| This work suggests a control method for the terrain-following formation motion of a group of communicating autonomous agents. The presented approach centers on defining a suitable set of constraints for formation keeping task that shall be fulfilled while agents are negotiating an unknown terrain toward the predefined goal location. It allows agents to maintain a general geometric formation shape, while allowing each individual formation member freedom of maneuver, required for terrain collision free motion. Formation structure is defined with the use of virtual leader. Formation keeping constraints are defined with plane surfaces, specified relative to position and navigation vector of the virtual leader. Formation navigation and guidance constraints are defined using navigation vectors of formation members and the virtual leader. Alternative designs for the constraints derived with parabolic, cone, and cylindrical surfaces are considered. Formation control is derived using the Udwadia-Kalaba equation, following corresponding approach to the development of control methods for constraint based dynamical systems, including leader-follower systems defined using geometric constraints. Approach to terrain following motion requiring agents to stay within bounds of cylindrical corridor volumes built around their respective navigation vectors is assumed. Individual formation primitives and multi-level, hierarchical, formation structures are considered. Simulations, based on three degrees of freedom nonlinear model of an agent, performed using Mathematica and specifically developed combined Maya-Mathematica modeling and simulation system, demonstrate that a flexible terrain following formation motion is achieved with the presented sets of constraints. |
