This paper presents a novel distributed model predictive control (MPC) formulation without terminal cost and a corresponding distributed synthesis approach for distributed linear discrete-time systems with coupled constraints. The proposed control scheme introduces an explicit stability condition as an additional constraint based on relaxed dynamic programming. As a result, contrary to other related approaches, system stability with the developed controller does not rely on designing a terminal cost. A distributed synthesis approach is then introduced to handle the stability constraint locally within each local agent. To solve the underlying optimization problem for distributed MPC, a violation-free distributed optimization approach is developed, using constraint tightening to ensure feasibility throughout iterations. A numerical example demonstrates that the proposed distributed MPC approach ensures closed-loop stability for each feasible control sequence, with each agent computing its control input in parallel.

In this paper, we introduce a ROS based framework designed for the planning and control of robotic systems within the context of precision agriculture, with an emphasis on human-in-the-loop capabilities. Utilizing Linear Temporal Logic to articulate complex task specifications, our algorithm creates high-level robotic plans that are not only correct by design but also adaptable in real time by human operators. This dual-focus approach ensures that while humans have the flexibility to modify the high-level plan on-the-fly or even take over low-level control of the robots, the system inherently safeguards against any human actions that could potentially breach the predefined task specifications. We demonstrate our algorithm within the dynamic and challenging environment of a real vineyard, where the collaboration between human workers and robots is critical for tasks such as harvesting and pruning, and show the practical applicability and robustness of our software. This work marks a pioneering application of formal methods to complex, real-world agricultural environments.