关于机器人动力学模型的线性化

本文给出了一种沿标称轨迹线性化机器人动力学模型的有效方法.方法具有简单、系统、以及计算量小的优点。对于一个具有6自由度的机器人,用本文的方法建立它的线性化动力学模型(包括沿标称轨迹的广义力计算)所需要的最大计算量为2600个乘法与2711个加法,它可以在微型或小型计算机上实时实现。在计算上,本文的方法是现存所有方法中计算速度最快的.     

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.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

多移动机械臂系统动力学建模以及稳定性分析

随着社会生产力的发展和发展需求的提高,移动机械臂凭借着自身优势,受到学术界和工业界的广泛关注.但在许多工作场景下,单个移动机械臂有着自由度数以及载荷的限制,无法顺利完成任务.为了更好地满足任务需求,多移动机械臂系统应运而生.在上述工业背景下,本文建立了多移动机械臂系统的动力学模型,并针对该动力学方程进行了稳定性分析.首先通过拉格朗日方程建立单个移动机械臂的动力学方程,将多体动力学软件仿真结果同动力学模型数值计算结果进行对比,验证了模型的正确性.随后联立多个移动机械臂的动力学方程和操作对象的动力学方程,得到封闭形式的多移动机械臂系统的动力学方程.再利用关节位置误差和速度误差设计李雅普诺夫函数,通过反步法获得了关节力矩的控制律.最后在多体动力学软件仿真中,察看轨迹是否能跟踪上期望信号来检验控制律的有效性.     

Task-based configuration control of redundant manipulators

This article establishes new goals for redundancy resolution based on manipulator dynamics and end-effector characteristics. These goals can be accomplished by employing the recently developed configuration control approach. Redundancy resolution is achieved by controlling the joint inertia matrix or the end-effector mass matrix that affect the inertial torques or by reducing the joint torques due to gravity loading and payload. The manipulator mechanical advantage and velocity ratio are also used as performance measures to be improved by proper utilization of redundancy. Furthermore, end-effector compliance, sensitivity, and impulsive force at impact are introduced as redundancy-resolution criteria. The new goals for redundancy resolution presented in this article allow a more efficient utilization of the redundant joints based on the desired task requirements. Simple case studies using computer simulations are described for illustration.     

Adaptive control of free-floating space manipulators using dynamically equivalent manipulator model

In this paper, adaptive control of free-floating space manipulators is considered. The dynamics based on the momentum conservation law for the free-floating space manipulator has non-linear parameterization properties. Therefore, the adaptive control based on a linear parameterization model cannot be used in this dynamics. In this paper, the dynamics of the free-floating space manipulator system are derived using the Dynamically Equivalent Model (DEM) approach. The DEM is a fixed-base manipulator system and allows us to linearly parameterize the dynamic equations. Using this linearly parameterized dynamic equation, an adaptive control method is developed to control the system in joint space. Parameter identification and torque calculations are done using the DEM dynamics. Simulations show that the tracking errors of the manipulator joints to a given desired trajectory become zero when the calculated torques act on the joints of the space manipulator system.     

Stabilization of second-order nonholonomic systems in canonical chained form

Stabilization of a class of second-order nonholonomic systems in canonical chained form is investigated in this paper. First, the models of two typical second-order nonholonomic systems, namely, a three-link planar manipulator with the third joint unactuated, and a kinematic redundant manipulator with all joints free and driven by forces/torques imposing on the end-effector, are presented and converted to second-order chained form by transformations of coordinate and input. A discontinuous control law is then proposed to stabilize all states of the system to the desired equilibrium point exponentially. Computer simulation is given to show the effectiveness of the proposed controller.     

Application of a Perturbation Method for Realistic Dynamic Simulation of Industrial Robots

This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite element method is used to formulate the dynamic equations of the manipulator mechanism. In a closed-loop simulation the driving torques are generated by the control system. Friction torques at the actuator joints are introduced at the stage of perturbed dynamics. For a mathematical model of the friction torques we implemented the LuGre friction model that accounts both for the sliding and pre-sliding regime. To illustrate the method, the motion of a six-axes industrial Stäubli robot is simulated. The manipulation task implies transferring a laser spot along a straight line with a trapezoidal velocity profile. The computed trajectory tracking errors are compared with measured values, where in both cases the tip position is computed from the joint angles using a nominal kinematic robot model. It is found that a closed-loop simulation using a non-linear finite element model of this robot is very time-consuming due to the small time step of the discrete controller. Using the perturbation method with the linearised model a substantial reduction of the computer time is achieved without loss of accuracy.     

Dynamic tracking line: feasible tracking region of a robot inconveyor systems

The concept of dynamic tracking line is proposed as the feasible tracking region for a robot in a robot-conveyor system, which takes the conveyor speed into consideration. This paper presents an effective method to find the dynamic tracking line in a robotic workcell. The maximum permissible line-speed which is a quantitative measure of the robot capability for conveyor tracking, is defined on the basis of the relation between the end-effector speed and the bounds on the joint velocities, accelerations, and torques. This measure is derived in an analytic form using the parameterized dynamics and kinematics of the manipulator, and some of its properties are established mathematically. The problem of finding the dynamic tracking line is then formulated as a root-solving problem for a single-variable equation, and solved by the use of a simple numerical technique. Finally, numerical examples are presented to demonstrate the methodology and its applications in workspace specification.     

A new index of serial-link manipulator performance combining dynamic manipulability and manipulating force ellipsoids

The inertia matching ellipsoid (IME) is proposed as a new index of dynamic performance for serial-link robotic manipulators. The IME integrates the existing dynamic manipulability and manipulating-force ellipsoids to achieve an accurate measure of the dynamic torque-force transmission efficiency between the joint torque and the force applied to a load held by an end-effector. The dynamic manipulability and manipulating-force ellipsoids can both be derived from the IME as limiting forms, with respect to the weight of the load. The effectiveness of the IME is demonstrated numerically through the selection of an optimal leg posture for jumping robots and optimal active stiffness control, and experimentally through application to a pick-up task using a commercial manipulator. The index is also extended theoretically to the case of a manipulator mounted on a free-flying satellite.     

空间机器人捕获非合作目标后的消旋策略及阻抗控制

针对空间机器人捕获自旋目标卫星后的消旋与稳定操作提出了一种阻抗控制方法．首先,基于正序链和逆序链方法推导出空间机器人系统在操作空间中的动力学方程．然后,基于归一化时间设计了目标卫星的快速消旋策略,最优消旋时间由末端执行器的约束条件决定．最后,基于所推导操作空间下的动力学方程,提出了一种消除目标旋转运动并同时稳定基座的阻抗控制方法．在利用7自由度冗余机械臂消除自旋卫星并稳定其基座的案例中给出了仿真结果,验证了所提方法的性能及有效性．     

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.     

Multi-point impedance control for redundant manipulators

This paper proposes an impedance control method called the multi-point impedance control (MPIC) for redundant manipulators. The method can not only control end-effector impedance, but also regulate impedances of several points on the links of the manipulator, which are called virtual end-point impedances, utilizing arm redundancy. Two approaches for realizing the MPIC are presented. In the first approach, controlling the end-effector impedance and the virtual end-point impedances are considered as the tasks with the same level, and the joint control law developed in this approach can realize the closest impedances of the multiple points, including the end-effector and the virtual end-points to the desired ones in the least squared sense. On the other hand, in the second approach, controlling the end-effector impedance is considered the most important task, and regulating the impedances of the virtual end-points is considered as a sub-task. Under the second approach, the desired end-effector impedance can be always realized since the joint control torque for the regulation of the virtual end-point impedances is designed in such a way that it has no effect on the end-effector motion of the manipulator. Simulation experiments are performed to confirm the validity and to show the advantages of the proposed method.     

Dynamic Analysis and Control Synthesis of Grasping and Slippage of an Object Manipulated by a Robot

Grasping an object by a cooperating system such as multi-fingered hands and multi-manipulator robotic system has received much attention. Research has focused on analysis of force-closure grasps and the synthesis of optimal grasping, when there is no slipping condition. Although the control system is designed to keep the contact force in the friction cone and avoid the slipping condition, slippage can occur for many reasons. In this research, dynamics analysis and control synthesis of a manipulator moving an object on a horizontal surface using the contact force of an end-effector are performed considering the slipping condition. Equality and inequality equations of frictional contact conditions are replaced by a single second-order differential equation with switching coefficients in order to facilitate the dynamic modeling. Accuracy of this modeling is verified by comparing the results of the model with those of SimMech. Using this modeling of friction, a set of reduced order form is obtained for equations of motion of the system. A new method is proposed to control the object motion and the end-effector undesired slippage based on the reduced form. Finally, performance of the method is evaluated both numerically and experimentally.     

Investigation of joint clearance effects on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator

In this study, the effects of joint clearance on the dynamic performance of a planar 2-DOF pick-and-place parallel manipulator are investigated. The parallel manipulator is modeled by multi-body system dynamics. The contact effect in revolute joints with clearance is established by using a continuous analysis approach that is combined with a contact force model considering hysteretic damping. The evaluation of the contact force is based on Hertzian contact theory that accounts for the geometrical and material properties of the contacting bodies. Furthermore, the incorporation of the friction effect in clearance joints is performed using a modified Coulomb friction model. By numerical simulation, variations of the clearance joint's eccentric trajectory, the joint reaction force, the input torque, the acceleration, and trajectory of the end-effector are used to illustrate the dynamic behavior of the mechanism when multiple clearance revolute joints are considered. The results indicate that the clearance joints present two obvious separation leaps in a complete pick-and-place working cycle of the parallel manipulator, following a collision. The impact induces system vibration and thus reduces the dynamic stability of the system. The joint clearances affect the amplitudes of the joint reaction force, the input torque, and the end-effector's acceleration, additionally the joint clearances degrade the kinematic and dynamic accuracy of the manipulator's end-effector. Finally, this study proposes related approaches to decrease the effect of joint clearances on the system's dynamic properties for such parallel manipulator and prevent “separation-leap-impact” events in clearance joints.     

New optimization method to solve motion planning of dynamic systems: application on mechanical manipulators

In this paper, a new method is proposed to solve a nonlinear optimal control problem and determine the Dynamic Load-Carrying Capacity (DLCC) of fixed and mobile manipulators in point-to-point motion. Solution methods for designing nonlinear optimal controller in closed loop form are usually based on indirect methods, but the proposed method is a combination of direct and indirect methods. The optimal control law with state feedback form, for nonlinear dynamic systems, is given by the solution to the nonlinear Hamilton–Jacobi–Bellman (HJB) equation. The Galerkin procedure and a nonlinear optimization algorithm are used to solve this equation numerically. Another innovation of this paper is optimal trajectory planning, which is done simultaneously with the controller design procedure. Finally, a new algorithm is developed to find DLCC of manipulators and the related optimal trajectory using proposed method. The validity of the method is demonstrated via simulation and experimental tests for a fixed manipulator and two-link wheeled mobile manipulator named Scout.     

Hybrid control: A constrained motion perspective

Control of manipulators during execution of tasks that require the end-effector to come into contact with objects in its work environment represents an important class of control problem. Hybrid control, a concept which defines the architecture of a class of control laws has been proposed as a method with which to solve this control problem. One interpretation of the hybrid control method is within the framework of constrained motion control. Constrained motion occurs during contact by the manipulator end-effector with rigid objects in the workplace, hence the motion of the manipulator is kinematically constrained. Papers have appeared in the robotics control literature addressing hybrid control within the constrained motion context which do not explicitly use the constrained dynamic formulation that correctly describes the dynamic behaviour of the manipulator. This article serves to link results from constrained motion control and the existing literature on the hybrid control method. In this article a formulation of the constrained manipulator dynamics is presented in which the hybrid control design is most naturally carried out. This formulation of the manipulator dynamics, previously proposed in the robotics literature, is such that the generalized force and position coordinates to be controlled are mutually orthogonal. Hence, the hybrid selection matrices, a key element of the hybrid control design philosophy, are implicit in this coordinate representation. A hybrid control design methodology is then formulated based on this development. Two hybrid control laws are proposed. For each hybrid control law, the global asymptotic stability is readily established due to the natural coordinate representation. One of these hybrid control laws, a constrained motion control law already proposed in the literature, is given to illustrate the equivalence of the hybrid control design and certain existing constrained motion control methods. Finally, a concrete example of a three-degree-of-freedom robotic manipulator illustrates the hybrid design methodology proposed.     

Formulation of the kinematic model of a general (6 DOF) robot manipulator using a screw operator

In general, the manipulator's end-effector can be located in a desired position and orientation in its work-space through angular and/or linear displacements of its joints. These joint coordinates can be obtained by solving the loop-closure equation of the manipulator's kinematic model. The most common method for obtaining this equation is based on the point coordinates 4×4 homogeneous transformation matrix. This method uses a special set of frames which are adapted to the manipulator's configuration. Within the last few years there has been some interest in the use of screw operators (line transformations) to model the kinematic configuration of manipulators and to form the loop-closure equation. In this article, a kinematic model of a general (6 DOF) manipulator is obtained through the application of a screw operator (dual-unit quaternion) to represent the screw displacements of the line coordinates of the manipulator link and joint axes. The loop-closure equation of the closed kinematic chain is obtained by introducing a hypothetical link/joint at the manipulator's end-effector location. The resultant non-linear loop-closure equation is then solved for the joint coordinates using a numerical technique. The method is illustrated with an example.     

基于自适应动态规划的移动装弹机械臂轨迹控制

针对移动装弹机械臂系统非线性、强耦合、受多种不确定因素影响的问题,本文基于自适应动态规划方法,提出了仅包含评价网络结构的轨迹跟踪控制方法,有效减小了系统跟踪误差.首先,考虑到系统非线性特性、变量间强耦合作用及重力因素的影响,通过拉格朗日方程建立了移动装弹机械臂的动力学模型.其次,针对系统存在不确定性上界未知的问题,建立单网络评价结构,通过策略迭代算法,求解哈密顿–雅可比–贝尔曼方程,基于李雅普诺夫稳定性理论,设计了自适应动态规划轨迹跟踪控制方法.最后,通过仿真实验将该控制方法与自适应滑模控制方法进行了对比,进一步检验了所设计控制方法的有效性.     

Canonical parameterization of excess motor degrees of freedom withself-organizing maps

The problem of sensorimotor control is underdetermined due to excess (or "redundant") degrees of freedom when there are more joint variables than the minimum needed for positioning an end-effector. A method is presented for solving the nonlinear inverse kinematics problem for a redundant manipulator by learning a natural parameterization of the inverse solution manifolds with self-organizing maps. The parameterization approximates the topological structure of the joint space, which is that of a fiber bundle. The fibers represent the "self-motion manifolds" along which the manipulator can change configuration while keeping the end-effector at a fixed location. The method is demonstrated for the case of the redundant planar manipulator. Data samples along the self-motion manifolds are selected from a large set of measured input-output data. This is done by taking points in the joint space corresponding to end-effector locations near "query points", which define small neighborhoods in the end-effector work space. Self-organizing maps are used to construct an approximate parameterization of each manifold which is consistent for all of the query points. The resulting parameterization is used to augment the overall kinematics map so that it is locally invertible. Joint-angle and end-effector position data, along with the learned parameterizations, are used to train neural networks to approximate direct inverse functions.