Jonathan Lawton

A decentralized approach to formation maneuvers

This paper presents a behavior-based approach to formation maneuvers for groups of mobile robots. Complex formation maneuvers are decomposed into a sequence of maneuvers between formation patterns. The paper presents three formation control strategies. The first strategy uses relative position information configured in a bidirectional ring topology to maintain the formation. The second strategy injects interrobot damping via passivity techniques. The third strategy accounts for actuator saturation. Hardware results demonstrate the effectiveness of the proposed control strategies.

A coordination architecture for spacecraft formation control

This paper addresses the problem of coordinating multiple spacecraft to fly in tightly controlled formations. The main contribution of the paper is to introduce a coordination architecture that subsumes leader-following, behavioral, and virtual-structure approaches to the multiagent coordination problem. The architecture is illustrated through a detailed application of the ideas to the problem of synthesizing a multiple spacecraft interferometer in deep space.

A feedback architecture for formation control

This paper addresses the problem of coordinating multiple spacecraft to fly in tightly controlled formations. The main contribution of the paper is to introduce a coordination architecture that subsumes leader-following, behavioral, and virtual-structure approaches to the multi-vehicle coordination problem. The architecture is illustrated through an application of the ideas to the problem of synthesizing a multiple spacecraft interferometer in deep space.

Elementary attitude formation maneuvers via leader-following and behavior-based control

The objective of this paper is to present formation control laws for maintaining the relative attitude between a formation of free ying spacecraft in deep space. The paper presents two control strategies based on leader-following and emergent behavior approaches. The leader-following control has appeared elsewhere and is included for completeness. The main contribution of this paper is a new emergent behavior approach to the relative attitude control problem for spacecraft formations. In addition, we prove analytically that our approach guarantees formation keeping while maintaining relative alignment bounds throughout the maneuver. Simulation results compare leader-following with our approach.

An adaptive control approach to satellite formation flying with relative distance constraints

We present a spacecraft control for rigid fleet rotations. This is done by creating a fleet template which is slowly rotated to generate desired trajectories for each individual spacecraft. By rotating the template slowly enough each spacecraft is able to track these trajectories to within a given tolerance in the presence of actuator saturation. Simulations for a three spacecraft fleet are given.

Model independent eigenaxis maneuvers using quaternion feedback

The main contribution of the paper is the derivation of a model independent feedback control law that causes a rigid body to execute a near eigenaxis maneuver. The degree of approximation is a function of the control gains and the initial attitude error. Using passivity techniques, the dependence of the control strategy on velocity information is eliminated. The technique used to derive the control strategy is a novel orthogonal decomposition of the unit quaternion into a component along the direction of the eigenaxis and a component that is orthogonal to that direction.

Numerically efficient approximations to the Hamilton-Jacobi-Bellman equation

We present an implementation of the successive Galerkin approximation (SGA) algorithm to the Hamilton-Jacobi-Bellman equation that is less sensitive to Bellmans curse of dimensionality. The SGA algorithm takes an arbitrary stabilizing control law and improves the performance of the control law. An elementary application of the SGA algorithm results in many multidimensional integrations that increase exponentially as a function of the size of the state space and polynomially as a function of the size of the Galerkin basis. The main result of this paper is the elimination of the exponentially growing number of multidimensional integrals. To do so we make several minimally restrictive assumptions about the dynamics of the system and the Galerkin basis elements. As a result we reduce the problem to the calculation of 1D integrals: the number of these integrations increases polynomially as a function of the size of the state space and linearly as a function of the size of the Galerkin basis.

Attitude regulation about a fixed rotation axis

The attitude control problem of rotating a rigid body from its current attitude to a desired attitude such that the instantaneous rotation axis is aligned with an externally defined axis of rotation is considered. The keyidea is to factor the attitude quaternion into rotations parallel and perpendicular to the desired rotation axis. State feedback and output feedback control strategies are designed to minimize the perpendicular component. Simulation results are provided to illustrate the salient features of the approach.

Successive Galerkin approximation of nonlinear optimal attitude

This paper presents the application of the successive Galerkin approximation (SGA) to the Hamilton-Jacobi-Bellman equation to obtain solutions of the optimal attitude control problem. Galerkins method approximates the value function by a truncated Galerkin series expansion. To do so, a truncated Galerkin basis set is formed. A sufficient number of functions must be included in this Galerkin basis set in order to guarantee that the solution will be a stabilizing control. By increasing the size of the Galerkin basis the quality of the approximation is improved at the cost of rapid growth in the computation load of the SGA. A major result of this paper is the development of the Galerkin basis set in the context of the optimal attitude control problem.

Two hybrid control schemes for nonholonomic robots

This paper describes two hybrid control laws for Hilare-type mobile robots, together with experimental verification of their performance. The first control is mathematically motivated. The second control is motivated by the geometry of the problem. While both controls are shown to regulate the robot to a specified position and orientation, their performance is different. To evaluate the performance of the controls, we define seven criteria that we would like the closed-loop system to exhibit. The experimental performance of the two hybrid control laws are evaluated against these criteria.