Path Planning and Control for Multi-Manipulator Systems under Spatio-Temporal Constraints

Cooperative manipulation, where multiple robotic manipulators coordinate to transport an object, presents significant challenges due to the physical coupling between manipulators, the complexity of motion planning in constrained environments, and the need for precise control without full system knowledge. These challenges are further exacerbated when tasks impose not only spatial constraints but also strict timing requirements, as specified through signal temporal logic. Under such complex requirements, cooperative manipulation remains a relatively underexplored area. These shortcomings motivate the present thesis. Broadly, by blending tools from control theory, formal methods, and motion planning, this thesis aims to deepen our understanding of how to accomplish such complex tasks within the cooperative manipulation setting. Specifically, we develop controllers and planning algorithms that enable the specification, planning, and execution of cooperative robotic manipulation under such tasks. We approach this problem in three parts. In the first part, we develop control algorithms that take task specifications in the form of signal temporal logic and encode them through funnel-based formulations. Our main results include performing cooperative manipulation under signal temporal logic tasks with both shared task knowledge among all agents and task knowledge limited to a single agent. To achieve this, we design a prescribed performance control scheme that ensures the boundedness of errors within the funnels, thereby enforcing task satisfaction. We present both experimental and simulation validations of the proposed algorithms. In the second part, we shift focus from designing controllers to developing planning algorithms for satisfying signal temporal logic specifications. This shift provides additional flexibility, allowing us to broaden the class of specifications considered. Our main results include the development of a cooperative sampling-based planning algorithm for two autonomous agents, which is then extended to multiple agents through a distributed optimisation approach. In both approaches, we perform sampling in both spatial and temporal domains to search for trajectories that satisfy signal temporal logic formulas. We present several examples to demonstrate the performance of the algorithms, along with experimental validation and proofs of probabilistic completeness. In the final part of the thesis, we address cooperative manipulation through constrained environments. We integrate the control and planning components through a trajectory optimisation framework that continues to address signal temporal logic tasks under environmental constraints. The main contributions include decoupling the planning of mobile bases from that of the manipulator arms, and developing an inverse kinematics algorithm combined with a control design strategy to track the resulting joint-space trajectories while avoiding obstacles. We present simulation results to validate the effectiveness of the proposed approach.