framework Based on Distributed Predictive Control and Control Barrier Functions

This dissertation explores the development of sophisticated distributed layered control algorithms focused on the navigation, planning, and control of multi-agent quadrupedal robots collaborating in uncertain environments. Quadrupedal robots are high-dimensional, complex systems that are inherently unstable, posing significant challenges in designing predictive control laws. Template models offer a solution by providing a bridging layer of reduced-order models with fewer state variables and linearized dynamics. However, this approach compromises the agility and full potential of these sophisticated machines, as template models may fail to capture the intricate nonlinear dynamics of quadrupedal robots. Furthermore, in multi-robot systems (MRS) where numerous robots operate concurrently, it becomes crucial to develop strategies embedding collision safety mechanisms. One approach involves embedding Euclidean distance constraints in the predictive control formulation. While effective, this method significantly complicates the optimal control (OC) problem and increases computational overhead. To mitigate these challenges, this dissertation explores hierarchical and distributed control frameworks, focusing on developing real-time feasible controllers that guarantee collision avoidance while preserving the agility of these hardware platforms by utilizing fully nonlinear template models. In particular, this research investigates a multi-layered framework consisting of potential fields at the high-level layer, a distributed nonlinear model predictive control (DNMPC) based middle-level layer responsible for uncertainty mitigation, and full-order nonlinear controllers at the low-level layer. Additionally, the latter part of this dissertation examines the integration of safety-ensuring control barrier functions (CBFs) into the nonlinear model predictive control (NMPC) layer, thereby providing rigorous mathematical guarantees for collision avoidance. The crux of this research lies in addressing the following questions: How do we design layered control frameworks to guarantee optimal gait planning and collision avoidance while maintaining computational tractability? How do we mitigate uncertainty in the environment in real-time using safety-critical control algorithms?