Showing papers in "Journal of Robotic Systems in 1996"

Distributed algorithms for formation of geometric patterns with many mobile robots

Abstract: We discuss a method for controlling a group of mobile robots in a distributed manner. The method is distributed in the sense that all robots, or most of the robots in some cases, plan their motion individually based upon the given goal of the group and the observed positions of other robots. We illustrate the method by showing how a large number of robots can form an approximation of a circle, a simple polygon, or a line segment in the plane. We also show how the robots can distribute themselves nearly uniformly within a circle or a convex polygon in the plane. Finally, we show how the robots can be divided into two or more groups. It turns out that in many cases most robots execute an identical, simple algorithm. The performance of the method is demonstrated by simulation. © 1996 John Wiley & Sons, Inc.

Coordination and decentralized cooperation of multiple mobile manipulators

Abstract: Mobile manipulation capabilities are key to many new applications of robotics in space, underwater, construction, and service environments. This article discusses the ongoing effort at Stanford University for the development of multiple mobile manipulation systems and presents the basic models and methodologies for their analysis and control. This work builds on four methodologies we have previously developed for fixed-base manipulation: the Operational Space Formulation for task-oriented robot motion and force control; the Dextrous Dynamic Coordination of Macro/Mini structures for increased mechanical bandwidth of robot systems; the Augmented Object Model for the manipulation of objects in a robot system with multiple arms; and the Virtual Linkage Model for the characterization and control of internal forces in a multi-arm system. We present the extension of these methodologies to mobile manipulation systems and propose a new decentralized control structure for cooperative tasks. The article also discusses experimental results obtained with two holonomic mobile manipulation platforms we have designed and constructed at Stanford University. © 1996 John Wiley & Sons, Inc.

Evaluating efficiency of self-reconfiguration in a class of modular robots

Abstract: In this article we examine the problem of dynamic self-reconfiguration of a class of modular robotic systems referred to as metamorphic systems. A metamorphic robotic system is a collection of mechatronic modules, each of which has the ability to connect, disconnect, and climb over adjacent modules. A change in the macroscopic morphology results from the locomotion of each module over its neighbors. Metamorphic systems can therefore be viewed as a large swarm of physically connected robotic modules that collectively act as a single entity. What distinguishes metamorphic systems from other reconfigurable robots is that they possess all of the following properties: (1) a large number of homogeneous modules; (2) a geometry such that modules fit within a regular lattice; (3) self-reconfigurability without outside help; (4) physical constraints which ensure contact between modules. In this article, the kinematic constraints governing metamorphic robot self-reconfiguration are addressed, and lower and upper bounds are established for the minimal number of moves needed to change such systems from any initial to any final specified configuration. These bounds are functions of initial and final configuration geometry and can be computed very quickly, while it appears that solving for the precise number of minimal moves cannot be done in polynomial time. It is then shown how the bounds developed here are useful in evaluating the performance of heuristic motion planning/reconfiguration algorithms for metamorphic systems. © 1996 John Wiley & Sons, Inc.

A class of nonlinear PD-type controllers for robot manipulators

Abstract: In this article we present the stability analysis of a class of PD-type controllers for position and motion control of robot manipulators. The main feature of this class of controllers is that the proportional and derivative gains can be nonlinear functions of the robot states. These controllers can be obtained from control strategies that adjust the controller gains depending on the robot states. It is shown that global asymptotic stability of the control system is achieved provided that the P and D gains have suitable structure. As an outcome, we propose a global regulator constrained to deliver torques within prescribed limits of the actuator's capabilities. Experimental results on a two degrees of freedom direct drive arm show the usefulness of the proposed scheme.

Solving the forward kinematics of parallel manipulators with a genetic algorithm

Abstract: A floating point genetic algorithm is proposed to solve the forward kinematic problem for parallel manipulators. This method, adapted from studies in the biological sciences, allows the use of inverse kinematic solutions to solve forward kinematics as an optimization problem. The method is applied to two 3-degree-of-freedom planar parallel manipulators and to a 3-degree-of-freedom spherical manipulator. The method converges to a solution within a broader search domain compared to a Newton-Raphson scheme. © 1996 John Wiley & Sons, Inc.

A hybrid actuator scheme for robust position control of a flexible single‐link manipulator

Abstract: This article presents a novel hybrid actuator scheme to actively and robustly control the endpoint position of a very flexible single-link manipulator. The control scheme consists of two actuators; a motor mounted at the beam hub and a piezoceramic bonded to the surface of the flexible link. The control torque of the motor, which produces a desired angular motion, is determined by employing the sliding mode control theory on the equation of motion of the rigid link having the same mass as that of the proposed flexible link. The torque is then applied to the flexible manipulator to activate the commanded motion. During the motion, the undesirable oscillation caused by the torque, based on the rigid link dynamics, is actively suppressed by applying a feedback control voltage to the piezoceramic actuator. Consequently, desired tip motion is achieved. Both regulating and tracking control responses are analyzed through experimental implementation to demonstrate high performance characteristics to be accrued from the proposed methodology. © 1996 John Wiley & Sons, Inc.

Dynamic modeling and control of a multi‐robot system for assembly of flexible payloads with applications to automotive body assembly

Abstract: The field of multi-robot control has almost exclusively addressed issues that are of relevance to the manipulation of payloads that are rigid. A number of studies have examined the multi-robot manipulation of rigid payloads with one or more lower-pair joints such as hand tools, i.e., pliers. In this work, we examine certain modeling and control aspects associated with the assembly of flexible payloads with a multi-robot system. While this particular problem is of a general nature, our work is motivated by the particular problem presented by the assembly of automotive bodies from sheet metal parts. State of the art assembly of automotive bodies involves the use of a great number of costly hardware fixtures that are used to orient and clamp each piece of bent sheet metal prior to robot welding. Currently under development, a new assembly technology called flexible fixtureless assembly is being designed to replace fixtures with robotic technology. Each robot grasps one piece of sheet metal, and correctly positions and orients the part to mate them to permit a third robot to weld them. The assembly process is complicated by the fact that the sheet metal parts are flexible, cannot be permanently deformed during mating and must be positioned to within a relatively small position tolerance. This article describes work performed to model the dynamics of a multi-robot system consisting of two robot manipulators bringing sheet metal parts of an automotive body into contact. This dynamic model is used as a tool to facilitate the investigation of control strategies for the execution of this task. To adequately model the system, the sheet metal parts are first discretized into finite shell elements. The flexible payload dynamics are derived via the Lagrangian formulation and combined with the robot dynamics to form one robot-payload system. The system equations are first simplified by making use of some of the properties of the assembly process. This allows certain of the interaction effects between flexible and rigid body coordinates to be ignored. Contact between the sheet metal payloads during the mating process is modeled with an exponential barrier function. Application of Guyan reduction leads to a lower order dynamic model of the sheet metal payloads and a simplified dynamic model of the two robot system suitable for numerical simulation. The model developed is then used to investigate several candidate control methods for the mating of two sheet metal parts. Simulation results are presented for proportional and derivative control with gravity compensation, computed torque control, and master slave hybrid position force control. Simulation results reveal that all three control methods are able to achieve contact force and position stability. Adequate performance of the proportional and derivative control demonstrates that standard industrial controls implemented in commercial robots may be used to control robots for fixtureless assembly tasks. © 1996 John Wiley & Sons, Inc.

Generalization of Newton‐Euler model for flexible manipulators

Abstract: In this article we propose an extension of the Newton-Euler models to the case of flexible robots. Such models are mainly used today for rigid manipulators. In this case they have given the best results to solve the simulation and control problem, as far as time consumption and programming simplicity are concerned. The extension that we propose is based on the theoretical notion of description formalism of a motion and on the use of the D'Alembert principle. The proposed model is intrinsic and concerns any open chain with ponctual joints.

A fast, robust solution to the Stewart platform forward kinematics

Abstract: The Stewart platform is a six degree-of-freedom fully-in-parallel linkage well-suited to robotic tasks where structural rigidity and high small motion bandwidth are required. In this article we describe an approach for computing the forward kinematics of this device that is both fast and robust. Our solution is based on the simultaneous solution of three constraint equations using a Newton-Raphson scheme. A well-known property of Newton-Raphson is its tendency to fail when the constraint equations become poorly conditioned, and the main contribution of this article is the development of two algorithms for overcoming this limitation and hence for providing robustness. Certain other matters, such as the singular configurations of the Stewart platform and its assembly modes, are touched upon.

A Balancing Technique to Stabilize Local Torque Optimization Solution of Redundant Manipulators

Abstract: A technique that stabilizes the existing local torque optimization solutions for redundant manipulators is proposed in this article. The technique is based on a balancing scheme, which balances a solution of joint torque-minimization against a solution of joint velocity-minimization. Introducing the solution of joint velocity-minimization in the approach prevents occurrence of high joint velocities, and thus results in stable optimal arm motions and guarantees the joint velocities at end of motion to be near zero. Computer simulations were executed on a three-link planar rotary manipulator to verify the performance of the proposed local torque optimization technique and to compare its performance with existing ones for various straight line trajectories. © 1996 John Wiley & Sons, Inc.

Adaptive control of flexible manipulators carrying large uncertain payloads

Abstract: An adaptive controller is presented for a manipulator with revolute joints and structurally flexible links which carries a rigid payload with unknown mass properties. Under the assumption that the payload mass is much greater than that of the manipulator, globally stable tracking of the Cartesian end-effector coordinates is established. Key ideas underlying the controller development are the passivity of a mapping involving the end-effector rates as part of the output and a fixed parameter feedforward which preserves this property. The concept of filtered error is borrowed from previous work on rigid arms and suitably modified in developing the adaptive law. Although measurements of the tip positions and rates are needed, there is no requirement for sensing of the elastic coordinates. A numerical example involving a six DOF manipulator with flexible links demonstrates excellent tracking with respect to a simulation based on the exact motion equations. © 1996 John Wiley & Sons, Inc.

Motion planning for mobile manipulators with a non-holonomic constraint using the FSP (full space parameterization) method

Abstract: The efficient utilization of the motion capabilities of mobile manipulators, i.e., manipulators mounted on mobile platforms, requires the resolution of the kinematically redundant system formed by the addition of the degrees of freedom (DOF) of the platform to those of the manipulator. At the velocity level, the linearized Jacobian equation for such a redundant system represents an underspecified system of algebraic equations, which can be subject to a varying set of contraints such as a non-holonomic constraint on the platform motion, obstacles in the workspace, and various limits on the joint motions. A method, which we named the Full Space Parameterization (FSP), has recently been developed to resolve such underspecified systems with constraints that may vary in time and in number during a single trajectory. In this article, we first review the principles of the FSP and give analytical solutions for constrained motion cases with a general optimization criterion for resolving the redundancy. We then focus on the solutions to (1) the problem introduced by the combined use of prismatic and revolute joints (a common occurrence in practical mobile manipulators), which makes the dimensions of the joint displacement vector components non-homogeneous, and (2) the treatment of a non-holonomic constraint on the platform motion. Sample implementations on several large-payload mobile manipulators with up to 11 DOF are discussed. Comparative trajectories involving combined motions of the platform and manipulator for problems with obstacle and joint limit constraints, and with non-holonomic contraints on the platform motions, are presented to illustrate the use and efficiency of the FSP approach in complex motion planning problems. © 1996 John Wiley & Sons, Inc.

On the robust control of robot manipulators including actuator dynamics

Abstract: A robust nonlinear control law that incorporates the manipulator dynamics as well as dynamics of actuators is developed in this article. The inertial parameters of the manipulator and the electrical parameters of the actuators are considered to be of uncertain values. In contrast to the known methods, the presented design procedure is based on less restrictive assumptions regarding the characteristics of uncertainties. We just assume that unknown parameters are bounded, which is evidently true for any robotic system. Exponential stability of the developed controller is proved by the Lyapunov method. © 1996 John Wiley & Sons, Inc.

Experiments in contact control

Abstract: The implementation, experimentation, and application of contact control schemes for a 7-DOF Robotics Research arm is presented. Three types of control schemes are presented: compliance cntrol, force control, and dual-mode control. This presentation is concluded with the application of the proposed schemes to perform a contact-based eddy-current inspection task.

Learning control for a class of nonlinear differential-algebraic systems with application to constrained robots

Abstract: In this article, a learning control design method for analyzing the convergence of nonlinear systems described by a class of differential-algebraic equations' is developed. This method generalizes the previous methods for the study of the learning control problem of constrained mechanical systems to include a wider class of systems. Furthermore, the proposed design method allows us to analyze the role of force learning in the learning control of such a control system. We derive a sufficient condition for the convergence of both the motion and contact force of the systems as the operations are repeated. An application of the proposed controller to robotic manipulators with holonomic constraints is discussed, and simulation results of a constrained cylindrical robot are presented.

Mapping in unknown graph-like worlds

Abstract: We consider the problem of constructing a map of an unknown environment by an autonomous agent such as a mobile robot. Because accurate positional information is often difficult to ensure, we consider the problem of exploration in the absence of metric (positional) information. Worlds are represented by graphs (not necessarily planar) consisting of a fixed number of discrete places linked by bidirectional paths. We assume the robot can consistently enumerate the edges leaving a vertex (that is, it can assign a cyclic ordering). A mobile robot is assigned the task of creating a topological map, i.e. a graph-like representation of the places in the world and their connectivity, by moving from place to place along the paths it encounters. It can detect edges and count them, but cannot directly sense the labels associated with a place or an edge. In principle, this type of representation could be used for non-spatial environments such as computer networks. We present an approach to the exploration of unknown environments for which local sensing information alone is insufficient to distinguish distinct places, based simply on the structure of the world itself. Places are identified by a non-unique signature and by using a collection of such non-unique local signatures, an extended signature may be constructed that determines the robot's position (although in certain “degenerate” worlds additional information is required). We describe the “exploration tree” as a representation of a collection of alternative descriptions of the environment. In addition, heuristics are presented that can accelerate the search for the correct world model. © 1996 John Wiley & Sons, Inc.

Forward displacement analysis and uncertainty configurations of parallel manipulators with a redundant branch

Abstract: The effect of adding a redundant branch in terms of reduction of the number of assembly modes and elimination of potential uncertainty configuration types is investigated for a class of parallel manipulators. Considered is a broad class that includes all three-branch manipulators where each branch is comprised of a serial arrangement of three main-arm joints supporting a common payload platform through a passive spherical branch end joint-group. The addition of a redundant branch effectively yields a four-branch manipulator class. Considered in particular is a 3-4 form of the manipulator where two branch ends meet at one point on the mobile platform. Symmetric main-arm joint sensing and actuation (two sensed/acutated main-arm joints per branch) is utilized. Synthetic geometry is used to study the number of assembly configurations of the resulting 3-4 four-branch parallel manipulators. It is presented that the number of assembly modes of three-branch parallel manipulators with passive spherical branch end joints can be reduced by utilizing a redundant branch. It is shown that there exist up to eight and up to four assembly modes when all unsensed joints are revolute and when all unsensed joints are prismatic, respectively. Combinations of unsensed prismatic and revolute joints are also investigated. It is determined that there are up to eight and up to four assembly modes when the unsensed main-arm joint of one of the concurrent branches is prismatic and when the unsensed joints of both concurrent branches are prismatic joints, respectively. Resolving the potential assembly modes require only the consideration of, at highest, second-order single-variable polynomials. In addition, kinematic design considerations allowing reduction of feasible assembly modes are discussed. The investigation of potential uncertainty configuration types is based on examining degeneracies of the screw systems formed by wrenches associated with the forces that the actuated-joints can apply. All linear dependency cases that could potentially cause uncertainties for the class of four-branch manipulators are identified. It is shown that while significantly reducing potential uncertainty configuration types, the addition of a redundant branch number cannot eliminate all potential dependency (uncertainty) cases completely. For the remaining potential uncertainty configuration types, the characteristics of the corresponding unconstrained instantaneous degrees of freedom are discussed.

Methods for low-velocity friction compensation: Theory and experimental study

Abstract: A study is conducted of different classes of controllers for mechanisms under the influence of low velocity friction Many methods are proposed in the literature for friction compensation, but there has been no significant analysis of these methods with respect to each other Also lacking in the literature is some form of categorization under which it is possible to describe and study their performance This article provides an experimental and analytical study of controllers previously proposed for low velocity friction compensation Because each controller is evaluated on the same experimental platform, the results can be quantified to provide an approach by which to evaluate the performance of the controllers relative to each other Some simulations will also be performed to show the effect of certain system parameters on the performance of these controllers

Motion coordination and reactive control of autonomous multi‐manipulator systems

Abstract: The emerging field of service robots demands new systems with increased flexibility. The flexibility of a robot system can be increased in many different ways. Mobile manipulation-the coordinated use of manipulation capabilities and mobility-is an approach to increase robots flexibility with regard to their motion capabilities. Most mobile manipulators that are currently under development use a single arm on a mobile platform. The use of a two-arm manipulator system allows increased manipulation capabilities, especially when large, heavy, or non-rigid objects must be manipulated. This article is concerned with motion control for mobile two-arm systems. These systems require new schemes for motion coordination and control. A coordination scheme called transparent coordination is presented that allows for an arbitrary number of manipulators on a mobile platform. Furthermore, a reactive control scheme is proposed to enable the platform to support sensor-guided manipulator motion. Finally, this article introduces a collision avoidance scheme for mobile two-arm robots. This scheme surveys the vehicle motion to avoid platform collisions and arm collisions caused by self-motion of the robot.

Ultrasonic sensor data integration and its application to environment perception

Abstract: To move in an unknown or uncertain environment, a mobile robot must collect information from various sensors and use it to construct a representation of the external world. Ultrasonic sensors can provide range data for this purpose in a simple and cost-effective way. However, most ultrasonic sensors are not sufficient for environment recognition because of their large beam opening angles. In this article the beam-opening-angle problem is solved by fusing data from multiple ultrasonic sensors. We propose two methods for sensor data fusion. One uses an artificial neural network (ANN), and the other is based on a mathematical model. Simulations and experiments show that the mathematical model is more accurate when there is no noise in the sensor readings, but the ANN method is better when the sensors are subject to much noise. To extract line segments from the ultrasonic image, we develop a line extractor that is more efficient than traditional line fitting methods in this application. Experimental results show that this method is effective for environment perception in a robotic system.

Adaptive path planning and obstacle avoidance for a robot with a large degree of redundancy

Abstract: A new algorithm for path planning and obstacle avoidance for redundant planar robots is proposed. The task of path planning is formulated as a sequence of nonlinear programming problems. For each problem, the objective is to minimize the distance between the current location of the end-effector and a desired location. Two penalties are added to each objective function to ensure that the robot is not colliding with any obstacle and that its links are not crossed over. The effects of mechanical stops and limits for maximum joint movements are also incorporated as inequality constraints. The algorithm uses an adaptive scheme to activate the fewest number of the outboardmost joints, and none of the inboard ones if possible, to reach a desired location. The algorithm is especially useful when the number of joints is large. © 1996 John Wiley & Sons, Inc.

A two-DOF manipulator with adjustable compliance capabilities and comparison with the human finger

Abstract: This article addresses compliance control issues and develops an actuator that modulates the stiffness and independently sets the angular positioning of a revolute joint. The capability to decouple the position from the compliance modulations is instrumental in a wide range of robotic contact operations. It is shown that a five input control scheme fully characterizes the position and compliance of a two-DOF manipulator. In an effort to characterize the control capabilities of a human finger, the compliance values of the proximal and middle joints are assessed experimentally. The results of the experiment show that a five input control is evidently within the human finger capabilities. In an effort to enhance the compliance capabilities of robotic systems, the authors believe that the newly developed actuation scheme will impact the automation of manufacturing tasks in which contact operations are inevitable. © 1996 John Wiley & Sons, Inc.

Vision resolvability for visually servoed manipulation

Abstract: This article introduces a sensor placement measure called vision resolvability. The measure provides a technique for estimating the relative ability of various visual sensors, including monocular systems, stereo pairs, multi-baseline stereo systems, and 3D rangefinders, to accurately control visually manipulated objects. The resolvability ellipsoid illustrates the directional nature of resolvability, and can be used to direct camera motion and adjust camera intrinsic parameters in real-time so that the servoing accuracy of the visual servoing system improves with camera-lens motion. The Jacobian mapping from task space to sensor space is derived for a monocular system, a stereo pair with parallel optical axes, and a stereo pair with perpendicular optical axes. Resolvability ellipsoids based on these mappings for various sensor configurations are presented. Visual servoing experiments demonstrate that vision resolvability can be used to direct camera-lens motion to increase the ability of a visually servoed manipulator to precisely servo objects. © 1996 John Wiley & Sons, Inc.

Door-opening behavior of an autonomous mobile manipulator by sequence of action primitives

Abstract: A goal of this research is to accomplish a long distance navigation task by an autonomous mobile manipulator, including a behavior of Passing through a doorway. In our approach to this problem, we apply the concept of action primitives to the mobile manipulator control system. Action primitives are defined as unit elements of a complex behavior (such as door opening behavior), which control a robot according to a sequence of planned motion primitives. An important feature of the concept is that each action primitive is designed to include an error adjustment mechanism to cope with the accumulated position error of the mobile base. In this article, we report on the design and implementation of action primitives for a door opening task, and show experimental results for Passing through a doorway by an autonomous mobile manipulator using sequences of action primitives.

An impact control scheme inspired by human reflex

Abstract: In this article, we propose a control scheme to deal with unexpected impacts Impact is inevitable when robot manipulators interact with the environment Undesirable impacts may induce large interaction forces harmful to robot manipulators and the environment Impacts may also excite oscillations, and even result in manipulator instability When unexpected impacts occur, a very limited amount of time is available for control Thus, a reflex mechanism, which emulates the functioning of human reflexes, is included in the proposed scheme Human reflex is a kind of human action that requires no conscious effort; consequently, it responds to external stimuli without much delay Simulations are performed to verify the effectiveness of the proposed scheme under a wide range of environmental variations and impact velocities

A constrained optimization approach to resolving manipulator redundancy

Abstract: A redundant manipulator can achieve additional tasks by utilizing the degree of redundancy, in addition to a basic motion task. While some additional tasks can be performed by optimizing a proper objective function, other additional tasks can be performed by satisfying a set of kinematic inequality constraints. In this article, we reformulate a redundancy resolution problem with multiple criteria into a local equality and inequality constrained optimization problem, and propose a method to solve it at velocity level. The proposed method is efficient, especially when the number of additional tasks is larger than the degree of redundancy. It also systematically assigns the priorities between the additional tasks. Besides the computational efficiency, the method has a cyclic property.

Static calibration of industrial manipulators: Design of an optical instrumentation and application to SCARA robots

Abstract: This article presents a method for the static calibration of industrial robots based on optical measurements using a laser. Measured pose errors are used to estimate the geometric errors in the links. This allows the prediction of the pose error for every robot configuration, permitting the improvement of accuracy by means of slight variations of the joint motions. After a theoretical introduction on the methodology, it is applied to a SCARA robot analyzing the design of the set-up and the final precision that could be achieved. Preliminary experimental results are also presented. © 1996 John Wiley & Sons, Inc.

On the local fault tolerance of a kinematically redundant manipulator

Abstract: This work examines the local fault tolerance of a kinematically redundant manipulator to failures that result in the immobilization of one or more joints. Immobilizing a joint results in additional singularities, which are called locally fault intolerant configurations. These configurations are characterized by the null space of the manipulator Jacobian. The effect that joint failures have on manipulator dexterity is then investigated. It is shown that the reduction in the manipulator's dexterity is also related to the null space of the manipulator Jacobian.

Sensor-Based Collision Avoidance: Theory and Experiments

Abstract: A new on-line control strategy for sensor-based collision avoidance of manipulators and supporting experimental results are presented in this article. This control strategy is based on nullification of virtual forces applied to the end-effector by a hypothetical spring-plus-damper attached to the object's surface. In the proposed approach, the real-time arm control software continuously monitors the object distance measured by the arm-mounted proximity sensors. When this distance is less than a preset threshold, the collision avoidance control action is initiated to inhibit motion toward the object and thus prevent collision. This is accomplished by employing an outer feedback loop to perturb the end-effector nominal motion trajectory in real-time based on the sensory data. The perturbation is generated by a proportional-plus-integral (PI) collision avoidance controller acting on the difference between the sensed distance and the preset threshold. This approach is computationally very fast, requires minimal modification to the existing manipulator positioning system, and provides the manipulator with an on-line collision avoidance capability to react autonomously and intelligently. A dexterous RRC robotic arm is instrumented with infrared proximity sensors and is operated under the proposed collision avoidance strategy. Experimental results are presented to demonstrate end-effector collision avoidance both with an approaching object and while reaching inside a constricted opening.

A composite adaptive control with flexible quantity feedback for flexible-link manipulators

Abstract: This article presents a mixture of joint subsystem-based adaptive control and simple flexible quantity feedback for flexible-link manipulators The complex full flexible-arm system is composed of two severely coupling subsystems called the joint subsystem and flexible subsystem Linear parametrization is first used to design an adaptive law for identifying the unknown parameters of a flexible manipulator based only on the joint subsystem Joint-angle trajectory tracking can thus be achieved using the derived stable nonlinear adaptive control with the estimates of unknown parameters To stabilize the flexible subsystem, we can simply add the feedback of transversal acceleration or deflection at the end point and/or along the flexible beam The suggested approach is much simpler than those based on the full dynamics model of a flexible arm in required computations Computer simulations on a single-link and a two-link flexible arm are tested to illustrate the validity of the strategy for both trajectory tracking and active damping © 1996 John Wiley & Sons, Inc