A synthesis approach of distributed model predictive control for homogeneous multi-agent system with collision avoidance

For the tracking and formation problem of multi-agent systems with collision avoidance, a synchronous distributed model predictive control (DMPC) algorithm is proposed. We consider the deterministic, linear, time-invariant, and homogeneous dynamics for all agents. In the synchronous DMPC, all the agents solve their optimisation problems synchronously, taking advantage of their neighbours’ assumed predictive information, to obtain the current optimal inputs. Considering the uncertain deviation existing between the assumed and actual predictive information of each agent, we contribute to design a deviation-dependent collision avoidance constraint, which is imposed in the individual optimisation problem to guarantee the safety of each agent. We constrain the uncertain deviation by designing a time-varying compatibility constraint in the two-norm form, which is imposed in the individual optimisation problem to play an important role in both the collision avoidance and exponential stability. By applying the proposed algorithm, the guarantees for the recursive feasibility, exponential stability and collision avoidance are all proved. A simulation example is provided to illustrate the practicability and effectiveness of this approach.