Kevin M. Lynch

Mechanics and control of swimming: a review

The bodies and brains of fish have evolved to achieve control objectives beyond the capabilities of current underwater vehicles. One route toward designing underwater vehicles with similar capabilities is to better understand fish physiological design and control strategies. This paper has two objectives: 1) to review clues to artificial swimmer design taken from fish physiology and 2) to formalize and review the control problems that must be solved by a robot fish. The goal is to exploit fish locomotion principles to address the truly difficult control challenges of station keeping under large perturbations, rapid maneuvering, power-efficient endurance swimming, and trajectory planning and tracking. The design and control of biomimetic swimming machines meeting these challenges will require state-of-the-art engineering and biology.

Stability and Convergence Properties of Dynamic Average Consensus Estimators

We analyze two different estimation algorithms for dynamic average consensus in sensing and communication networks, a proportional algorithm and a proportional-integral algorithm. We investigate the stability properties of these estimators under changing inputs and network topologies as well as their convergence properties under constant or slowly-varying inputs. In doing so, we discover that the more complex proportional-integral algorithm has performance benefits over the simpler proportional algorithm

Multi-Agent Coordination by Decentralized Estimation and Control

We describe a framework for the design of collective behaviors for groups of identical mobile agents. The approach is based on decentralized simultaneous estimation and control, where each agent communicates with neighbors and estimates the global performance properties of the swarm needed to make a local control decision. Challenges of the approach include designing a control law with desired convergence properties, assuming each agent has perfect global knowledge; designing an estimator that allows each agent to make correct estimates of the global properties needed to implement the controller; and possibly modifying the controller to recover desired convergence properties when using the estimates of global performance. We apply this framework to the problem of controlling the moment statistics describing the location and shape of a swarm. We derive conditions which guarantee that the formation statistics are driven to desired values, even in the presence of a changing network topology.

Brief paper: Decentralized estimation and control of graph connectivity for mobile sensor networks

The ability of a robot team to reconfigure itself is useful in many applications: for metamorphic robots to change shape, for swarm motion towards a goal, for biological systems to avoid predators, or for mobile buoys to clean up oil spills. In many situations, auxiliary constraints, such as connectivity between team members and limits on the maximum hop-count, must be satisfied during reconfiguration. In this paper, we show that both the estimation and control of the graph connectivity can be accomplished in a decentralized manner. We describe a decentralized estimation procedure that allows each agent to track the algebraic connectivity of a time-varying graph. Based on this estimator, we further propose a decentralized gradient controller for each agent to maintain global connectivity during motion.

Decentralized Environmental Modeling by Mobile Sensor Networks

Cooperating mobile sensors can be used to model environmental functions such as the temperature or salinity of a region of ocean. In this paper, we adopt an optimal filtering approach to fusing local sensor data into a global model of the environment. Our approach is based on the use of proportional-integral (PI) average consensus estimators, whereby information from each mobile sensor diffuses through the communication network. As a result, this approach is scalable and fully decentralized, and allows changing network topologies and anonymous agents to be added and subtracted at any time. We also derive control laws for mobile sensors to move to maximize their sensory information relative to current uncertainties in the model. The approach is demonstrated by simulations including modeling ocean temperature.

Kinematic controllability for decoupled trajectory planning in underactuated mechanical systems

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collision-free trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.

Dynamic nonprehensile manipulation: Controllability, planning, and experiments

We are interested in using low-degree-of-freedom robots to perform complex tasks by nonprehensile manipulation (manipulation without aformorforce-closure grasp). By notgrasping, the robot can usegravitational, centrifugal, and Coriolisforces as virtual motors to control more degrees of freedom of the part. The part s extra motionfreedoms are exhibited as rolling, slipping, and free flight. This paper describes controllability, motion planning, and implementation ofplanar dynamic nonprehensile manipukltion. We show that almost any planar object is controllable by point contact, and the controlling robot requires only twvo degrees of freedom (a point translating in the plane). We then focus on a one-joint manipulator (with a two-dimensional state space), and show that even this simplest of robots, by using slipping and rolling, can control a planar object to a fulldimensional subset of its six-dimensional statespace. We have developed a one-jointrobotto perform a variety of dynamic tasks, including snatching an object ftom a table, rolling an object on the surface of the arm, and throwing and catching. Nonlinear optimization is used to plan robot trajectories that achieve the desired object motion via coupling forces though the nonprehensile contact.

Collision-Free Trajectory Planning for a 3-DoF Robot with a Passive Joint

This paper studies motion planning from one zero-velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint. Such a robot is small-time locally controllable on an open subset of its zero-velocity section, allowing it to follow any path in this subset arbitrarily closely. However, some paths are “preferred” by the dynamics of the manipulator in that they can be followed at higher speeds. In this paper, the authors describe a computationally efficient trajectory planner that finds fast, collision-free trajectories among obstacles. The planner decouples the problem of planning feasible trajectories in the robot’s six-dimensional state space into the computationally simpler problems of planning paths in the three-dimensional configuration space and time scaling the paths according to the manipulator dynamics. This decoupling is made possible by the existence of velocity directions, fixed in the passive link frame, which can be executed at arbitrary speeds. Results of the planner have been implemented on an experimental underactuated manipulator. To the authors’ knowledge, it is the first implementation of a collision-free motion-planning algorithm for a manipulator subject to a second-order nonholonomic constraint.

Distributed estimation and control of swarm formation statistics

We describe distributed estimation algorithms that allow robots in a communication network to maintain estimates of summary statistics describing the shape of the swarm. We show that these estimators, combined with motion controllers implemented on each robot, result in the swarm formation statistics being driven to desired values in the presence of a changing network topology and the addition and deletion of robots

Parts Feeding on a Conveyor with a One Joint Robot

Abstract. This paper explores a method of manipulating a planar rigid part on a conveyor belt using a robot with just one joint. This approach has the potential of offering a simple and flexible method for feeding parts in industrial automation applications. In this paper we develop a model of this system and of a variation which requires no sensing. We have been able to characterize these systems and to prove that they can serve as parts feeding devices for planar polygonal parts. We present the planners for these systems and describe our implementations.