Showing papers in "Journal of Robotic Systems in 1993"

The NIST robocrane

Abstract: The Robot Systems Division of the National Institute of Standards and Technology (NIST) has been experimenting for several years with new concepts for robot cranes. These concepts utilize the basic idea of the Stewart platform parallel link manipulator. The unique feature of the NIST approach is to use cables as the parallel links and to use winches as the actuators. As long as the cables are all in tension, the load is kinematically constrained and the cables resist perturbing forces and moments with equal stiffness to both positive and negative loads. The result is that the suspended load is constrained with a mechanical stiffness determined by the elasticity of the cables, the suspended weight, and the geometry of the mechanism. Based on these concepts, a revolutionary new type of robot crane, the NIST ROBOCRANE, has been developed that can control the position, velocity, and force of tools and heavy machinery in all six degrees of freedom (x, y, z, roll, pitch, and yaw). Depending on what is suspended from its work platform, the ROBOCRANE can perform a variety of tasks. Examples are: cutting, excavating and grading, shaping and finishing, lifting, and positioning. A 6-m version of the ROBOCRANE has been built and critical performance characteristics analyzed.

The applications of harmonic functions to robotics

Abstract: Harmonic functions are solutions to Laplace's equation. Such functions can be used to advantage for potential-field path planning because they do not exhibit spurious local minima. Harmonic functions are shown here to have a number of properties that are essential to robotics applications. Paths derived from harmonic functions are generally smooth. Harmonic functions also offer a complete path-planning algorithm. We show how a harmonic function can be used as the basis for a reactive admittance control. Such schemes allow incremental updating of the environment model. Methods for computing harmonic functions respond well to sensed changes in the environment, and can be used for control while the environment model is being updated.

Dynamic analysis and control of a Stewart platform manipulator

Abstract: The Stewart platform is a six-axis parallel robot manipulator with a force-to-weight ratio and positioning accuracy far exceeding that of a conventional serial-link arm. Its stiffness and accuracy approach that of a machine tool yet its workspace dexterity approaches that of a conventional manipulator. In this article, we study the dynamic equations of the Stewart platform manipulator. Our derivation is closed to that of Nguyen and Pooran because the dynamics are not explicitly given but are in a step-bystep algorithm. However, we give some insight into the structure and properties of these equations: We obtain compact expressions of some coefficients. These expressions should be interesting from a control point of view. A stiffness control scheme is designed for milling application. Some path-planning notions are discussed that take into account singularity positions and the required task. The objective is to make the milling station into a semiautonomous robotic tool needing some operator interaction but having some intelligence of its own. It should interface naturally with part delivery and other higher-level tasks. 0 1993 John Wiley & Sons, Inc.

Adaptive control of a stewart platform‐based manipulator

Abstract: A joint-space adaptive control scheme for controlling noncompliant motion of a Stewart platform-based manipulator (SPBM) was implemented in the Hardware Real-Time Emulator at Goddard Space Flight Center. The six-degrees of freedom SPBM uses two platforms and six linear actuators driven by dc motors. The adaptive control scheme is based on proportional-derivative controllers whose gains are adjusted by an adaptation law based on model reference adaptive control and Liapunov direct method. It is concluded that the adaptive control scheme provides superior tracking capability as compared to fixed-gain controllers.

A family of stewart platforms with optimal dexterity

Abstract: Stewart platform configurations (architectures and poses) optimizing local dexterity are investigated. The condition number of the Jacobian matrix is used to quantify the dexterity of the manipulator. For a platform-centered Jacobian reference location and a given characteristic length for scaling purposes, a two-parameter family of optimal configurations is shown to exist. Two suitable architectural parameters defining the family are identified and properties of the optimal configurations are discussed. The optimization results are shown to be easily extended for other Jacobian reference locations and for other singular value-based local dexterity measures. It is suggested that the existence of a two-parameter family of optimal local configurations could be exploited to aid in the resolution of optimal architectures for global measures.

An efficient method for inverse dynamics of manipulators based on the virtual work principle

Abstract: The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.

Direct adaptive impedance control of robot manipulators

Abstract: This article presents an adaptive scheme for controlling the end-effector impedance of robot manipulators. The proposed control system consists of three subsystems: a simple “filter” that characterizes the desired dynamic relationship between the end-effector position error and the end-effector/environment contact force, an adaptive controller that produces the Cartesian-space control input required to provide this desired dynamic relationship, and an algorithm for mapping the Cartesian-space control input to a physically realizable joint-space control torque. The controller does not require knowledge of either the structure or the parameter values of the robot dynamics and is implemented without calculation of the robot inverse kinematic transformation. As a result, the scheme represents a general and computationally efficient approach to controlling the impedance of both nonredundant and redundant manipulators. Furthermore, the method can be applied directly to trajectory tracking in free-space motion by removing the impedance filter. Computer simulation results are given for a planar four degree-of-freedom redundant robot under adaptive impedance control. These results demonstrate that accurate end-effector impedance control and effective redundancy utilization can be achieved simultaneously by using the proposed controller.

Method for kinematic calibration of stewart platforms

Abstract: A Stewart platform is a six degrees of freedom parallel manipulator composed of six variable-length legs connecting a fixed base to a movable plate. Like all parallel manipulators, Stewart platforms offer high force/torque capability and high structural rigidity in exchange for small workspace and reduced dexterity. Because the solution for parallel manipulators' forward kinematics is in general much harder than their inverse kinematics, a typical control strategy for such manipulators is to specify the plate's pose in world coordinates and then solve the individual leg lengths. The accuracy of the robot critically depends on accurate knowledge of the device's kinematic parameters. This article focuses on the accuracy improvement of Stewart platforms by means of calibration. Calibration of Stewart platforms consists of construction of a kinematic model, measurement of the position and orientation of the platform in a reference coordinate frame, identification of the kinematic parameters, and accuracy compensation. A measurement procedure proposed in this article allows a great simplification of the kinematic identification. The idea is to keep the length of the particular leg, whose parameters are to be identified, fixed while the other legs change their lengths during the measurement phase. By that, redundant parameters can be eliminated systematically in the identification phase. The method also shows the estimation of each leg's parameters separately because the measurement equations are fully decoupled, which results in a drastical reduction of the computational effort in the parameter identification. Simulation results assess the performance of the proposed approach. © 1993 John Wiley & Sons, Inc.

Geometric analysis of antagonistic stiffness in redundantly actuated parallel mechanisms

Abstract: Parallel closed-chain mechanical architectures allow for redundant actuation in the force domain. Antagonistic actuation, afforded by this input force redundancy, in conjunction with nonlinear linkage geometry creates an effective stiffness directly analogous to that of a wound metal spring. A general stiffness model for such systems is derived and it is shown that the constitutive relationship between actuation effort and active stiffness is the second-order kinematic constraint set relating the actuation sites. The extent of stiffness modulation possible is then evaluated and necessary conditions for full stiffness modulation are obtained. Configuration-dependent, second-order, geometric singularities affecting stiffness generation are illustrated in terms of a three-degree-of-freedom parallel spherical mechanism example and discussed in relation to their more commonly investigated first-order counterparts that affect force and velocity transmission. Finally, a load distribution methodology for simultaneous motion and stiffness generation is introduced, and it is shown that with hyperredundant actuation the internal load state of the mechanism can be controlled independent of its motion and effective stiffness. © 1993 John Wiley & Sons, Inc.

Exact methods for determining the kinematics of a stewart platform using additional displacement sensors

Abstract: The Stewart platform (SP) is a parallel closed-kinematic chain robotic mechanism that is capable of providing high structural and positional rigidity. Because of its unique capability, the platforms have been employed in many control engineering applications such as simulator shakers, robotic manipulators, etc. However, a main problem often found in the implementation of a real-time controller for the platform is the lack of an efficient algorithm for solving its highly nonlinear forward kinematic transformation (FKT), where one seeks to find the translational and orientational altitudes of the moveable platform from knowing the lengths of the platform linkages. This article describes two new direct and exact methods for computing the translational and rotational displacements of an SP by employing extra transnational displacement sensors (TDSs), in addition to the existing TDSs for the six links of the SP. The key for the approach lies in knowing where to employ the TDSs for determining positional vectors of strategic platform locations. By taking advantage of a tetrahedral geometry, closed-form solutions for the FKT can then be derived and directly evaluated. The new methods produce accurate solutions with only minimal computation necessary. The advantages and disadvantages of the proposed methods are discussed and compared to an existing method. The exact methods are being investigated for an on-line implementation of a nonlinear adaptive control system and redundancy scheme for a 25-ton Stewart platform-based Crew Station/Turret Motion Base Simulator (CS/TMBS) at the U.S. Army Tank-Automotive Command (TACOM).

Synthesis and analysis of a new class of six-degree-of-freedom parallel minimanipulators

Abstract: A new class of six-degree-of-freedom parallel minimanipulators capable of providing high resolution and high-stiffness for fine position and force control in a hybrid serial-parallel manipulator system is presented. Positional resolution and stiffness of minimanipulators are improved using two-degree-of-freedom planar linkages as drivers. The minimanipulators are based on only three inextensible limbs, as opposed to most of the six-limbed parallel manipulators, which makes it possible to reduce its direct kinematics to solving a polynomial in a single variable and to diminish possibility of mechanical interference between limbs. The base-mounted minimanipulator actuators are characterized by high payload capacity, small actuator size, and low power dissipitation.

Inverse kinematics and inverse dynamics for control of a biped walking machine

Abstract: Analytical techniques are presented for the motion planning and control of a 12 degree-of-freedom biped walking machine. From the Newton-Euler equations, joint torques are obtained in terms of joint trajectories, and the inverse dynamics are developed for both the single-support and double-support cases. Physical admissibility of the biped trajectory is characterized in terms of the equivalent force-moment and zero-moment point. This methodology has been used to obtain reference inputs and implement the feedforward control of walking robots. A simulation example illustrates the application of the techniques to plan the forward-walking trajectory of the biped robot. The implementation of a prototype mechanism and controller is also described.

Joint trajectory generation for redundant robots in an environment with obstacles

Abstract: Collision avoidance is an absolutely essential requirement for a robot to complete a task in an environment with obstacles. For kinematically redundant robots, collision avoidance can be achieved by making full use of the redundancy. In this article, the problem of determining collision-free joint space trajectories for redundant robots in an environment with multiple obstacles is considered, and the “command generator” approach is employed to generate such trajectories. In this approach, a nondifferentiable distance objective function is defined and is guaranteed to increase wherever possible along the trajectory through a vector in N(J), the null space of Jacobian matrix J. Algorithms that implement this nondifferentiable optimization problem are fully developed. It is shown that the proposed collision-free trajectory generation scheme is efficient and practical. Extensive simulation results of a four-link robot example are presented and analyzed.

Six‐degree‐of‐freedom active vibration isolation using a stewart platform mechanism

Abstract: The design and control problems of a class of multidegree-of-freedom vibration isolation systems (VISs) based on a Stewart platform mechanism are studied. A prototype of a six-degree-of-freedom VIS for precision control of a wide range of space-based structures implemented in Intelligent Automation, Inc. is described. The feasibility of using a Stewart platform to achieve 6-degree-of-freedom vibration control in space applications is shown. A new Terfenol-D actuator characterized by significantly longer stroke than any commercially available Terfenol-D actuator and direct flux and strain sensors integral to the actuator is described.

Nonlinear control with end-point acceleration feedback for a two-link flexible manipulator: Experimental results

Abstract: Experimental results for end-point positioning of multi-link flexible manipulators through end-point acceleration feedback are presented in this article. The advocated controllers are implemented on a two-link flexible arm developed at the Control/Robotics Research Laboratory at Polytechnic University. The advocated approach in this article is based on a two-stage control design. The first stage is a nonlinear (1) feedback linearizing controller corresponding to the rigid body motion of the manipulator. Because this scheme does not utilize any feedback from the end-point motion, significant vibrations are induced at the end effector. To this effect, and to enhance the robustness of the closed-loop dynamics to parameter variations, the inner loop is augmented with an outer loop based on a linear output LQR design that utilizes an end-point acceleration feedback. The forearm of the manipulator is significantly more flexible as compared with the upper arm. Experimental and simulation results validate the fact that the end-effector performance is significantly better with the proposed (1) feedback linearizing control as compared with the linear independent joint PD control. In addition, the nonlinear control offers other advantages in terms of smaller and smoother actuator torques and reducing the effects of nonlinearities. Close conformation between simulation and experimental results validates the accuracy of the model.

Estimate of the two smallest singular values of the Jacobian Matrix: Application to damped least‐squares inverse kinematics

Abstract: The smallest singular value of the Jacobian matrix is known to be the sole reliable measure of closeness to singular configurations; its computation via a full singular value decomposition, however, is demanding in view of real-time applications. In this article, a standard singular value estimation procedure is extended to improve the handling of singular values crossing along a given trajectory. The proposed algorithm maintains the computational efficiency of the original technique and shows higher estimation accuracy with respect to the original procedure. Case studies are developed to verify the effectiveness of the estimation procedure applied to an industrial manipulator. © 1993 John Wiley & Sons, Inc.

Experimental determination of dynamic parameters of robotic arms

Abstract: This article presents a practical method for determining the dynamic parameters of robotic arms. The two unique features of the method are that it determines the friction parameters along with the inertia and mass parameters and that it does not require the measurement of joint accelerations. The method is demonstrated experimentally by determining the dynamic parameters of a closed-chain direct-drive arm. The precision of the determined parameter was verified in the context of computed torquebased controllers. Statistical analysis also shows that the estimated values are reliable. © 1993 John Wiley & Sons, Inc.

Null space damping method for local joint torque optimization of redundant manipulators

Abstract: In this article, a null space damping method is proposed that solves the stability problem commonly encountered in existing local joint torque optimization techniques applied to redundant manipulators. The damped joint motion is stable and globally outperforms undamped techniques in the sense of torque minimization capability. In addition, simulation results show that the resulting damped joint motion becomes conservative after an initial transient stage for cyclic end-effector trajectories, while undamped pseudoinverse solutions are reported to never lead to conservative motion. Three undamped and damped joint torque optimization algorithms are considered and discussed with comparison to the previous literature. The effectiveness of the proposed null space damping method is demonstrated by the results of two computer simulations. In addition, the minimization of electrical power consumption is addressed with respect to the results of this article.

Design of global tracking controllers for flexible‐joint robots

Abstract: An approach to design control laws for trajectory tracking of robots having flexible joints is presented. An application to the adaptive control is also given with reference to a single-link robot with one revolute elastic joint whose parameters are unknown.

A fast procedure for manipulator inverse kinematics computation and singularities prevention

Abstract: In this article, a fast procedure for numerical manipulator inverse kinematics computation and singularities prevention is presented. The approach is based upon solving a linear system and automatically calculating some parameters. These parameters are properly used in either one of two original schemes that are also proposed to induce robustness to the pseudoinverse. Furthermore, here it is also shown how to properly implement one of these schemes in conjunction with a recently developed approach for the singularities prevention of redundant manipulators. The resultant algorithms are tested on the simulation of a planar redundant manipulator. From the results obtained, it is observed that the proposed approach compares favorably with the approaches using a Gaussian elimination procedure and with pseudoinverse robustness based on a manipulability measure.

Linear learning control of robot motion

Abstract: For the trajectory following problem of a robot manipulator, a new linear learning control law, consisting of the conventional proportional-integral-differential (PID) control law, with respect to position tracking error, and an iterative learning term is provided. The learning part is a linear feedback control of position, velocity, and acceleration errors (PDD2). It has been shown that, under the proposed learning control, the position, velocity, and acceleration tracking errors are asymptotically stable in the presence of highly nonlinear dynamics. The proposed control is robust in the sense that exact knowledge about nonlinear dynamics is not required except for the bounding functions on their magnitudes. Further, neither is linear approximation of nonlinear dynamics nor repeatability of robot motion required.

Friction modeling and compensation for an industrial robot

Abstract: This article describes the detailed friction modeling of the General Electric GP132 industrial robot. Friction is an area whose importance is often discounted in the development of control systems because it is thought to be insignificant or unmodelable. This work demonstrates that friction does have a predictable structure, and that significant performance improvement can be realized through its proper compensation. Experiments performed to determine the static, Coulomb, and viscous friction of the GP132 are presented. In addition to these components, the robot is shown to have significant gravity load-dependent and position-dependent friction. The accuracy of the friction models are verified through several experiments and are shown to be considerably better than previously formulated models.

Review and unification of reduced‐order force control methods

Abstract: In this article, we compare some of the recent methods developed for simultaneous position and force control of a single n-link constrained robot manipulator. Mathematical models of the constrained manipulator are introduced and the advantages and disadvantages of the associated control formulations are discussed. The similarities between each of the proposed formulations are also highlighted. Finally, a transformation is presented that generalizes the methods of decoupling force from the position dynamics.

Variable structure trajectory control of an elastic robotic arm

Abstract: This article introduces a variable structure system scheme to control the end effector trajectory of a two-link flexible robotic arm. Because control of the actual tip position leads to unstable zero dynamics, control of points in the neighborhood of the tip is considered. An output is chosen as the sum of the joint angle and tip elastic deformation times a constant factor for each link. For the chosen output, a discontinuous output control law is derived based on the variable structure theory. The control law thus derived accomplishes the desired trajectory tracking of the output. A linear stabilizer is designed using the pole assignment technique for the final capture of the terminal state and stabilization of the elastic modes. Simulation results are presented to show that in the closed-loop system large maneuvers can be performed in the presence of payload uncertainty, thereby exhibiting the robustness of the controller.

Tracking control for end‐effector position and orientation of structurally flexible manipulators

Abstract: A simple and effective feedback control strategy is presented for end-effector position and orientation tracking of structurally flexible manipulators free of external forces as in space applications. The fully feedback-driven approach employs an augmented dynamical description in which derivatives of the control inputs are included in the state. This ensures smooth control inputs to the manipulator joints. The feedback law uses gain scheduling of a series of steady-state regulators derived by considering the manipulator at intermediate (nominally rigid and stationary) configurations along the desired trajectory. The performance of the control method is demonstrated in simulations of a planar three-link manipulator system. Examples show that the controller can be applied successfully in discrete-time, and that spillover does not appear to be a problem.

Grasp synthesis for planar and solid objects

Abstract: This article presents an analysis of the mechanics for multifingered grasps of planar and solid objects. We present a method that is intuitive and computationally efficient. We combine the search for finger grasp positions with finger (manipulation and squeezing) force calculations into a single method. Physically, the squeezing and frictional effects between the fingers and the grasped objects are fully visualized through our approach. Mathematically, we reduced the complexity of finger force calculations when comparing our scheme with previously available schemes. Examples are used to illustrate the effectiveness and efficiency of our scheme. Based upon the analysis of grasp mechanics, an algorithm for quantatively choosing the grasp points is proposed to ensure stable grasps.

Kinematic decoupling in mechanisms and application to a passive hand controller design

Abstract: Observations regarding the kinematics of mechanisms are applied to the synthesis of a passive hand controller. It is argued that stiffness (and damping) properties are central to the effectiveness of such devices and in particular that the simplicity of these properties is crucial. What simple means is analyzed and it is shown that only certain types of manipulators can appropriately be used. In effect, decoupling is shown to be architecture and configuration dependent. The properties of parallel mechanisms are reviewed and found appropriate for restricted-workspace hand controllers. A particular kinematic design is then derived and a practical implementation described. 0 1993 John Wiley & Sons, Inc.

New approach for aggregating multi‐sensory data

Abstract: The task of sensory data fusion may involve the aggregation of sensory measurements that may be from different phenomenological domains and that, in many cases, could embrace some conflicting information cues. It is rather a challenge to find suitable strategies by which measurements obtained by the different sensors of the system can be aggregated so that a consistent interpretation of these measurements is achieved. In this article, we present a novel approach to achieve this goal. A recursive group utility function that is capable of bringing the group of sensors into consensus is used. After each sensor in the group gathers information relevant to the sensory task, the group engages in what we call the uncertainty estimation stage. This is an information theorybased process that allows each sensor to assess its self-uncertainty and the conditional uncertainties of other sensors. This process facilitates the computation of a weighting scheme that operates recursively on sensor observations until the group reaches a consensus. Whenever new observations are made, the uncertainty estimates of sensors are updated and used to compute a new weighting scheme. To demonstrate the efficacy and to show how the methodology works, the article discusses how the method can be used to tackle the multi-sensor object identification problem. © 1993 John Wiley & Sons, Inc.

Real-Time Trajectory Generation in Multi-RCCL

Abstract: This article describes the design of the trajectory generator for a robot programming system called Multi-RCCL, which is a package of “C” routines for doing real-time manipulator control in a UNIX environment. RCCL has been used successfully in developing robot control applications in numerous research and industry facilities over the last several years. One of its strongest features is the ability to integrate real-time sensor control into the manipulator task specification. RCCL primitives supply the trajectory generator with target points for motions in joint or Cartesian coordinates. Other primitives allow the code developer to specify on-line functions that can modify the target points, or possibly cancel motion requests, in response to various sensor or control inputs. The design requirements of the trajectory generator are that it be able to integrate these on-line modifications into the overall robot motion and provide a smooth path between adjacent motions even when sensor inputs make the future trajectory uncertain. © 1993 John Wiley & Sons, Inc.

Optimal Trajectory Planning for a Space Robot Docking with a MovingTarget via Homotopy Algorithms

Abstract: The mathematical formulation of optimal trajectory planning for a space robot docking with a moving target is derived. The calculus of variations is applied to the problem so that the optimal robot trajectory can be obtained directlt from the target information without first planning the trajectory of the end-effector. The nonlinear two-point boundary value problem resulting from the problem formulation is solved numerically by a globally convergent homotopy algorithm. The algorithm guarantees convergence to a solution for an arbitrarily chosen initial guess. Numerical simulation for three examples demonstrates the approach.