Naomi Ehrich Leonard

Virtual leaders, artificial potentials and coordinated control of groups

We present a framework for coordinated and distributed control of multiple autonomous vehicles using artificial potentials and virtual leaders. Artificial potentials define interaction control forces between neighboring vehicles and are designed to enforce a desired inter-vehicle spacing. A virtual leader is a moving reference point that influences vehicles in its neighborhood by means of additional artificial potentials. Virtual leaders can be used to manipulate group geometry and direct the motion of the group. The approach provides a construction for a Lyapunov function to prove closed-loop stability using the system kinetic energy and the artificial potential energy. Dissipative control terms are included to achieve asymptotic stability. The framework allows for a homogeneous group with no ordering of vehicles; this adds robustness of the group to a single vehicle failure.

Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment

We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy decouples, in part, the cooperative management of the network formation from the network maneuvers. The underlying coordination framework uses virtual bodies and artificial potentials. We focus on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb.

Collective Motion, Sensor Networks, and Ocean Sampling

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored

Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem

We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.

Stabilization of Planar Collective Motion: All-to-All Communication

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level

Stabilization of Planar Collective Motion With Limited Communication

This paper proposes a design methodology to stabilize relative equilibria in a model of identical, steered particles moving in the plane at unit speed. Relative equilibria either correspond to parallel motion of all particles with fixed relative spacing or to circular motion of all particles around the same circle. Particles exchange relative information according to a communication graph that can be undirected or directed and time-invariant or time-varying. The emphasis of this paper is to show how previous results assuming all-to-all communication can be extended to a general communication framework.

Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping

For pt.I, see ibid., vol.45, p.2253-70 (2000). We extend the method of controlled Lagrangians (CL) to include potential shaping, which achieves complete state-space asymptotic stabilization of mechanical systems. The CL method deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.

Multi-AUV Control and Adaptive Sampling in Monterey Bay

Operations with multiple autonomous underwater vehicles (AUVs) have a variety of underwater applications. For example, a coordinated group of vehicles with environmental sensors can perform adaptive ocean sampling at the appropriate spatial and temporal scales. We describe a methodology for cooperative control of multiple vehicles based on virtual bodies and artificial potentials (VBAP). This methodology allows for adaptable formation control and can be used for missions such as gradient climbing and feature tracking in an uncertain environment. We discuss our implementation on a fleet of autonomous underwater gliders and present results from sea trials in Monterey Bay in August, 2003. These at-sea demonstrations were performed as part of the Autonomous Ocean Sampling Network (AOSN) II project

Vehicle networks for gradient descent in a sampled environment

Fish in a school efficiently find the densest source of food by individually responding not only to local environmental stimuli but also to the behavior of nearest neighbors. It is of great interest to enable a network of autonomous vehicles to function similarly as an intelligent sensor array capable of climbing or descending gradients of some spatially distributed signal. We formulate and study a coordinated control strategy for a group of autonomous vehicles to descend or climb an environmental gradient using measurements of the environment together with relative position measurements of nearest neighbors. Each vehicle is driven by an estimate of the local environmental gradient together with control forces, derived from artificial potentials, that maintain uniformity in group geometry.

A convergent dynamic window approach to obstacle avoidance

The dynamic window approach (DWA) is a well-known navigation scheme developed by Fox et al. and extended by Brock and Khatib. It is safe by construction, and has been shown to perform very efficiently in experimental setups. However, one can construct examples where the proposed scheme fails to attain the goal configuration. What has been lacking is a theoretical treatment of the algorithms convergence properties. Here we present such a treatment by merging the ideas of the DWA with the convergent, but less performance-oriented, scheme suggested by Rimon and Koditschek. Viewing the DWA as a model predictive control (MPC) method and using the control Lyapunov function (CLF) framework of Rimon and Koditschek, we draw inspiration from an MPC/CLF framework put forth by Primbs to propose a version of the DWA that is tractable and convergent.