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This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided. Index Terms-Motion planning, nonlinear control, robotics manipulators, vector potential fields. NOMENCLATURE NC Navigation control. PF Potential field. VPF Vector potential field. SPF Scalar potential field. BVP Boundary value problem. VBVP Vector boundary value problem. SBVP Scalar boundary value problem. BEM Boundary element method. LAC Local alignment control. PPC Penetration prevention control. BLAC Boundary local alignment control. BPPC Boundary penetration prevention control.

Spatial multi-agency has been receiving growing attention from researchers exploring many of the aspects and modalities of this phenomenon. The aim is to develop the theoretical background needed for a multitude of applications involving the sharing of resources by more than one agent. A traffic management system is one of these applications. Here, a large group of mobile robots that are operating in communication-limited, and sensory-limited modes are required to cope with each others presence as well as the contents of their environment while preserving their ability to reach their preset, independent goals. This work explores the construction of a decentralized traffic controller for a large group of agents sharing a workspace with stationary forbidden regions. The suggested multi-agent motion controller is complete provided that a lenient condition on the geometry of the workspace is upheld. It has a low computational effort that linearly increases with the number of agents. The controller is also self-organizing; therefore, it is able to deal, on its own, with incomplete information and unexpected situations. In addition to the above, the controller has an open structure to enable any agent to join or leave the group without the remaining agents having to adjust the manner in which they function. To meet these requirements, a definition of decentralization is suggested. This definition equates decentralization to self-organization in a group of agents operating in an artificial life mode. The definition is used to provide guidelines for the construction of the multi-agent controller. The controller is realized using the potential field approach. Theoretical developments, as well as simulation results, are provided.2

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