Differential communication with distributed MPC based on occupancy grid

Analytical Aspects of Distributed MPC Based on an Occupancy Grid for Mobile Robots

“…Based on Reference [10], we introduce the problem and necessary definitions for the robots, occupancy grid, and constraint construction shortly: Here, we utilise a distributed system of P ∈ N mobile robots. The robots follow a time discrete model stated as a control-affine system:…”

“…Cell size: In Reference [10], we proposed a minimum cell size c based on the maximum control value which can be imposed on the robot. This minimum cell size has to cover all possible moves of the robot in Z; therefore, it is lower bounded for each vector field f 0 and f i with i ∈ {1, .…”

“…The predicted trajectories are quantised obtaining grid indices and used to communicate them between the robots. This approach, introduced in References [9,10], allows to keep the problem suitable for optimisation algorithms in a continuous setting while taking advantage in the communication reduction via discretisation. The optimisation and therefore the communication is carried out in a sequential manner according to Reference [11]; the future predicted state trajectories of each robot (here, discrete occupancy tuples) are communicated iteratively for each time instant.…”

“…The optimisation and therefore the communication is carried out in a sequential manner according to Reference [11]; the future predicted state trajectories of each robot (here, discrete occupancy tuples) are communicated iteratively for each time instant. While in the former work [9,10] conditions considering initial and recursive feasibility were examined, the focus here is set to derive conditions for convergence and practical stability of the overall system.…”

“…In these articles, the convergence or stability aspects were shown by utilising either a Lyapunov function or a controller, which guarantees the decrease of costs in any time instant, or of terminal constraints or costs, which then forces the predicted trajectory to achieve an end point or region, or to steer that by a terminal cost penalty or a connective constraint, ensuring that, e.g., a minimum distance or explicit bounds on the optimal value function were used to calculate the suboptimality degree of a finite horizon controller. As the considered scenario here is noncooperative and as a Lyapunov function for one robot may be infeasible if one robot has to increase its costs by taking a detour and if terminal regions or costs will restrict the freedom of feasible trajectories, we use a weaker assumption, which is similar to the movement pattern from former numerical results based on the pattern of a roundabout; see Figures 4 and 7 in Reference [10].…”