The Dynamics of a Forced Sphere-Plate Mechanical System

We study the dynamics and explore thecontrollability of a family of sphere-plate mechanical systems. Theseare nonholonomic systems with a five-dimensional configuration spaceand three independent velocities. They consist of a sphere rollingin contact with two horizontal plates. Kinematic models ofsphere-plate systems have played an important role in the controlsystems literature addressing the kinematics of rolling bodies, aswell as in discussions of nonholonomic systems. However, kinematicanalysis falls short of allowing one to understand the dynamicbehavior of such systems. In this work we formulate and study adynamic model for a class of sphere-plate systems in order to answerthe question: "Is it possible to impart a net angular momentum to asphere which rolls without slipping between two plates, given thatthe position of the top plate is subject to exogenousforces?"The research and scientific content in this material will appearin IEEE Transactions on Automatic Control.</Center

Stabilization of LTI Systems with Communication Constraints

This work is aimed at exploring the interaction of communication andcontrol in systems whose sensors and actuators are distributed across ashared network. Examples of such systems include groups of autonomousvehicles, MEMS arrays and other network-controlled systems. Wegeneralize recent results concerning the stabilization of LTI systemsunder limited communication. We seek a stabilizing static outputfeedbackcontroller whose communication with the underlying plant follows a givenperiodic pattern. We present an algorithm that allows us to pass to atime-invariant formulation of the problem and use simulated annealing tosearch for stabilizing feedback gains

Generalized Inverses for Finite-Horizon Tracking

Control and communication issues aretraditionally "decoupled" in discussions of decision and controlproblems, as this simplifies the analysis and generally works well forclassical models. This fundamental assumption deserves re-examinationas control applications spread into new areas where system complexityis significant. Such areas include the coordinated control of aerialvehicles (UAVs), MEMS devices, multi-joint manipulators and othersettings where many systems must share the attention of adecision-maker. We consider a new class ofsampled-data systems (termed "computer-controlled systems") thatoffer the possibility of jointly optimizing between control andcommunication goals. Computer-controlled LTI systems can be viewed aslinear operators between appropriate inner-product spaces. Thegeneralized inverses of these operators are used to solve a class offinite-horizon tracking problems.This work was presented at the IEEE Conf. on Decision and Control, Dec. 1999. </Center

Robot Formations: Learning Minimum-Length Paths on Uneven Terrain

We discuss a prototypeproblem involving terrain exploration and learning by formations ofautonomous vehicles. We investigate an algorithm forcoordinating multiple robots whose task is to find the shortest pathbetween a fixed pair of start and target locations, without access toa "global" map containing those locations.Odometry information alone isnot sufficient for minimizing path length if the terrain is uneven orif it includes obstacles. We generalize existing results on a simplecontrol law, also known as "local pursuit," which is appropriate inthe context of formations and which requires limited interactionbetween vehicles. Our algorithm is iterative and converges to alocally optimal path. We include simulations and experimentsillustrating the performance of the proposed strategy.The research and scientific content in this material has been published in the IEEE Mediterranean Conference on Control and Automation, July 2000.</Center

Stabilization of LTI Systems with Communication Constraints

This work is directed towards exploring interactions ofcommunication and control in systems with communication constraints.Examples of such systems include groups of autonomousvehicles, MEMS arrays and systems whose sensors and actuators aredistributed across a network. We extend some recent results involvingthe stabilization of LTI systems under limited communication andaddress a class of feed-forward control problems for the systems ofinterest

Feedback Control Systems as Users of a Shared Network: Communication Sequences that Guarantee Stability

We investigate the stability of a collection of systems which are governed by linear dynamics and operate under limited communication. We view each system and its feedback controller as users on an idealized shared network which grants access only to a few system-controller pairs at any one time. A communication sequence, which plays the role of a network admission policy, specifies the amount of time available for each system to complete its feedback loop. Using Lyapunov theory, we give a sufficient condition for the existence of a stabilizing communication sequence and show how one can be constructed in a way that minimizes network usage. Our solution depends on the parameters of the underlying system(s) and on the number of controller-plant connections that can be maintained simultaneously. We include simulation results illustrating the main ideas.This paper will appear in IEEE Conference on Decision and Control, 2001

Biologically Inspired Algorithms for Optimal Control

In the past few years, efforts to codify the organizing principles behind biological systems have been capturing the attention of a growing number of researchers in the systems and control community. This endeavor becomes increasingly important as new technologies make it possible to engineer complex cooperating systems that are nevertheless faced with many of the challenges long-overcome by their natural counterparts. One area in particular where biology serves as an inspiring but still distant example, involves systems in which members of a species cooperate to form collectives whose abilities are beyond those of individuals. This paper looks to the process by which ants optimize their foraging trails as inspiration for an organizing principle by which groups of dynamical systems can solve a class of optimal control problems. We explore the use of a strategy termed `local pursuit', which allows members of the group to overcome their limitations with respect to sensing range and available information through the use of neighbor-to-neighbor interactions. Local pursuit enables the group to find an optimal solution by iteratively improving upon an initial feasible control. We show that our proposed strategy subsumes previous pursuit-based models for ant-trail optimization and applies to a large array of problems, including many of the classical situations in optimal control. The performance of our algorithm is illustrated in a series of numerical experiments. Ongoing work directions related to local pursuit are also discussed in this document

Biologically-Inspired Optimal Control via Intermittent Cooperation

We investigate the solution of a large class of fixed-final-state optimal control problems by a group of cooperating dynamical systems. We present a pursuit-based algorithm -- inspired by the foraging behavior of ants -- that requires each system-member of the group to solve a finite number of optimization problems as it follows other members of the group from a starting to a final state. Our algorithm, termed "sampled local pursuit", is iterative and leads the group to a locally optimal solution, starting from an initial feasible trajectory. The proposed algorithm is broad in its applicability and generalizes previous results; it requires only short-range sensing and limited interactions between group members, and avoids the need for a "global map" of the environment or manifold on which the group evolves. We include simulations that illustrate the performance of our algorithm

Stabilization of Networked Control Systems under Feedback-based Communication

We study the stabilization of a networked control system (NCS) in which multiple sensors and actuators of a physical plant share a communication medium to exchange information with a remote controller. The plant's sensors and actuators are allowed only limited access to the controller at any one time, in a way that is decided on-line using a feedback-based communication policy. Our NCS model departs from those in previous formulations in that the controller and plant handle communication disruptions by ``ignoring'' (in a sense that will be made precise) sensors and actuators that are not actively communicating. We present an algorithm that provides a complete and straightforward method for simultaneously determining stabilizing gains and communication policies and avoids the computational complexity and limitations associated with some previously proposed models. We introduce three feedback-based scheduling policies that quadratically stabilize the closed-loop NCS while achieving various objectives related to the system's rate of convergence, the priorities of different sensors and actuators, and the avoidance of chattering