John T. Wen

The attitude control problem

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a Lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body. The controllers share the common structure of a proportional-derivative feedback plus some feedforward which can be zero (the model-independent case), the Coriolis torque compensation, or an adaptive compensation. These controller structures are compared in terms of the requirement on the a priori model information, guaranteed transient performance, and robustness. The global stability of the Luh-Walker-Paul robot end-effector controller is also analyzed in this framework. >

New class of control laws for robotic manipulators Part 1. Non–adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manip...

Time domain and frequency domain conditions for strict positive realness

The author states various time-domain and frequency-domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions. Their relationship is clarified by means of a three-tier diagram; each tier represents a set of equivalent conditions successively stronger than the lower tier. The main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems. >

Preisach modeling of piezoceramic and shape memory alloy hysteresis

Smart materials such as piezoceramics, magnetostrictive materials, and shape memory alloys exhibit hysteresis, and the larger the input signal the larger the effect. Hysteresis can lead to unwanted harmonics, inaccuracy in open loop control, and instability in closed loop control. The Preisach independent domain hysteresis model has been shown to capture the major features of hysteresis arising in ferromagnetic materials. Noting the similarity between the microscopic domain kinematics that generate static hysteresis effects in ferromagnetics, piezoceramics, and shape memory alloys (SMAs), we apply the Preisach model for the hysteresis in piezoceramic and shape memory alloy materials. This paper reviews the basic properties of the Preisach model, discusses control-theoretic issues such as identification, simulation, and inversion, and presents experimental results for piezoceramic sheet actuators bonded to a flexible aluminum beam, and a Nitinol SMA wire muscle that applies a bending force to the end of a beam.

A unifying passivity framework for network flow control

Network flow control regulates the traffic between sources and links based on congestion, and plays a critical role in ensuring satisfactory performance. In recent studies, global stability has been shown for several flow control schemes. By using a passivity approach, this paper presents a unifying framework which encompasses these stability results as special cases. In addition, the new approach significantly expands the current classes of stable flow controllers by augmenting the source and link update laws with passive dynamic systems. This generality offers the possibility of optimizing the controllers, for example, to improve robustness in stability and performance with respect to time delays, unmodeled flows, and capacity variation.

Trajectory tracking control of a car-trailer system

This paper presents the experimental results of the tracking control of a car-trailer system. The proposed scheme involves three steps: 1) generate a path off-line using a path space iterative algorithm; 2) linearize the kinematic model about a trajectory which is constructed using the path; and 3) apply a time-varying linear quadratic regulator to track the trajectory. Experiments presented include parallel parking a car, docking a tractor-trailer vehicle, and parallel parking a double tractor-trailer vehicle.

Motion and force control of multiple robotic manipulators

This paper addresses the motion and force control problem of multiple robot arms manipulating a cooperatively held object. A general control paradigm is introduced which decouples the motion and force control problems. For motion control, different control strategies are constructed based on the variables used as the control input in the controller design. There are three natural choices; acceleration of a generalized coordinate, arm tip force vectors, and the joint torques. The first two choices require full model information but produce simple models for the control design problem. The last choice results in a class of relatively model independent control laws by exploiting the Hamiltonian structure of the open loop system. The motion control only determines the joint torque to within a manifold, due to the multiple-arm kinematic constraint. To resolve the nonuniqueness of the joint torques, two methods are introduced. If the arm and object models are available, an optimization can be performed to best allocate the desired and effector control force to the joint actuators. The other possibility is to control the internal force about some set point. It is shown that effective force regulation can be achieved even if little model information is available.

Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation

In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.

A path space approach to nonholonomic motion planning in the presence of obstacles

This paper presents an algorithm for finding a kinematically feasible path for a nonholonomic system in the presence of obstacles. We first consider the path planning problem without obstacles by transforming it into a nonlinear least squares problem in an augmented space which is then iteratively solved. Obstacle avoidance is included as inequality constraints. Exterior penalty functions are used to convert the inequality constraints Into equality constraints. Then the same nonlinear least squares approach is applied. We demonstrate the efficacy of the approach by solving some challenging problems, including a tractor-trailer and a tractor with a steerable trailer backing in a loading dock. These examples demonstrate the performance of the algorithm in the presence of obstacles and steering and jackknife angle constraints.

Rigid body attitude coordination without inertial frame information

We study a motion coordination problem where the objective is to achieve identical orientation and synchronous rotation for a group of rigid bodies. Unlike existing designs which assume that the inertial frame is available to each agent, we develop a passivity-based design which relies only on relative attitude information with respect to neighboring agents. The desired equilibria, where all the rigid bodies possess the same attitude and rotate at a desired angular velocity, are shown to be locally asymptotically stable and a manifold of undesired equilibria may exist. We then consider the situation where the reference angular velocity is available only to the leader, and propose a distributed adaptive controller with which the other agents reconstruct this reference angular velocity.