Dynamic selection of actuators for lumped and distributed parameter systems

The theory of relaxed controls is used to solve the problem of selection, at each instant of time, of one out of many actuators in order to obtain a desired result. For lumped parameter systems it is shown that there exist optimal solutions for the problem involving the minimization of a quadratic cost functional. Necessary conditions for optimality are established and a numerical algorithm to determine the optimal solution is proposed. The method developed for lumped parameter systems is extended to distributed systems and, in particular, to the problem of Optimal allocation of actuators.     

Inverse dynamics based robust control method for position commanded servo actuators in robot manipulators

In this paper, a simple torque to position conversion method is proposed for position commanded servo actuators used in robot manipulators. The torque to position conversion is based on the low level controller of the servomotor. The proposed conversion law is combined with a backstepping sliding mode control method to realize a robust dynamic controller. The proposed torque based method can control a servomotor which can otherwise be operated only through position inputs. This method facilitates dynamic control for position controlled servomotors and it can be extended to position commanded robotic manipulators also. Simulation and experimental studies are conducted to validate the proposed torque to position conversion based robust control method.     

Distributed structural dynamics control of flexible manipulators —I. Structural dynamics and distributed viscoelastic actuator

Reducing structural dead weight has become of increasing importance in the design of new generation lightweight and high-speed robot manipulators. However, due to the nature of structural flexibility, the dynamic oscillation associated with robot structures can affect the operation accuracy and precision. This work, in two parts, presents a study on the vibration control of elastic or flexible robot structures. Effects of distributed passive (Part I) and active (in Part II) actuators on elastic robot structures are studied. The proposed distributed passive viscoelastic actuator (in Part I) is a layer (or layers) of viscoelastic polymer directly attached to the flexible robot element, the oscillation of which is to be controlled. The passive actuator is activated by the oscillation of the robot structure and it automatically dissipates vibration energy and constrains the undesirable motion to eliminate the disturbance and to maintain a precise robot trajectory. A finite element program capable of analyzing flexible links is developed. Results obtained from the finite element simulation are presented.     

Integrated distributed sensing and active vibration suppression of flexible manipulators using distributed piezoelectrics

Structural oscillation of flexible robot manipulators would severely hamper their operation accuracy and precision. This article presents an integrated distributed sensor and active distributed vibration actuator design for elastic or flexible robot structures. The proposed distributed sensor and actuator is a layer, or multilayer of piezoelectric material directly attached on the flexible component needed to be monitored and controlled. The integrated piezoelectric sensor/actuator can monitor the oscillation as well as actively and directly constrain the undesirable oscillation of the flexible robot manipulators by direct/converse piezoelectric effects, respectively. A general theory on the distributed sensing and active vibration control using the piezoelectric elements is first proposed. An equivalent finite element formulation is also developed. A physical model with distributed sensor/actuator is tested in laboratory; and a finite element model with the piezoelectric actuator is simulated. The distributed sensing and control effectiveness are studied.     

Control of flexible manipulators via singular perturbations and distributed vibration damping

A composite control strategy for a two-link flexible manipulator is analyzed which combines hub actuation with distributed vibration control. The hub actuation is based upon an integral manifold approach in which the system dynamics are approximately linearized to any order of a small parameter E representing stiffness of the robot arms. A polymer film is proposed as a distributed actuator to dampen vibrations due to elasticity in the links. Simulation results are provided which show that the addition of the distributed actuator significantly reduces the displacement and velocity of the first flexible mode in each link compared to hub actuation alone. Editor: T. Vincent     

On the dynamics and control of flexible joint space manipulators

Space manipulator systems are designed to have lightweight structure and long arms in order to achieve reduction of fuel consumption and large reachable workspaces, respectively. Such systems are subject to link flexibilities. Moreover, space manipulator actuators are usually driven by harmonic gear mechanisms which lead to joint flexibility. These types of flexibility may cause vibrations both in the manipulator and the spacecraft making the positioning of the end-effector very difficult. Here, both types of flexibilities are lumped at the joints and the dynamic equations of a general flexible joint space manipulator are derived. Their internal structure is highlighted and similarities and differences with fixed-base robots are discussed. It is shown that one can exploit the derived dynamic structure in order to design a static feedback linearization control law and obtain an exact linearization and decoupling result. The application of such controllers is desired in space applications due to their small computational effort. In case of fixed-base manipulators, the effective use of a static feedback controller is feasible only if a simplified model is considered. Then, the proposed static feedback linearization control law is applied to achieve end-effector precise trajectory tracking in Cartesian space maintaining a desirable non-oscillatory motion of the spacecraft. The application of the proposed controller is illustrated by a planar seven degrees of freedom (dof) system.     

A systematic method of dynamics for flexible robot manipulators

In this article, a systematic method to derive dynamic equations of motion for flexible robot manipulators is developed by using the Lagrangian assumed modes method. The proposed method can be applied to dynamic simulation and control system design for flexible robot manipulators. In the proposed method, the link deflection is described by a truncated modal expansion. The operations of only 3x3 matrices and/or 3 × 1 vectors exist in the method. All the dynamics computations are performed in the link coordinate systems, where the kinematics informations are computed with the forward recursion from the base to the hand tip and the dynamics informations are computed with the return recursion. As generally compared with other existing methods, the method proposed in this article is, computationally, more simple, systematic, and efficient. A computational simulation for a single-link flexible robot manipulator is presented to verify the proposed method. © 1992 John Wiley & Sons, Inc.     

Low-level flexible planning for mobile manipulators: a distributed perception approach

The paper proposes a method to improve flexibility of the motion planning process for mobile manipulators. The approach is based on the exploitation of perception data available only from simple proximity sensors distributed on the robot. Such data are used to correct pre-planned motions to cope with uncertainties and dynamic changes of the scene at execution time. The algorithm computes robot motion commands aimed at fulfilling the mission by combining two tasks at the same time, i.e. following the planned end-effector path and avoiding obstacles in the environment, by exploiting robot redundancy as well as handling priorities among tasks. Moreover, a technique to smoothly switch between the tasks is presented. To show the effectiveness of the method, four experimental case studies have been presented consisting in a place task executed by a mobile manipulator in an increasingly cluttered scene.     

Singularity loci of planar parallel manipulators with revolute actuators

The determination of the singularity loci of planar parallel manipulators is addressed in this paper. The inverse kinematics of two kinds of planar parallel manipulators (a two-degree-of-freedom manipulator and a three-degree-of-freedom manipulator) are first computed and their velocity equations are then derived. At the same time, the branches of the manipulators are distinguished by the introduction of a branch index K_i. Using the velocity equations, the singularity analysis of the manipulators is completed and expressions which represent the singularity of the manipulators are obtained. A polynomial form of the singularity loci is also derived. For the first type of singularity of parallel manipulators, the singularity locus is obtained by finding the workspace limits of the manipulators. For the second type of singularity, the loci are obtained through the solution of nonlinear algebraic equations obtained from the velocity analysis. Finally, the graphical representation of the complete singularity loci of the manipulators is illustrated with examples. The algorithm introduced in this paper allows the determination of the singularity loci of planar parallel manipulators with revolute actuators, which has been elusive to previous approaches.     

Efficient workspace generation for binary manipulators with many actuators

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. Major benefits of binary actuation are that extensive feedback control is not required, task repeatability can be very high, and two-state actuators are generally very inexpensive, thus resulting in low-cost robotic mechanisms. Determining the workspace of a binary manipulator is of great practical importance for a variety of applications. For instance, a representation of the workspace is essential for trajectory tracking, motion planning, and the optimal design of binary manipulators. Given that the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, 0(2), brute force representation of binary manipulator workspaces is not feasible in the highly actuated case. This article describes an algorithm that performs recursive calculations starting at the end-effector and terminating at the base. The implementation of these recursive calculations is based on the macroscopically serial structure and the discrete nature of the manipulator. As a result, the method is capable of approximating the workspace in linear time, O(n), where the slope depends on the acceptable error. © 1995 John Wiley b Sons, Inc.     

基于分布参数机械臂协调操作柔性负载双时标控制

基于分布参数系统理论,建立机械臂协调操作柔性负载系统的动力学模型.利用奇异摄动方法,对动力学模型进行双时标分解,得到一个表征系统大范围刚性运动的集中参数慢变子系统和表征系统弹性振动的分布参数快变子系统.分别设计了自适应模糊滑模慢变控制器和振动反馈快变控制器,并通过分析快变子系统主算子及其生成C_O半群的特性,证明了分布参数闭环子系统的渐近稳定性.最后,通过仿真实验验证了所提出方法的有效性.     

Inverse dynamics of redundant manipulators using a minimum number of control forces

The number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for generating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum number of actuators is proposed. The number of actuators is equal to the dimension of the task space, and the control forces are solved simultaneously with the corresponding system motion. It is shown that because all degrees of freedom are not actuated, the control forces may lose the ability to make an instantaneous effect on the end-effector acceleration at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in the neighborhood of the singular configurations by utilizing higher-order derivative information, so that the singularities in the numerical procedure are avoided. Asymptotically stable inverse dynamics closed-loop control in the presence of perturbations is also discussed. The algorithm is further generalized to closed chain manipulators. Three-link and two-link redundant planar manipulators are analyzed to illustrate the validity of the approach. © 2995 John Wiley & Sons, Inc.     

Control of constrained manipulators with flexible joints

This paper presents results on control design of constrained manipulators with flexible joints. It will be assumed that such manipulators are under gravity and contact reaction effects. It is also assumed that measurable joint variables are limited to rotor angles and its velocities. A simple biased proportional and derivative feedback controller is shown to be able to drive the manipulator to a desired configuration specified in link angles with desired contact force specified in the direction normal to the constraint surface at the desired position. A sufficient condition for global stability will be established by using a Lyapunov function which is constructed taking into account the spring stiffness, gravity factors and constraint functions. An example is studied and computer simulation results are presented to show closed-loop performance. Editor: M. Corless     

Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach

An inverse dynamics control algorithm is developed for hybrid motion and contact force trajectory tracking control of flexible joint parallel manipulators. First, an open-tree structure is considered by the disconnection of adequate number of unactuated joints. The loop closure constraint equations are then included. Elimination of the joint reaction forces and the other intermediate variables yield a fourth-order relation between the actuator torques and the end-effector position and contact force variables, showing that the control torques do not have an instantaneous effect on the end-effector contact forces and accelerations because of the flexibility. The proposed control law provides simultaneous and asymptotically stable control of the end-effector contact forces and the motion along the constraint surfaces by utilizing the feedback of positions and velocities of the actuated joints and rotors. A two degree of freedom planar parallel manipulator is considered as an example to illustrate the effectiveness of the method.     

Adaptive control of robot manipulators with flexible joints

Presents an adaptive control scheme for flexible joint robot manipulators. Asymptotic stability is insured regardless of the joint flexibility value, i.e., the results are not restricted to weak joint elasticity. Moreover, the joint flexibility is not assumed to be known. Joint position and velocity tracking errors are shown to converge to zero with all the signals in the system remaining bounded     

An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators

In this article, we present an inverse dynamics control strategy to achieve small tracking errors for a class of multi-link structurally flexible manipulators. This is done by defining new outputs near the end points of the arms as well as by augmenting the control inputs by terms that ensure stable operation of the closed loop system under specific conditions. The controller is designed in a two-step process. First, a new output is defined such that the zero dynamics of the original system are stabilized. Next, to ensure stable asymptotic tracking, the control input is modified such that stable asymptotic tracking of the new output or approximate tracking of the actual output may be achieved. This is illustrated for the case of single- and two-link flexible manipulators. ©1997 John Wiley & Sons, Inc.     

Sensors and actuators in distributed systems

The concepts of strategic sensors and actuators are introduced for a class of distributed parameter systems. This emphasizes the spatial structure and location of the sensors and controls in order that observability and controllability can be achieved.     

Time-optimal control of kinematically redundant manipulators with limit heat characteristics of actuators

In this study, we present a time-optimal control scheme for kinematically redundant manipulators to track a predefined geometric path, subject to the limit heat characteristics of actuators (a DC motor was assumed to be the actuator used). Constraints due to the rated torque and the rated velocity of the motor would not be valid for continuous use of manipulators, since the required mechanical output of the actuator (DC motor) exceeds its maximum power capacity and far more exceeds its heat-converted power limit. The heat-converted power limit of the DC motor is thus considered as the actuation bound of the actuator and the time-optimal trajectories are generated by using the phase-plane analysis and the linear programming technique subject to this bound. Computer simulation was also executed on a three-link planar rotary manipulator to demonstrate the effectiveness of the proposed scheme.     

A new inverse kinematics algorithm for binary manipulators with many actuators

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadthfirst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the 'mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briefly describe a new manipulator design for which this algorithm is applicable.     

Inverse kinematics of variable-geometry truss manipulators

A new class of robotic arm consists of a periodic sequence of truss substructures, each of which has several variable-length members. Such variable-geometry truss manipulators (VGTMs) are inherently highly redundant and promise a significant increase in dexterity over conventional anthropomorphic manipulators. This dexterity may be exploited for both obstacle avoidance and controlled deployment in complex workspaces. The inverse kinematics problem for such unorthodox manipulators, however, becomes complex because of the large number of degrees of freedom, and conventional solutions to the inverse kinematics problem become inefficient because of the high degree of redundancy. This paper presents a solution to this problem based on a spline-like reference curve for the manipulator's shape. Such an approach has a number of advantages: (1) direct, intuitive manipulation of shape; (2) reduced calculation time; and (3) direct control over the effective degree of redundancy of the manipulator. Furthermore, although the algorithm has been developed primarily for variable-geometry-truss manipulators, it is general enough for application to other manipulator designs.