Spatiotemporal MCA Approach for the Motion Coordination of Heterogeneous MRS

In this work, a collision-free motion-planning technique for multiple robots based on Multilayered Cellular Automata (MCA) has been studied. What we want to realize is a Coordinator for multi-robot systems which decides the motions of a team of robots while they interact with the environment and react as fast as possible to the dynamical events. Many authors have proposed different solutions for the Path/Motion Planning problem during the last twenty-five years for single and multiple robots. For example, a solution based on a geometrical description of the environment had been proposed since 1979 (e.g., Lozano-Pérez & Wesley, 1979, Lozano-Pérez, 1983). The motion-planners (path-planners) working on these types of models generate very precise optimal trajectories and they can solve really difficult problems, also taking into account non-holonomic constraints, but they are also very time consuming. To face a real dynamical world with many events, a robot must constantly sense the world and re-plan as fast as possible, according to the ewly acquired information. Other authors have developed alternative approaches less precise but more efficient: the Artificial Potential Fields Methods. In the eighties, Khatib first proposed this method for the real-time collision avoidance problem of a manipulator in a continuous space (Khatib, 1986). Jahanbin and Fallside first introduced a wave propagation algorithm in the Configuration Space C-Space on discrete maps (Distance Transform, Jahanbin & Fallside, 1988). In (Barraquand et al., 1992), the authors used the Numerical Potential Field Technique on the C-Space to build a generalized Voronoi Diagram. Zelinsky extended the Distance ransform to the Path Transform (Zelinsky, 1994). Tzionas et al. in (Tzionas et al., 1997) described an algorithm for a diamond-shaped holonomic robot in a static environment where they let a CA build a Voronoi Diagram. In (Warren, 1990) the coordination of robots is proposed using a discretized 3D C Space Time (2D workspace plus Time) for robots with the same shape (only square and circle) and a quite simple kinematics (translation only). LaValle in (LaValle, 1998) applies the concepts of the Game Theory and multi-objective optimization to the centralized and decoupled planning. A solution in the C-Space Time is proposed in (Bennewitz, 2001), where the authors use a decoupled and prioritized path planning in which they repeatedly reorder the robots to try to find a solution. It can be proven that these approaches are not complete. In this work, we want to design a motion coordinator for a set of heterogeneous mobile robot (different shapes and kinematics), able to determine the motions of the mobile agents in order to avoid collisions with obstacles and with other robots. We have adopted Cellular Automata as formalism for merging a grid model of the world (Occupancy Grid) with the C-Space Time of multiple robots and Numerical (Artificial) Potential Field Methods, with the purpose to give a simple and fast solution for the motion-planning problem for multiple mobile robots, in particular for robots with different shapes and kinematics. This method uses a directional (anisotropic) propagation of distance values between adjacent automata to build a potential hypersurface embedded in a 5D space. Applying a constrained version of the descending gradient on the persurface, it is possible to find out all the admissible, equivalent and shortest (for a given metric of the discretized space) trajectories connecting two poses for each robot C-Space Time