This paper presents a heading drift correction method and experimental results for position tracking of human movement based on the use of foot-mounted inertial/magnetic sensor modules. A position tracking algorithm was previously developed, which incorporated a zero velocity update technique for correcting accelerometer drift. Previous experiments indicated the presence of a persistent heading drift in the estimated position. In this paper, a simple method for correcting this drift is presented. The method requires the user to walk over a closed loop path with the foot-mounted sensor module. Assuming a constant sensor bias for this initial walk, the resulting position error is then used to accomplish an in situ correction for position estimates during future walks. Experimental results validate the effectiveness of the drift correction method and show a significant improvement in position tracking accuracy. Accuracy is determined based on the final position estimates following walks of 100 and 400 meters. Estimated distance traveled averages within 0.2% of actual distance traveled and distance from the actual position averages within 0.28% of actual distance traveled.

Accurate estimation of orientation based on data from small low-cost strapdown inertial and magnetic sensors is often inaccurate during highly dynamic motion or when trying to track movements that include two or more periods characterized by significantly different frequencies. This paper presents a complementary filtering algorithm for estimating orientation based on inertial/magnetic sensor measurements. The algorithm takes advantage of the complementary nature of the information offered by high-frequency angular rate sensor data and low frequency accelerometers and magnetometers. The filtering algorithm utilizes a single gain that can be adaptively adjusted to achieve satisfactory performance while tracking two or more different types of motion. An additional feature of our approach involves the simple estimation of the gyro bias during periods exhibiting low dynamics and its subsequent use to correct the instantaneous gyro measurements. Simulation and experimental results are presented that demonstrate the performance of the algorithm during slow or nearly static movements, as well as, those which are highly dynamic. Experimental results indicate that the algorithm is able to track pitch and roll during dynamic motion with an RMS error of less than two degrees. This is believed to be superior to current proprietary commercial algorithms.

Testing and evaluation of a novel pen input device are presented in this paper. The pen input device could be used to write on any type of surface including desktops, blackboards, or in the air. It is constructed by attaching an inertial/magnetic sensor module to a writing instrument such as a pencil, a marker, or a piece of chalk. The inertial/magnetic sensor module has three accelerometers, three angular rate sensors, and three magnetometers. A tracking algorithm and a calibration algorithm are described. The tracking algorithm is for estimating the pen tip trajectories based on the sensor measurements, and the calibration algorithm is for estimating the relative position of the sensor module on the writing instrument. Experimental results for writing alphanumeric characters are presented. The relationship between tracking accuracy and writing speed is also discussed.

An autonomous distributed control algorithm for multiple spacecraft performing simultaneous close proximity maneuvers has been developed. Examples of these maneuvers include automated on-orbit inspection, assembly, or servicing. The proposed control algorithm combines the control effort efficiency of the Linear Quadratic Regulator (LQR) and the robust collision avoidance capability of the Artificial Potential Function (APF) method. The LQR control effort serves as the attractive force toward goal positions, while APF-based repulsive functions provide collision avoidance for both fixed and moving obstacles. Comprehensive validation and performance evaluation of the control algorithm is conducted by numerical simulations. The simulation results show the developed LQR/APF algorithm to be both robust and efficient for controlling multiple spacecraft during simultaneous docking maneuvers.

Numerous applications require a self-contained personal navigation system that works in indoor and outdoor environments, does not require any infrastructure support, and is not susceptible to jamming. Posture tracking with an array of inertial/magnetic sensors attached to individual human limb segments has been successfully demonstrated. The "sourceless" nature of this technique makes possible full body posture tracking in an area of unlimited size with no supporting infrastructure. Such sensor modules contain three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers. This paper describes a method for using accelerometer data combined with orientation estimates from the same modules to calculate position during walking and running. The periodic nature of these motions includes short periods of zero foot velocity when the foot is in contact with the ground. This pattern allows for precise drift error correction. Relative position is calculated through double integration of drift corrected accelerometer data. Preliminary experimental results for various types of motion including walking, side stepping, and running document accuracy of distance and position estimates.

Real-time tracking of human body motion is an important technology in synthetic environments, robotics, and other human-computer interaction applications. This paper presents an extended Kalman filter designed for real-time estimation of the orientation of human limb segments. The filter processes data from small inertial/magnetic sensor modules containing triaxial angular rate sensors, accelerometers, and magnetometers. The filter represents rotation using quaternions rather than Euler angles or axis/angle pairs. Preprocessing of the acceleration and magnetometer measurements using the Quest algorithm produces a computed quaternion input for the filter. This preprocessing reduces the dimension of the state vector and makes the measurement equations linear. Real-time implementation and testing results of the quaternion-based Kalman filter are presented. Experimental results validate the filter design, and show the feasibility of using inertial/magnetic sensor modules for real-time human body motion tracking

A human body motion tracking system based on use of the MARG (Magnetic, Angular Rate, and Gravity) sensors has been under development at the Naval Postgraduate School and Miami University. The design of a quaternion-based Kalman filter for processing the MARG sensor data was described in [1]. This paper presents the real-time implementation and testing results of the quaternion-based Kalman filter. Experimental results validate the Kalman filter design, and show the feasibility of the MARG sensors for real-time human body motion tracking.

Rigid body orientation can be estimated in a "sourceless manner" through the use of small three degree of freedom sensor modules containing orthogonally mounted triads of micromachined angular rate sensors, accelerometers, and magnetometers. With proper filter design, drift errors can be eliminated. However, variations in the direction of the local magnetic field reference vector can cause errors in the estimated orientation. The experimental work described in this paper attempts to quantify these errors with an eye toward the development of corrective algorithms. To determine the types and magnitudes of errors that can be expected, three different types of inertial/magnetic sensor modules were subjected to controlled changes in the direction and magnitude of the local magnetic field. The amount of magnetic variation caused by several common objects was also measured in order to gain insight into the magnitude of errors that can be expected during operation in a typical environment. The experiments indicate that variations in the direction of the local magnetic field lead to errors only in azimuth estimation when using inertial/magnetic sensor modules. In a common room environment, errors due to local variations caused by objects such as electrical heaters, CRT monitors, and metal furniture can be expected to be no more than 16 degrees. In most cases these errors can be avoided by maintaining a separation of approximately two feet from the source of interference.

A novel approach to agile motion coordination for a mobile robot is presented. Agile maneuvering is represented by the ability of the mobile robot to track sharply discontinuous trajectories. A supervisory control framework is developed that orchestrates switching among multiple controllers to track nonsmooth trajectories. The stability of the individual controllers and the internal dynamics are proved. The stability of the switching scheme is analyzed using multiple Lyapunov functions. Results from a detailed computer simulation are presented to demonstrate the efficacy of this new approach.

Real-time tracking of human body motion has applications in tele-operation, synthetic reality and others. A motion tracking system based on use of the MARG sensors has been under development at Naval Postgraduate School and Miami University. The magnetic, angular rate, and gravity (MARG) sensor modules use a combination of three orthogonal magnetometers, three orthogonal angular rate sensors, and three orthogonal accelerometers to measure 3-D orientation of individual limb segments in order to determine posture. This paper presents the latest results of the MARG human body motion tracking system. The design and implementation of a control interface unit (CIU), a real-time 3-D human avatar called "Andy", and a concurrent client-server program are discussed. Experimental testing and evaluation of the overall MARG system is also presented. The system is able to track multiple human limbs in real time. The captured human motion data can be visualized over the Internet by multiple clients using the 3-D avatar.

This presents the latest design and implementation of the magnetic, angular rate, and gravity (MARG) sensor module. The MARG sensor module is designed for measuring 3-DOF orientations in real time without singularities. Each MARG sensor contains orthogonally mounted triads of micromachined rate sensors, accelerometers, and magnetometers for a total of nine sensor components. With an integrated microcontroller, the overall factor is less than one cubic inch. Digital data output rate is 100 Hz. To simplify calibration procedures and filtering algorithms, it is important that the response of the individual sensor components is linear within the typical operating regions. Experiments were conducted utilizing a precision tilt table and results indicate that all the sensor components are linear. A simple hand calibration method that requires no specialized equipment is also described. It was validated by experiments that indicate hand calibration produces results that are nearly equivalent to those obtained following precision tilt table calibration.

This paper presents an improved Kalman filter for real-time tracking of human body motions. An earlier version of the filter was presented at IROS 2001. Since then, the filter has been substantially improved. Real-time tracking of rigid body orientation is accomplished using the MARG (magnetic, angular rate, and gravity) sensors. A MARG sensor measures the three-dimensional local magnetic field, three-dimensional angular rate, and three-dimensional acceleration. A Kalman filter is designed to process measurements provided by the MARG sensors, and to produce real-time orientation represented in quaternions. There are many design decisions as related to choice of state vectors, output equations, process model, etc. The filter design presented in this paper utilizes the Gauss-Newton method for parameter optimization in conjunction with Kalman filtering. The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.

Presents an extended Kalman filter for real-time estimation of rigid body orientation using the newly developed MARG (magnetic, angular rate, and gravity) sensors. Each MARG sensor contains a three-axis magnetometer, a three-axis angular rate sensor, and a three-axis accelerometer. The filter represents rotations using quaternions rather than Euler angles, which eliminates the long-standing problem of singularities associated with attitude estimation. A process model for rigid body angular motions and angular rate measurements is defined. The process model converts angular rates into quaternion rates, which are integrated to obtain quaternions. The Gauss-Newton iteration algorithm is utilized to find the best quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. The best quaternion is used as part of the measurements for the Kalman filter. As a result of this approach, the measurement equations of the Kalman filter become linear, and the computational requirements are significantly reduced, making it possible to estimate orientation in real time. Extensive testing of the filter with synthetic data and actual sensor data proved it to be satisfactory. Test cases included the presence of large initial errors as well as high noise levels. In all cases the filter was able to converge and accurately track rotational motions.

Rigid body orientation can be determined without the aid of a generated source using nine-axis MARG (Magnetic field, Angular Rate, and Gravity) sensor unit containing three orthogonally mounted angular rate sensors, three orthogonal linear accelerometers and three orthogonal magnetometers. This paper describes a quaternion-based complementary filter algorithm for processing the output data from such a sensor. The filter forms the basis for a system designed to determine the posture of an articulated body in real-time. In the system the orientation relative to an Earth-fixed reference frame of each limb segment is individually determined through the use of an attached MARG sensor. The orientations are used to set the posture of an articulated body model. Details of the fabrication of a prototype MARG sensor are presented. Calibration algorithms for the sensors and the human body model are also presented. Experimental results demonstrate the effectiveness of the tracking system and verify the correctness of the underlying theory.

A small AUV navigation system (SANS) has been developed at the Naval Postgraduate School. The SANS is an integrated GPS/INS navigation system composed of low-cost, small-size components. It is designed to demonstrate the feasibility of using a low-cost inertial measurement unit to navigate between intermittent GPS fixes. This paper reports recent improvements to the SANS hardware, latest testing results after compensating heading-dependent derivations in the TCM-2 compass measurements, and development of an asynchronous Kalman filter for improved position estimation.

This paper presents an unified approach to the task space analysis of a wheeled mobile manipulator interacting with the environment. The system considered consists of two articulated manipulators atop a wheeled mobile platform handling a common object. We derive the task space ellipsoid, both kinematics and dynamics, for a wheeled mobile manipulator which takes into account manipulation and locomotion. The ellipsoid is able to visualize how the manipulator and the platform can contribute to a task execution by integrating the mobility of the platform with the manipulability of the arms as one unified measure. This measure can be useful not only for the task space analysis of a single mobile manipulator, but also for the coordination of multiple arms, mobile robots or mobile manipulators.

A dynamic traction control scheme for mobile robots/vehicles with two steerable and drivable wheels is presented. The kinematic modeling and position/orientation control of such a mobile robot/vehicle was studied previously by the authors (1996). In this paper, a dynamic feedback control algorithm is developed based on the dynamics of the vehicle, which not only enables the vehicle to move from any initial configuration (position and orientation) to any final configuration, but also strives to optimally distribute the tractive efforts between the two wheels for better performance. It is also shown that the same cannot be achieved by any static feedback controller. Such a control algorithm will be useful where surface conditions vary, and tractive torques between the wheels need to be dynamically allocated to maintain the required dynamic performance.

Many manipulation tasks involve transition from unconstrained to constrained motion marked by the contact with a constrained surface. This phenomenon divides the task into more than one phase, each of which requires a different control strategy. Switching from one control strategy to another leads to control discontinuities. The paper seeks to design a controller that avoids such discontinuities. The principle is based on the analysis of impulsive constraints. It is argued that, in theory, such a discontinuity can be avoided by modeling the cause of the force discontinuity of the end-effector as the velocity discontinuity of the constraint surface as opposed to the discontinuity of the Lagrange multiplier. This velocity discontinuity can then be dealt with by a continuous control strategy. A controller is designed based on this principle. Input-output linearization is performed to linearize and decouple the system. Simulation and experimental results are presented to demonstrate the effectiveness of this new approach.

Many robotic systems are subject to nonholonomic as well as holonomic constraints. Rolling contact between two rigid bodies is a typical example of such a system. In the study, a unified state space formulation of robotic systems subject to both holonomic and nonholonomic constraints is presented. The position-level holonomic constraints are first replaced by a set of velocity-level constraint equations that asymptotically converge to the original holonomic constraints. Having represented both holonomic and nonholonomic constraints in a common form, a state space representation of the constrained systems is then developed. A numerical algorithm for implementing the state space representation is also described. The proposed formulation eliminates the need to solve holonomic constraints either analytically or numerically, and ensures that holonomic constraints are always satisfied, particularly in computer simulations. The formulation makes it possible to treat systems with holonomic constraints, with nonholonomic constraints, or with both holonomic and nonholonomic constraints in a unified framework. Two examples are presented to illustrate the application of the unified formulation.

When two or more arms are used to manipulate a large object, it is preferable not to have a rigid grasp in order to gain more dexterity in manipulation. It may therefore be necessary to control contact motion between the object and the effector(s) on one or more arms. This paper addresses the dynamic control of two arms cooperatively manipulating a large object with rolling contacts. In the framework presented here, the motion of the object as well as the loci of the contact point either on the surface of each effector or on the object can be directly controlled. The velocity and acceleration equations for three-dimensional rolling contacts are derived in order to obtain a dynamic model of the system. A nonlinear feedback control algorithm that decouples and linearizes the system is developed. This is used to demonstrate the control of rolling motion along each arm and the adaptation of grasps to varying loads.

Many manipulation tasks involve transition from unconstrained to constrained motion marked by the contact with a constrained surface. This phenomenon divides the task into more than one control strategies plagued with control discontinuity. This paper seeks to design a controller which avoids such discontinuity. The principle is based on the analysis of impulsive constraints. It is shown that, in theory, such discontinuity can be avoided by replacing the force discontinuity of the end-effector by velocity discontinuity of the constraint surface. This velocity discontinuity can then be dealt with using a continuous control strategy. A controller has been designed based on this principle. Input-output linearization has been performed to linearize and decouple the system.

This paper deals with a coordinated task between a human and a mobile manipulator in which the human operator takes an initiative of the task execution. The task trajectory can be modified arbitrarily by the human, and the mobile manipulator will follow the trajectory while executing the task together, e.g., transporting a large object. This requires two issues to be resolved simultaneously, that is, the coordination of locomotion and manipulation and the task execution such as carrying an object. Force control scheme is integrated with the coordination algorithm of locomotion and manipulation. The force control part sustains the object while the coordination between the manipulator and the platform is maintained at position level such that the manipulator does not fully extend or retract. Computer simulations are provided to show the efficacy of the proposed approach.

The kinematic modeling and feedback control of a mobile robot/vehicle with two independently steerable wheels is studied. Two-wheel steer vehicles are highly maneuverable in confined space and their orientation can be made independent of the position trajectory. However, the control of such vehicle is less intuitive and difficult. A dynamic feedback control algorithm is developed, which enables the vehicle to move from any initial configuration (position and orientation) to any final configuration. It is also shown that the same cannot be achieved by any static feedback controller. Simulation results are presented to verify the independent control of the two position variables and the orientation variable.

A mobile manipulator composed of a manipulator and a mobile platform has a much larger workspace than a fixed-base manipulator due to the mobility provided by the platform. While the on-board manipulator reaches out and performs manipulation tasks, the role of the mobile platform is to position the manipulator in a preferred configuration. In this paper, we study the effect of the dynamic interaction between the manipulator and the mobile platform of a mobile manipulator on the task performance. We consider the task that the end point of the manipulator tracks a desired trajectory in a fixed reference frame. The effect of the dynamic interaction on the tracking performance is examined by comparing four different cases: 1) with full compensation of the dynamic interaction with each other; 2) with the mobile platform compensating the dynamic interaction caused by the manipulator; 3) with the manipulator compensating the dynamic interaction caused by the mobile platform; and 4) without any compensation of the dynamic interaction at all. Simulation results from representative trajectories are presented to illustrate the effect.

In the absence of obstacles, the study of mobile manipulators is mainly concerned with the coordination of locomotion and manipulation. In the presence of obstacles, one must simultaneously consider the obstacle avoidance problem and the coordination problem. This paper presents a control method for mobile manipulators that integrates an obstacle avoidance scheme with a coordination scheme. The obstacle avoidance scheme is based on superquadric potential functions. The coordination scheme is based on preferred operating regions. The controller allows a mobile manipulator to retain optimal or sub-optimal configurations while avoiding obstacles. Simulation results are presented to demonstrate the effectiveness of the control method.

The control of mechanical systems subjected to rolling contacts is studied. Rolling contacts result in both holonomic and nonholonomic constraints. The focus of this paper is on formulating the differential motion equations and algebraic constraint equations into the standard state space representation of dynamic control systems. The position-level holonomic constraints are approximated by a set of velocity-level constraint equations that asymptotically converge to the original holonomic constraints. The approximation removes the numerical instability and ensures the satisfaction of holonomic constraints, particularly in computer simulations. Further, the approximation eliminates the need to solve holonomic constraints either analytically or numerically. The resulting approach makes it possible to treat systems with holonomic constraints, systems with nonholonomic constraints, and systems with both holonomic and nonholonomic constraints in a unified framework. The approach facilitates the computer simulation of mechanical systems with rolling constraints.

Presents a collaborative effort to design and implement a cooperative material handling system by a small team of human and robotic agents in an unstructured indoor environment. The authors' approach makes fundamental use of the human agents' expertise for aspects of task planning, task monitoring, and error recovery. The authors' system is neither fully autonomous nor fully teleoperated. It is designed to make effective use of the human's abilities within the present state of the art of autonomous systems. The authors' robotic agents refer to systems which are each equipped with at least one sensing modality and which possess some capability for self-orientation and/or mobility. The authors' robotic agents are not required to be homogeneous with respect to either capabilities or function. The authors' research stresses both paradigms and testbed experimentation. Theory issues include the requisite coordination principles and techniques which are fundamental to a cooperative multiagent system's basic functioning. The authors have constructed an experimental distributed multiagent-architecture testbed facility. The required modular components of this testbed are currently operational and have been tested individually. The authors' current research focuses on the agents' integration in a scenario for cooperative material handling.

In a decentralized multi-robot system, each robot is controlled by an independent controller and the information obtained by each robot through its proprioceptive sensing devices is not shared with other robots. If the coordination of multiple robots in a cooperative manipulation task is to be accomplished, each robot must be able to exhibit controlled interaction with other robots and objects with minimal information. In this paper, the authors address the problem of maintaining rolling contact between a robot arm and an external, moving object. The authors assume that a nominal model of the motion of the moving object is available. The dynamic system that characterizes the motion of the robot arm and the moving object is acatastatic and nonholonomic. The authors design a nonlinear feedback for such a system that successfully maintains rolling contact. Simulation results are presented to demonstrate the effectiveness of the system.>

A mobile manipulator composed of a manipulator and a mobile platform has a much larger workspace than a fixed-base manipulator. While the on-board manipulator reaches out and performs manipulation tasks, the role of the mobile platform is to position the manipulator in a preferred configuration. In this paper, we study the effect of the dynamic interaction between the manipulator and the mobile platform of a mobile manipulator on the task performance. We consider the task that the end point of the manipulator tracks a desired trajectory in a fixed reference frame. The effect of the dynamic interaction on the tracking performance is examined by comparing four different cases: (1) without any compensation of the dynamic interaction at all; (2) with the mobile platform compensating the dynamic interaction caused by the manipulator; (3) with the manipulator compensating the dynamic interaction caused by the mobile platform; and (4) with full compensation of the dynamic interaction with each other.>

The optimization of trajectories and actuator torques for a dual arm manipulation system is considered. Given the starting and final configurations, we find the trajectories that minimize: (a) the integral of the norm of the vector of derivatives of the actuator forces; and (b) the integral of the norm of the actuator forces. In this way both kinematic and actuator redundancy are resolved. The optimization problem reduces to solving a two-point boundary valve problem for coupled, nonlinear differential equations. The effect of different parameters such as preload and inertia are investigated and the results are compared with those obtained using other well-known cost functions.>

When multiple arms are used to manipulate a large object, it is beneficial and sometimes necessary to maintain and control contacts between the object and the effector (the contacting surface of an arm) through force closure. Rolling and/or sliding can occur at these contacts, and the system is, in general, characterized by holonomic as well as nonholonomic (including unilateral) constraints. In this paper, the control of planar rolling contacts is investigated. Multi-arm manipulation systems are typically redundant. In the authors' approach, a minimal set of inputs is employed to control the trajectory of the system while the surplus inputs control the contact conditions. The trajectory includes the gross motion of the object as well as the rolling motion at each contact. A nonlinear feedback scheme for simultaneous control of motion as well as contact conditions is presented. A new algorithm which adapts a two-effector grasp with rolling contacts to external loads and the trajectory is developed. Simulations and experimental results are used to illustrate the salient features in control and planning.>

In a versatile, intelligent, multirobot system, each robot is controlled by independent controllers and information obtained by a robot through proprioceptive sensing (joint position, velocity, torques etc.) is not shared with other robots. If the coordination of robots in a cooperative manipulation task is to be accomplished, each robot must be able to exhibit controlled interaction with other robots and objects with minimal information. The authors address the problem of maintaining rolling contact between am actively controlled mechanical linkage and an external moving surface, assuming that a nominal model of the gross motion of the moving surface is available. Thus the control problem involves a dynamic system that is acatastic and nonholonomic. Nonlinear feedback is used to decouple and linearize the time-varying system. Examples and results from computer simulations are used to show that the normal and tangential forces as well as the relative rolling motion can be controlled satisfactorily.

Since the dynamics of a wheeled mobile robot is nonlinear, the feedback linearization technique is commonly used to linearize the input-output map. The input-output linearized system has a nonlinear internal dynamics. In this paper, the internal dynamics of the mobile robot under the look-ahead control is first characterized. The look-ahead control takes the coordinates of a reference point in front of the mobile robot as the output equation. Using a novel Lyapunov function, the stability of the internal dynamics is then analyzed. In particular, it is shown that the internal motion of the mobile robot is asymptotically stable when the reference point is commanded to move forward, whereas the internal motion is unstable when the reference point moves backward. Simulation and experimental results are provided to verify the analysis.

The authors address force control in overconstrained dynamic systems with special emphasis on robot control. Previous approaches to force control are studied, and many of these are shown to be unsuitable for dynamic force control. Practical and theoretical considerations for designing force control algorithms are discussed. Experimental and simulation results that validate the theoretical findings are presented for a single-degree-of-freedom pneumatic force controller.>

The authors present a unified formulation for the control problem of multiple arm systems which accommodates both holonomic and nonholonomic constraints. Several unique control properties of nonholonomic systems are discussed. Several useful results regarding input-output linearization and the zero dynamics in such systems are proved. The analysis and controller design are discussed for multi-arm systems. Results from computer simulations are presented to demonstrate the control algorithms. Simulation results illustrate that rolling and sliding can be effectively controlled.>

An object much larger than a robot end-effector can not be rigidly grasped. Instead, it is necessary to support the object with multiple effectors. The effectors need not be grippers-they may be surfaces on the arm(s). Multiple arm manipulation without rigid grasps is investigated. The interaction between a robot and the object is characterized by unilateral constraints. The closed chain topology, redundancy in actuation, and the nonlinear coupled equations of motion make the problem formidable. The approach used is to utilize a minimal set of inputs to control the trajectory. The surplus inputs are used to control the contact conditions (rolling, sliding, etc.).>

Dynamic modeling and coordinated control of two-arm pushing operations are studied. The performance of such tasks requires the simultaneous control of the motion trajectory of the grasped object and the interaction force. The control of the interaction force is needed to ensure that the object is not dropped and to avoid excessive pressing. The motion and force control problem is further complicated by the presence of unilateral constraints since the manipulators can only push the object. The control problem is first formulated in the state space. A coordinated control method that utilizes a state feedback to decouple the motion control subsystem and force control subsystem is then presented. The unilateral constraints are satisfied during the entire motion period using a proposed force control planning algorithm. The effectiveness of the control method is verified by simulations.>

A nonlinear feedback robot controller that incorporates the robot manipulator dynamics and the robot joint motor dynamics is proposed. The manipulator dynamics and the motor dynamics are coupled to obtain a third-order-dynamic model, and differential geometry control theory is applied to produce a linearized and decoupled robot controller. The derived robot controller operates in the robot task space, thus eliminating the need for decomposition of motion commands into robot joint space commands. Computer simulations are performed to verify the feasibility of the proposed robot controller. The controller is further experimentally evaluated on the PUMA 560 robot arm. The experiments show that the proposed controller produces good trajectory tracking performances and is robust in the presence of model inaccuracies. Compared with a nonlinear feedback robot controller based on the manipulator dynamics only, the proposed robot controller yields conspicuously improved performance.>

An approach to the control of constrained dynamic systems such as multiple arm systems, multifingered grippers, and walking vehicles is described. The basic philosophy is to utilize a minimal set of inputs to control the trajectory and the surplus input to control the constraint or interaction forces and moments in the closed chain. A dynamic control model for the closed chain is derived that is suitable for designing a controller in which the trajectory and the interaction forces and moments are explicitly controlled. Nonlinear feedback techniques derived from differential geometry are then applied to linearize and decouple the nonlinear model. These ideas are illustrated through a planar example in which two arms are used for cooperative manipulation. Results from a simulation are used to illustrate the efficacy of the method.< >

The coordinated control of two manipulators in the presence of environmental constraints is studied. Such a control method is needed in applications in which the two manipulators grasp a common object and move it along a surface while exerting a certain amount of contact force. The two manipulators constrain each other and are also constrained by the environment. It is observed that the motion and constraint equations obtained directly from mechanics are not suitable for control purposes. A set of equivalent equations is derived in the standard nonlinear system representation with clear state equations and output equations. A nonlinear feedback that linearizes and decouples the dynamic nonlinear system of the two constrained manipulators is found. The coordinated controller design is then carried out for the linearized system.>

Based on a differential geometric feedback linearization technique for nonlinear time-varying systems, a dynamic force control method for robot arms is developed. It uses active force-moment measurements at the robot wrist. The controller design fully incorporates the robot-arm dynamics and is so general that it can be reduced to pure position control, hybrid position/force control, and pure force control. The controller design is independent of the tasks to be performed. Computer simulations show that the controller improves the position error by a factor of ten in cases in which position errors generate force measurements. A theorem on linearization of time-varying system is also presented.>

In this paper the dynamic equation describing two cooperating robot arms which simultaneously are working on the same object is established by considering the whole system as a closed kinematic chain. This formulation has the advantage of automatically handling the coordination and load distribution between the robot arms through the dynamic equation. It can also be generalized to a multi-robot arm system. The control problem is solved as a design problem for a linear system by first applying a nonlinear feedback and nonlinear coordinate transformation to linearize the nonlinear dynamic equation, and then employing the linear optimal control theory to design a robust controller in the task space. This new dynamic control method establishes a direct control response to task space commands facilitating dynamics based task encoding in robotics.

A new control method is presented for the coordinated control of two robot arms based on exact system linearization by appropriate non-linear feedback. The two arms are assumed to be working on the same object simultaneously. The control method uses a dynamic coordinator acting on relative position and velocity error and/or on relative force-torque errors between the two arms. Simulation results are presented for the coordinated control of two PUMA 560 robot arms using an optimal dynamic coordinator. For completeness, the paper also presents (i) a new revised set of inertia parameters for all six links of PUMA 560 robot arm, (ii) the form of nonlinear feedback and diffeomorphic state transformation which linearizes the control of PUMA 560 working in all six degrees of freedom, and (iii) the reduced numeric form of all dynamic equations for PUMA 560 working in three (positioning) degrees of freedom.