Exact robot navigation using artificial potential functions

Abstract

We present a new methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design. Complete information about the freespace and goal is encoded in the form of a special artificial potential function-a navigation function-that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. Since navigation functions exist for any robot and obstacle course, our methodology is completely general in principle. However, this paper is mainly concerned with certain constructive techniques for a particular class of motion planning problems. Specifically, we present a formula for navigation functions that guide a point-mass robot in a generalized sphere world. The simplest member of this family is a space obtained by puncturing a disc by an arbitrary number of smaller disjoint discs representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation that we show how to build. Our constructions exploit these coordinate transformations to adapt a navigation function on the model space to its more geometrically complicated (but topologically equivalent) instances. The formula that we present admits sphere-worlds of arbitrary dimension and is directly applicable to configuration spaces whose forbidden regions can be modeled by such generalized discs. We have implemented these navigation functions on planar scenarios, and simulation results are provided throughout the paper. Disciplines Robotics Comments

Application of transverse functions to control differentially driven wheeled robots using velocity fields

“…The results illustrated in Fig. 5 (28). For ε 2 ∈ (ρ 1 , π] there is no closed-analytical formula describing m ε 3 .…”

“…It can be noticed that for small ε 2 the maximum value of ε 3 ¼ 0.5. This result is not surprising, since it well corresponds to the condition which can be obtained for the approximated system defined by (28). For ε 2 2 (ρ ̄1 , π] there is no closed-analytical formula describing m ε3 .…”

“…[28]. Here it should be e phasized that since the upper norm of f is known from t design the desired safety margin can be precisely determine Additionally, we consider external zone E i in order to defin transient region where the given obstacle can interact with t robot, cf.…”

Part orientation with one or two stable equilibria using programmable force fields

“…In 31,32,42,46], micro-actuator arrays present us with the ability t o explicitly program the applied force at every point in a vector eld. 3 Several groups have described e orts to apply MEMS actuators to positioning, inspection, and assembly tasks with small parts 3, 14, 27, 33, 40, for example].…”

Optimal Coordinated Motions of Multiple Agents Moving on a Plane

“…In [12,34], a decentralized algorithm for multi-agent conflict resolution is proposed in the context of air traffic control. By modeling the agent motion as a Brownian motion with drift, the probability of conflict between two agents is estimated and then used to generate repulsive forces between the agents, inspired by the potential and vortex field methodology for path planning ( [27,36]). Compared with traditional potential field methods that use only the positions of the agents, this algorithm considers also their headings and speeds, and hence generates maneuvers with less abrupt turns.…”