The method of human-like handwriting and drawing is addressed with a three-link arm. Three strategies of trajectory planning are considered: the basic stroke method, the Bezier curve method, and the non-gradient numerical optimization method. Planar patterns of handwriting or drawing are converted into the vector form of joint angles in which sequence and speed of the movement can be designed to imitate human handwriting and drawing. A nonlinear three-link three-dimensional arm, similar to a human arm, is developed to track the planned trajectories. The feasibility of these methods is demonstrated by simulation.

Modeling complicated dynamics of humanoids is considered in this paper. It is proposed that the three-link module is a pivotal element in formulation of high-dimensional humanoids. The equations of motion of the module are first derived by projection of the free body equations of motion onto the space of the translation of an arbitrary point and Bryant angles and angular velocities. It is then shown that the formulation can be used as a construction module for systems with a larger number of segments. Holonomic and nonholonomic constraints are included to show the feasibility and versatility for representing other parts of the humanoid system. Digital computer simulations are presented to test the module's formulation and demonstrate its behavior in two maneuvers, jumping and sway.

In this paper, a model of a humanoid biped is developed. The dynamics are formulated to simulate responses to a sudden backwards translational disturbance of the support surface. The effect of joint stiffnesses, the role of vestibular and proprioceptive sensory apparatus in the maintenance of balance, and the involvement of the centers of mass and pressure are taken into consideration and shown in a number of simulations. Toward this end, a three-link sagittal biped with three muscle pairs at the ankle, knee, and hip, and two pairs of two-jointed muscles corresponding to quadriceps-hamstring and the gastrocnemius-antagonist group is subjected to computational experiments. Excursions of the center of gravity and the center of pressure are compared under different conditions. Comparisons to biological results are also discussed.

The structures observed in humans are being progressively applied to the theoretical approaches developed in robotics. To gain insight to the intricate mechanism of human motion, researchers sometimes use imaging technology to record the trajectories of humans performing various tasks. From these observations, they are able to estimate the forces and moments at each joint by an inverse dynamics computation. This problem is conceptually simple; however, in practice, the inverse solution requires the calculation of higher order derivatives of experimental observations contaminated by noise. The errors due to differentiation results in erroneous joint force and moment calculations. This paper provide a control theoretic framework for analyzing human motion which avoids derivative computations. The method is also suitable for synthesis of stable controllers for robotic and 'biorobic' applications which require tracking a desired reference trajectory under different loading conditions.

In this paper, a novel formulation of the dynamics, control and stability of a single rigid body is presented. Effects of gravity, and visco-elastic coupling to an inertial frame of reference at a single point of contact are included. This formulation is very convenient, and analytically tractable for animation and computer simulation of human, animal, robotic and humanoid movements, for studies of performance assessment and enhancement in natural and man-made systems, and in other studies of systems of connected rigid bodies. The representation includes simple and general linear and nonlinear position and velocity, i.e., state feedback structures that guarantee asymptotic stability of the system in the sense of Lyapunov. The Lyapunov function is simply the physical energy stored in the system, namely, a quadratic in the state space of the system: the sum of kinetic, elastic and potential energies of the system The approach is extended to a rigid body coupled to an inertial frame of reference. Digital computer simulation of the behavior of the system under disturbance are presented.

Biological systems are highly nonlinear, have at least one pair of muscles actuating every degree of freedom at any joint, and possess neural transmission delays in their feedforward (efferent) and feedback (afferent) paths. This nonlinear time delay system, involved in movement and continuous interaction with the environment, is precise, stable, and very adaptive. The problem of trajectory tracking control of a three-link sagittal model of the shank, thigh and trunk is considered in this study. The controller is synthesized using the Q-parameterization method of controller design, for the class of stable nonlinear systems. The "free design" parameter is chosen to achieve certain performance and robustness objectives, the standard approach in H/sup /spl infin// control design. Performance of the system to a class of reference inputs and robustness issues pertaining to neglected nonlinearities, unmodeled dynamics and uncertainties in time delays, are addressed in the problem. Simulations are conducted to test the performance and feasibility of the controller for the task of squatting.

We present the design of an experimental prototype cable-driven suspended platform for robotic applications, and the feasibility of using this platform in certain industrial applications is considered. In order to study and improve dynamic stability, the point-to-point motion of the platform is observed and analyzed in a laboratory environment. To focus the study, the domain of experiments is restricted to only two-dimensional space. At the starting point, or departure, the platform displays a lag and at the destination, or terminal point, the platform has a significant overshoot which causes a large settling time. Certain methods are suggested and implemented for damping the oscillation and decreasing the settling time. In the three-dimensional domain, two experiments are performed: one experiment is devoted to drilling holes in a piece of wood and another to loosening a nut.

The problem of trajectory tracking control of a three dimensional (3D) model of the human upper torso and head is considered. The torso and the head are modeled as two rigid bodies connected at one point, and the Newton-Euler method is used to derive the nonlinear differential equations that govern the motion of the system. The two-link system is driven by six pairs of muscle like actuators that possess physiologically inspired alpha like and gamma like inputs, and spindle like and Golgi tendon organ like outputs. These outputs are utilized as reflex feedback for stability and stiffness control, in a long loop feedback for the purpose of estimating the state of the system (somesthesis), and as part of the input to the controller. Ideal delays of different duration are included in the feedforward and feedback paths of the system to emulate such delays encountered in physiological systems. Dynamical neural networks are trained to learn effective control of the desired maneuvers of the system. The feasibility of the controller is demonstrated by computer simulation of the successful execution of the desired maneuvers. This work demonstrates the capabilities of neural circuits in controlling highly nonlinear systems with multidelays in their feedforward and feedback paths. The ultimate long range goal of this research is toward understanding the working of the central nervous system in controlling movement. It is an interdisciplinary effort relying on mechanics, biomechanics, neuroscience, system theory, physiology and anatomy, and its short range relevance to rehabilitation must be noted.

In this study, a coupled pattern generator is used to achieve rhythmic gait movements by a planar five-link musculoskeletal biped model. In particular, five coupled oscillators are designed which provide the biped with the desired joint angles while a controller tracks the specified trajectories. The system is adaptive in that a high-level parameter controller can adjust the parameters of the pattern generator to change the frequency of the desired joint trajectories. Simulations show the biped walking while changing frequency of the gait as its joint angles track the pattern generator.

Rhythmic movements of a five-link sagittal biped with muscle-like actuators are considered. In walking contact is periodically made with the environment as the support phases change. The inputs to every actuator are modeled after the inputs to muscles in mammals. The system possesses intrinsic position and velocity feedback due to the actuator dynamics. A control strategy is articulated that is novel in that (a) it is physiologically viable, (b) it simplifies the dynamics, and (c) it adapts to speed of walking, going up and down stairs, going up or dozen inclines, maneuvering above obstacles or holes, and the tempo and stride length of walking. Simulations of the walk of a five-link sagittal biped are presented.

The simple rhythmic movements of a multi-link sagittal marionette with many muscle-like actuators are considered in this paper. The marionette is standing on the ground, and contact with surrounding objects is not permitted. Every actuator has two inputs: a firing rate, analogous to the collective action of the alpha motoneurons of a muscle, and a threshold signal, analogous to the effective action of the gamma motoneurons that excite the sensory organ of the natural muscle-the spindle. The system possesses intrinsic position and velocity feedback due to the structure of its actuators, and extrinsic feedback with transmission delays between the actuators and the control system. The extrinsic feedback is nonlinear and is fashioned after the spindle response in natural systems. Force and length sensors convey information from which the angular position of the marionette is estimated by simultaneous solution of a redundant set of equations. Thus, the marionette is endowed with partial somesthesis: awareness of the whereabouts of its limbs. A control strategy for simple rhythmic movements is developed. This is a preliminary effort to develop an analytical structure for a multiactuator system. The long range findings may shed some light on the elaborate control structure of the central nervous system in natural systems.>

Control strategies for a one-link model of the human forearm system are presented. Three attributes of the human forearm are implemented in the second order nonlinear model: neural transmission delays in the feedback paths, nonlinear behavior of the spindle reflex, and stiffness regulation through coactivation. Three feedback loops are present in the model: intrinsic feedback (undelayed) from the actuators, spindle feedback (delayed), and higher level controller feedback (delayed). The stability of the model is examined through computer simulation analysis. A method of speed control of the arm is presented that utilizes continuous transitions in the feedforward activation levels of the muscles. Two control strategies are utilized by the higher level controller: a proportional plus integral (PI) compensation strategy, and a fuzzy control strategy. Both strategies can endure long loop transmission delays without causing the system to become unstable. A comparison of the settling time of these two controllers in compensating for disturbances and loading errors is presented.>

A strategy is developed for stable movement of a marionette under a system of unidirectional muscle-like actuators. It is shown that the strategy provides positive forces and positive inputs to the actuators that can be made analogous to monotonic function of the firing rate of natural muscles. The strategy requires more pairs of actuators than the degrees of freedom of the system-hence a need for synergistic actuators. In contrast to string-pulled marionettes where the length of the string is controlled, the tension of the string is controlled. Consequently the actuators are supplied with spindle-like position and velocity sensors and with independent input signals from higher control centers analogous to gamma inputs in living systems. Furthermore, ideal transmission delays are included in the feedforward and feedback paths to imitate neural transmission delays in living systems. To test the control strategy a three-link ten-actuator system is modeled and its stability, point to point movement, and tremor-like oscillations are shown by simulation.>

The application of robotic manipulators to complex tasks such as assembly, or insertion often requires position/force control of the end-effector, and this has been widely studied. A related task is robot compliant motion over unknown objects. The goal is to move the effector, while maintaining contact, about the object. For this application a dynamic hybrid velocity/force controller is studied. The constraints are characterized in the manner proposed by M. Mason (1981). A nominal velocity trajectory is computed, and nominal hybrid joint commands are explicitly given in terms of the sensed joint coordinates and sensed local contact information. For robustness, servoing is added, and an example design is given. Finally, the step response of the controller is simulated for the case of rolling the effector about an unknown object.>

A mechanism for the control of the heel-off to toe-off motion of a dynamic biped gait is presented. It is argued that the reaction force between the ground and the biped foot is an important factor in a satisfactory implementation of dynamic gait. This force must be properly controlled while the foot is in the heel-off to toe-off phase. Since the foot rolls over the ground surface in this phase and the global description of the surface is unknown, the foot has to execute a nonholonomic constraint motion. The formulations of nonholonomic constraints and system dynamics under the constraints are derived for the roll-over motion. A feedback control mechanism is designed based on the formulations. The formulation and the feedback control mechanism are applied to a four-link biped model. Successful simulation results of the heel-off to toe-off motion prove that the formulation and control mechanism are valid for the nonholonomically constrained motion of the biped.>

Simultaneous stabilization and disturbance decoupling of constrained robotic systems with minimal inputs are addressed. The robotic system must be decoupled into disjoint manifolds of motion and constraint, and the small motion of the system in the respective tangential hyperplanes must be stable. The problem arises in rolling and gliding types of probing manipulation. Necessary conditions for block decoupling with minimum inputs require that the image of the input matrix have a nonnull component along the null space of a matrix function of the constraint equations. Necessary conditions for simultaneous stabilization and decoupling with minimal inputs are established. An example of a planar four-link biped robot and a method to avoid constraint surface penetration are presented.>

A Kalman-filter-based sensor fusion procedure is proposed for robotic manipulators on unknown curved surfaces. Models of ideal end-effector-surface contact properties are formulated in terms of a surface parameter vector. This vector becomes the state of an extended Kalman filter and completely defines the model of the surface. Filter input measurements can include, but are not limited to, force and joint kinematic data. It is assumed that control can be accomplished using existing techniques if accurate estimates of the surface normals (and hence, the tangent planes) are found. Therefore, a manipulator using incremental control based on local measurements might benefit from the online filter states. Filter covariance can then be considered an indicator for the point at which the unknown surface can be considered known.>

A Lyapunov-based approach for the design of a PD controller for robotic systems that are subject to multiple constraints is developed. A candidate Lyapunov function is proposed for the proof of stability using the mechanical energy equation for constrained systems. Sufficient conditions for local and global stability of the unconstrained system are given. An analysis is presented for the unconstrained case and extended to the constrained case. To check the effectiveness of the proposed controller, an eight-link 3D biped model is considered. The system dynamic equations are first derived. Constraint support forces are later added to the system. Simulation of the model motion when equipped with the proposed controller shows that it exhibits a stable response in the unconstrained case.>

A strategy for motion of a planar manipulator on an unknown surface is presented. To estimate a parameter vector for the surface, least-squares estimators are formulated that use both the kinematic and dynamic data available online. The authors begin with the presentation of a control strategy that uses local sensory data to guide the end effector incrementally over the surface. Force feedback is given, which is later shown to be successful in the uninterrupted maintenance of contact. Motion over the unknown shape is justified by demonstrating that a simple shape estimation algorithm can converge to give a parametric description of the surface. Geometric and differential models of the surface are presented and the estimation procedure is specified. Also presented are the results of a number of computer simulations for a three-link planar manipulator moving over an ellipse whose parameters are unknown to the controller. It is found that, in the presence of noise, dynamic data degrade the estimates.>

The dynamic equations for a two-robot system with and without load are formulated. For control purposes, the constraint forces are derived as functions of input and state. The inverse plant method and computation of the constraint forces are used to coordinate the control of the system. No pressure or force sensors are considered, and no force feedback is used. The effectiveness of the control strategy for point-to-point motion of the coordinated robots performing a lifting task is checked by digital computer simulations.>

The online kinematic problem for gliding or rolling on an unknown surface is addressed, treating it as a simple two-rigid-body problem. A planar rigid-body end effector is considered that maintains contact with a rigid body of unknown shape by gliding or rolling on it. The smooth surface of the end effector is assumed to be known implicitly or parametrically in its own coordinate system. The authors present the main results both in equation form and diagrammatically. The figure given implies that if the parameters of the robot are known as well as its state, the forces of contact can be computed. However, due to the extensive amount of data required for this condition to be met, the required sensory and computational machinery may be exorbitant. Moreover, the presence of noise and the cost of removing it sufficiently make this approach impractical at present.>

A back somersault maneuver is studied for a four-link planar biped by a digital computer simulation. The maneuver consists of the following. 1) The takeoff phase: the system is in contact with the ground, and the ground reaction forces are instrumental in propelling the system in the air with appropriate position angles and angular velocities. 2) The flight phase: this is the airborne phase of motion for the system. The motion in this phase is governed by the trajectory of the center of gravity and the conservation of angular momentum. 3) The landing phase: in this phase the biped reestablishes a point of contact with the ground. The contact is such that impulsive forces are minimum. The kinetic energy of the system is dissipated, and a final vertical standing stance is achieved. Two control strategies are proposed. In the takeoff and landing phases a feedback strategy is needed. The airborne phase is ballistic, and an open-loop control strategy is sufficient. In all three phases of motion the biped model follows a set of desired trajectories which are approximations of a gymnast's performance. Digital computer simulations are presented to illustrate the motions and the effectiveness of the control strategies.

The computation of applied torques in real time in the dynamic control of a strongly coupled multibody linkage system is complicated and time consuming. The Newton-Euler state-space formulation is used for computing the dynamics. By using this formulation, the backward recursion for calculating angular velocities and angular accelerations is eliminated. The calculation of linear acceleration is simplified, and it involves only two steps. This reduction in the height of the evaluation tree in calculating the applied torques makes parallel processing more effective. A multiprocessor system composed of a central CPU and a group of satellite CPU's is suggested for implementing the computations. The task of each satellite CPU is to take care of one link of the system by calculating all its related data. The central CPU's task is to compute the applied torques. Because of this arrangement, the required software system is the same for all satellite CPU's. This modularity reduces the burden of software design greatly. The proposed multiprocessing scheme results in a flexible and modular system which is adaptive for a variety of dynamic configurations. Computer simulation results of this strategy are presented to show that the suggested multiprocessing scheme achieves a good speedup factor over the uniprocessing system.

A five-link planar model of a hand with one finger is developed. The actuators are analogous to muscle force generators. Three control problems, stability, maintaining a constrained motion, and control of the force of constraint, are considered in this model. Two feedback loops-one time-invariant and one time-varying-appear to be adequate for control purposes. Digital computer simulations are presented to confirm the control strategy and its effectiveness.

Impact effects of biped contact with the environment are modeled and studied. A biped system is subjected to an instant velocity change at the moment of impact with the environment. This instant velocity change is derived as a function of the biped state and the contact speed. The effects of the impact on the state as well as on the constraints are studied in biped landing on heels and toes simultaneously or on toes first. Large angular velocities may be developed by a biped immediately after the impact. The control strategy that is called for in this case is zero final velocities and a somewhat arbitrary final position. Rate feedback and nonlinear position feedback are employed for stability. This type of feedback control is proved effective by a digital computer simulation of the biped system. The action of plantar fascia during toe landing is represented by a spring and dashpot pair. The arch of the foot is prevented by this action from collapsing. Digital computer simulations of toe landing are presented.

A feedback model of biped dynamics is proposed where the internal and external forces which act on the skeleton are unified as forces of constraint, some intermittent and some permanent. It is argued that these forces are, in general, functions of the state and inputs of the system. The inputs constitute gravity and muscular forces. This model is particularly suited for understanding the control problems in all locomotion. It encompasses constraints that may be violated as well as those that cannot be violated. Applications to motion in space, locking of a joint, landing on the ground, and Initiation of walk are discussed via a simple example. A general projection method for reduction to lower dimensional systems is provided where, by defining an appropriate coordinate transformation, a prescribed number of forces of constraint are eliminated. Finally an application of the model in estimating inputs (joint torques) is briefly discussed.

Motion of a biped in the sagittal plane is represented by a three-link planar model with torque actuators at every joint. With this model a method is proposed by which postural stability and four motions of the biped can be realized: sitting down, standing up, bending, and squatting. The method is used to derive open loop and feedback torques. Open loop torques are derived from the records of a man performing each of these four motions. The feedback torques are derived as linear sums of the sensed angles and angular rates. This work is relevant to estimating internal feedback gains in the human body solely from remote and external measurements.

The feasibility of a method for the identification of a three-dimensional object from information contained in the boundary of its silhouettes is demonstrated. A silhouette is characterized by parametric representation of its boundary curve in the complex plane. After normalization and transformation, a set of Fourier descriptors is derived for every silhouette. A minimum distance classifier uses the descriptors to identify the three-dimensional object and to estimate its position and attitude with respect to a known reference coordinate system. The method was tested for identification of four aircraft representing complex and nonconvex objects. Simulation results, quantitative and statistical, are presented.