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.

Constrained motion control using vector potential fields

Motion planning, or goal-oriented, context-sensitive, intelligent control is essential if an agent is to act in a useful manner. This paper suggests a new class of motion planners that can mark a constrained trajectory to a target zone in an environment that need not necessarily be a priori known. The novelty of the suggested planner lies in its ability to enforce region avoidance and direction satisfaction constraints jointly. To the best of the authors' knowledge, this is the first time that directional constraints have been addressed in the motion planning literature. To build such a planner, the potential field approach is used for inducing the control action. In addition, to cope with the presence of the above constraints (in particular, the directional constraints), a new type of potential field, called the nonlinear anisotropic harmonic potential field, is suggested. The planner has applications in traffic management and operations research among others. Development of the approach, proofs of correctness, and simulation results are supplied.

Motion planning in the presence of directional and regional avoidance constraints using nonlinear, anisotropic, harmonic potential fields: a physical metaphor

This paper introduces a new integrated path control strategy (combined path planning and motion control) for autonomous systems of arbitrary dimension. A harmonic artificial potential field is used to specify admissible trajectories leading around obstacles. Using a sliding mode controller, motion is generated along the gradient lines of the potential field, avoiding collisions with the obstacles. The extremely low computational complexity of the proposed method makes it very suitable for online applications. The strategy is applied to mobile robots moving amidst known obstacles. Only the obstacle closest to the robot is considered at each time instance. The switching of the two respective gradient fields along the equi-distance line between two obstacles leads to the interesting phenomenon of an additional "spatial" sliding surface, which is examined in detail. The algorithm guarantees approaching the goal point continuously, following a reasonably short path. Numerical examples are presented to demonstrate the utility of this new strategy. >

Sliding mode control for an obstacle avoidance strategy based on an harmonic potential field

The authors (1998) suggested a new class of intelligent motion controllers, called evolutionary, hybrid PDE-ODE controllers (EHPCs). A controller of such a class is designed for the special task of guiding an agent in a fully unknown environment to a target set along an obstacle-free trajectory. The authors briefly described an extension that would allow an EHPC to jointly condition a motion trajectory with both directional and region avoidance constraints. In this paper, an in-depth investigation of the proposed extension is provided. Also, mathematical proofs of both convergence, and the ability to enforce directional and region avoidance constraints are supplied.

Motion planning in the presence of directional and obstacle avoidance constraints using nonlinear, anisotropic, harmonic potential fields

A crash avoidance system for automobiles is developed based upon a distributed network of artificial neurons that mimic the neural organization of the escape system in the American cockroach. The cockroach escape circuit is shown to be an excellent source of inspiration for the development of a collision avoidance system. The crash avoidance system is implemented in an artificial neural network which is trained off-line, but then is shown to produce real-time performance. A collision avoidance scheme which makes use of a crash alarm strategy is developed for training the neural network. A dynamic model of a four-wheeled vehicle with front wheel steering and realistic performance constraints is used to test the crash avoidance system. Simulation results show that the well-trained neural network causes successful, reflexive crash avoidance behaviors in a dynamic environment without a priori information.

A crash avoidance system based upon the cockroach escape response circuit

A method for mobile robot motion planning is presented for both two- and three-dimensional robots. For the two-dimensional case, the algorithm is based on complex variable theory and conformal mapping. The method gives the robot the capability of avoiding obstacles more efficiently, smoothly, and at a constant curvilinear velocity. In order to establish the structure of the proposed velocity feedback obstacle avoidance scheme, several issues are addressed and successfully resolved. First, an analytical solution is derived for the case of circular obstacles. Second, the algorithm uses conformal mapping to establish the solution for an arbitrarily shaped obstacle based on the derived solution for a circular obstacle. The use of complex variable methodology with the objectives of exploiting the powerful technique of uniformal mapping constitutes the fundamental characteristic of the proposed technique. Third, by analogy, a solution to 3-D space-flying and subsea robots is also derived. >

D. Megherbi

Papers

Real-time velocity feedback obstacle avoidance via complex variables and conformal mapping