Showing papers by "Swaroop Darbha published in 2005"

A Resource Allocation Algorithm for Multi-Vehicle Systems with Non holnomic Constraints

Abstract: Multi-vehicle systems are naturally encountered in civil and military applications. Cooperation amongst individual "miniaturized" vehicles allows for flexibility to accomplish missions that a single large vehicle may not readily be able to accomplish. While accomplishing a mission, motion planning algorithms are required to efficiently utilize a common resource (such as the total fuel in the collection of vehicles) or to penalize a collective cost function (such as to minimize the maximum time taken by the vehicles to reach their intended target). The objective of this paper is to present a constant factor approximation algorithm for planning the path of each vehicle in a collection of vehicles, where the motion of each vehicle must satisfy non-holonomic constraints.

Information flow and its relation to the stability of the motion of vehicles in a rigid formation

Abstract: It is known in the literature on automated highway systems that information flow can significantly affect the propagation of errors in spacing in a collection of vehicles. This paper investigates this issue further for a homogeneous collection of vehicles, where in the motion of each vehicle is modeled as a point mass. The structure of the controller employed by the vehicles is as follows: U/sub i/(s)=C(s)/spl Sigma/ /sub j/spl isin/si/(X/sub i/ - X/sub j/ - L/sub ij//s) where U/sub i/(s) is the (Laplace transformation of) control action for the i/sup th/ vehicle, L/sub ij/is the position of the i/sup th/ vehicle, L/sub ij/ is the desired distance between the i/sup th/ and the j/sup th/ vehicles in the collection, C(s) is the controller transfer function and S/sub i/ is the set of vehicles that the i/sup th/ vehicle can communicate with directly. This paper further assumes that the information flow is undirected, i.e., i/spl isin/S/sub j//spl harr/j/spl isin/S/sub i/, and the information flow graph is connected. We consider information flow in the collection, where each vehicle can communicate with a maximum of q(n) vehicles, such that q(n) may vary with the size n of the collection. We first show that C(s) cannot have any zeroes at the origin to ensure that relative spacing is maintained in response to a reference vehicle making a maneuver where its velocity experiences a steady state offset. We then show that if the control transfer function C(s) has one or more poles located at the origin of the complex plane, then the motion of the collection of vehicles will become unstable if the size of the collection is sufficiently large. These two results imply that C(0)/spl ne/0 and C(0) is well defined. We further show that if q(n)/sup 3//n/sup 2//spl rarr/0 as n /spl rarr//spl infin/ then there is a low frequency sinusoidal disturbance of at most unit amplitude acting on each vehicle such that the maximum errors in spacing response increase at least as O (/spl radic/(n/sup 2/)/q(n)/sup 3/). A consequence of the results presented in this paper is that the maximum of the error in spacing and velocity of any vehicle can be made insensitive to the size of the collection only if there is at least one vehicle in the collection that communicates with at least O(n/sup 2/3/) other vehicles in the collection.

A Recursive Algorithm for Reducing the Order of Controller while Guaranteeing Performance

Abstract: In this paper, a procedure for the recursive reduction of the order of the stabilizing controller is introduced for SISO systems Since all achievable closed loop maps are affine in the Q (Youla) parameter, we devise a sufficient condition for order reduction: Suppose there exists a Q parameter to induce a pole zero cancellation in the closed loop map to decrease the order of the closed loop system by m, then the corresponding controller is reduced in order by m By appropriately choosing Q, we formulate a procedure for the recursive reduction of the order of the stabilizing controller and guarantee a performance describable through a complex stabilization technique