Global positioning of robot manipulators via PD control plus aclass of nonlinear integral actions

Deals with the position control of robot manipulators. Proposed is a simple class of robot regulators consisting of a linear proportional-derivative (PD) feedback plus an integral action of a nonlinear function of position errors. By using Lyapunov's direct method and LaSalle's invariance principle, the authors characterize a class of such nonlinear functions, and they provide explicit conditions on the regulator gains to ensure global asymptotic stability. These regulators offer an attractive alternative to global regulation compared with the well-known partially model-based PD control with gravity compensation and PD control with desired gravity compensation     

Pid Regulation Of Robot Manipulators With Elastic Joints

This paper studies the stability of a class of PID controller to stabilize robot manipulators with elastic joints. It is shown that a PD action on the rotor position and an integral control action on the link position suffice to provide semiglobal asymptotic stability of the desired link position.     

Elasto-geometrical error and gravity model calibration of an industrial robot using the same optimized configuration set

Position error is a significant limitation for industrial robots in high-precision machining and manufacturing. Efficient error measurement and compensation for robots equipped with end-effectors are difficult in industrial environments. This paper proposes a robot calibration method based on an elasto–geometrical error and gravity model. Firstly, a geometric error model was established based on the D-H method, and the gravity and compliance error models were constructed to predict the elastic deformation caused by the self-weight of the robot. Subsequently, the position error model was established by considering the attitude error of the robot flange coordinate system. A two-step robot configuration selection method was developed based on the sequential floating forward selection algorithm to optimize the robot configuration for calibrating the position error and gravity models. Then, the geometric error and compliance coefficient were identified simultaneously based on the hybrid evolution algorithm. The gravity model parameters were identified based on the same algorithm using the joint torque signal provided by the robot controller. Finally, calibration and compensation experiments were conducted on a KR-160 industrial robot equipped with a spindle using a laser tracker and internal robot data. The experimental results show that the robot tool center point error can be significantly improved by using the proposed method.     

On the Passivity-Based Impedance Control of Flexible Joint Robots

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.     

A simple PD controller for robots with elastic joints

The point-to-point control of manipulators having elastic joints is considered. It is shown that a simple PD (proportional plus derivative) controller, similar to that used for rigid robots, suffices to globally stabilize the elastic joint robots about a reference position. A robustness analysis is also given with respect to uncertainties on the robot parameters. The results of numerical simulation tests of a manipulator with three revolute elastic joints are presented     

Estimation and Compensation of Gravity and Friction Forces for Robot Arms: Theory and Experiments

This paper considers the estimation and compensation of the unknown gravity force and static friction for robot motion control. Utilizing the stability feature of PD set-point control, the estimates of gravity-related parameters and static friction can be solved from two steady state equations obtained by stopping robots at two nonsingular positions. The estimates obtained can then be used to eliminate the position error. Under a mild assumption that the mass center of each robot link is distributed on a straight line connecting two adjacent joints, the gravity force regression matrix becomes upper-triangle which can significantly simplify the algorithm. The positive experimental result obtained for practical verification is also presented.     

Polynomial family of PD-type controllers for robot manipulators

This paper addresses the problem of position control for robot manipulators. A new polynomial family of PD-type controllers with gravity compensation for the global position of robots manipulators is presented. The previous results on the linear PD controller are extended to the proposed polynomial family. The classical PD controller can be found among this large class of controllers when its proportional gain is a diagonal matrix. The main contribution of this paper is to prove that the closed-loop system composed by full nonlinear robot dynamics and the proposed family of controllers is globally asymptotically stable in agreement with Lyapunov's direct method and LaSalle's invariance principle. Besides the theoretical results, a real-time experimental comparison is also presented to illustrate the performance of the proposed family with other well-known control algorithms such as PD and PID schemes on a three degrees of freedom direct-drive arm.     

PD manipulator controller with fuzzy adaptive gravity compensation

This paper presents a PD manipulator controller with fuzzy adaptive gravity compensation. The main idea is to use a fuzzy adaptive controller to compensate for the gravity term of the robotic manipulator. This controller is designed by using Lyapunov's stability theorem, which guarantees system stability. Simulation is implemented on a two‐link manipulator by using MATALAB and SIMULINK. The results show that this fuzzy adaptive controller makes the manipulator trajectory converge to a desired position. Compared with other proposed fuzzy adaptive manipulator controllers, the PD manipulator controller with fuzzy adaptive gravity compensation is conceptually and structurally simpler and guarantees zero position error. ©2000 John Wiley & Sons, Inc.     

Tracking in nonlinear differential-algebraic control systems with applications to constrained robot systems

We consider the design of a feedback control law for control systems described by a class of nonlinear differential-algebraic equations so that certain desired outputs track given reference inputs. The nonlinear differential-algebraic control system being considered is not in state variable form. Assumptions are introduced and a procedure is developed such that an equivalent state realization of the control system described by nonlinear differential-algebraic equations is expressed in a familiar normal form. A nonlinear feedback control law is then proposed which ensures, under appropriate assumptions, that the tracking error in the closed loop differential-algebraic system approaches zero exponentially. Applications to simultaneous contact force and position tracking in constrained robot systems with rigid joints, constrained robot systems with joint flexibility, and constrained robot systems with significant actuator dynamics are discussed.     

An output feedback parallel force/position regulator for a robot manipulator in contact with a compliant environment

In this paper the problem of regulating force and position for a robot manipulator in contact with an elastically compliant environment is considered. In the framework of parallel force/position control, an output feedback regulator with gravity compensation and desired force feedforward is proposed which only requires measurements of force and position. Semiglobal stability of the closed-loop system around the equilibrium is shown via a Lyapunov argument.     

Walking pattern generation for a humanoid robot with compliant joints

This work presents a walking pattern generator based on the control of the center of mass (COM) states and its experimental validations on the compliant humanoid robot COMAN powered by intrinsically compliant joints. To cope with the inaccuracies of the joint position tracking resulted by the physical compliance, the proposed pattern generator uses the feedback states of the COM and on-line computes the updated COM references. The position and velocity of the COM are the state variables, and the constrained ground reaction force (GRF) limited by the support polygon is the control effort to drive the real COM states to track the desired references. The frequency analysis of the COM demonstrates its low frequency spectrum that indicates the demand of a low control bandwidth which is suitable for a robot system with compliant joints. The effectiveness of the proposed gait generation method was demonstrated by the experiments performed on the COMAN robot. The experimental data such as the COM position and velocity tracking, the GRF applied on feet, the measured step length and the walking velocity are analyzed. The effect of the passive compliance is also discussed.     

Decoupling and tracking control for elastic joint robots with coupled joint structure

The paper deals with the modeling, identification, and control of a flexible joint robot developed for medical applications at the German Aerospace Center (DLR). In order to design anthropomorphic kinematics, the robot uses a coupled joint structure realized by a differential gearbox, which however leads to strong mechanical couplings inside the coupled joints and must be taken into account. Therefore, a regulation MIMO state feedback controller based on modal analysis is developed for each coupled joint pair, which consists of full state feedback (motor position, link side torque, as well as their derivatives). Furthermore, in order to improve position accuracy and simultaneously keep good dynamic behavior of the MIMO state feedback controller, a cascaded tracking control scheme is proposed, based on the MIMO state feedback controller with additional feedforward terms (desired motor velocity, desired motor acceleration, derivative of the desired torque), which are computed in a computed torque controller and take the whole rigid body dynamics into account. Stability analysis is shown for the complete controlled robot. Finally, experimental results with the DLR medical robot are presented to validate the practical efficiency of the approaches.     

矢量场逐次逼近的康复机器人柔顺交互控制

为了实现康复机器人的主动柔顺交互,提出了一种基于矢量场逐次逼近的控制模型;设计了矢量场逐次逼近系统,可输出机器人关节期望位移,该输出能与输入的扭矩、表面肌电及脑电等信号在振幅、频率和相位上保持同步,且通过调节遗忘因子参数值,可改变主动柔顺交互的积极性;利用自行设计的穿着型下肢康复机器人样机进行柔顺辅助实验,以验证所提出控制模型的有效性;通过FFT（Fast Fourier transformation）频谱对机器人关节扭矩的组成成分进行了分析,并采用基于最小二乘法的参数辨识方法实施了重力补偿,以便康复机器人实时控制.实验结果表明,该控制模型对于实现康复机器人与人之间的柔顺交互是有效的.     

A semiglobally stable output feedback PI2D regulator forrobot manipulators

Provides an answer to the long-standing question of designing asymptotically stable proportional plus integral regulators with only position feedback for robots with uncertain payload. It has previously been shown in Kelly (1993) and Ailon and Ortega (1993) that globally asymptotically stable set-point regulators for robot manipulators without velocity measurement can be obtained replacing the velocity feedback of a proportional plus derivative controller by a filtered position feedback. In these schemes, the only robot prior information required is the evaluation of the gravity forces at the reference (constant) position. This prior knowledge is used to shape the robot potential energy to have a unique minimum at the desired position. A mismatch in the estimation of the gravity forces leads to a position steady-state error. The authors' main contribution in this paper is to obviate the need of this prior information via the inclusion of two integral terms, around the position error and the filtered position, respectively. Semiglobal stability of the resulting control law is established     

Control of Robots with Elastic Joints Interacting with Dynamic Environment

In this paper, the control of robots with elastic joints in contact with dynamic environment is considered. It is shown how control laws synthesized for the robots with rigid joints interacting with dynamic environment can also be used in the case of robots with elastic joints. The proposed control laws are based on a robot model interacting with dynamic environment, including the dynamics of actuators and the elasticity of joints. The proposed control laws possess two feedback loops: the outer, serving for on-line calculation of the motor shaft angle based on the position error or the contact force error, and the inner one, serving for performing stabilization around the calculated motor shaft angle. Simulation results which exhibit the application of the appropriate control laws are also presented.     

Nonlinear Feedback Control of a Gravity-Assisted Underactuated Manipulator With Application to Aircraft Assembly

A nonlinear feedback scheme for a gravity-assisted underactuated manipulator with second-order nonholonomic constraints is presented in this paper. The joints of the hyper articulated arm have no dedicated actuators but are activated by gravity. By tilting the base link appropriately, the gravitational torque drives the unactuated links to a desired angular position. With simple locking mechanisms, the hyperarticulated arm can change its configuration using only one actuator at the base. This underactuated arm design was motivated by the need for a compact snake-like robot that can go into aircraft wings and perform assembly operations using heavy end-effectors. The dynamics of the unactuated links are essentially second-order nonholonomic constraints for which there are no general methods to design closed-loop control. We propose a nonlinear closed-loop control law that is guaranteed to be stable in positioning one unactuated joint at a time. We synthesize a Lyapunov function to prove the convergence of this control scheme. The Lyapunov function also generates estimates of the domain of convergence of the control law for various control gains. The control algorithm is implemented on a prototype three-link system. Finally, we provide some experimental results to demonstrate the efficacy of the control scheme.     

Trajectory Tracking for Underwater Swimming Manipulators using a Super Twisting Algorithm

The underwater swimming manipulator (USM) is a snake‐like, multi‐articulated, underwater robot that is equipped with thrusters. One of the main purposes of the USM is to act like an underwater floating base manipulator. As such, it is essential to achieve good station‐keeping and trajectory tracking performance for the USM by using the thrusters and by using the joints to attain the desired position and orientation of the head and tail of the USM. In this ‘paper, we propose a sliding mode control (SMC) law, specifically the super‐twisting algorithm with adaptive gains, for the trajectory tracking of the USM's centre of mass. A higher‐order sliding mode observer is proposed for state estimation. Furthermore, we show the ultimate boundedness of the tracking errors. We demonstrate the applicability of the proposed control law and show that it leads to better performance than a linear PD‐controller.     

Robustness analysis of a pd controller with approximate gravity compensation for robot manipulator control

Asymptotically stable robot manipulator control in both joint space and Cartesian space can be achieved by using a PD controller with gravity torque compensation. However, the stability of this class of control law has not been analyzed with the use of estimated gravity torques. The objective of this article is to present such a stability proof assuming uncertainty in the gravity estimate. The proof is carried out for the Cartesian space controller. The result is supported by computer simulation. © 1994 John Wiley & Sons, Inc.     

卫星天线展开臂的随动吊挂重力补偿系统设计

为了给卫星天线展开臂的展开特性测试提供真实的零重力地面仿真环境,设计了卫星天线随动吊挂重力补偿系统.首先设计了与卫星天线展开臂结构相同的3轴随动吊挂机械臂,对卫星天线展开臂进行位置跟随,并通过有限元方法分析其受载时的位置精度;然后根据导纳控制方法设计出随动机械臂的力跟随控制器,采用基于位置内环的PD （比例-微分）力控制策略设计出拉力系统对吊索拉力的控制算法;最后通过实验考核了随动吊挂机械臂各关节对在轨运行模式下的天线展开臂相应关节的位置跟随性能和重力平衡补偿.实验结果表明各轴位置跟随误差均不超过±0.03°,稳定运行时吊索张力控制偏差均小于1.2% F.S.（全量程）,在天线展开机械臂的展开过程中实现了较高精度的位置跟随和重力补偿,满足天线展开测试要求.     

On generating the motion of industrial robot manipulators

In this study, an intelligent search algorithm is proposed to define the path that leads to the desired position and orientation of an industrial robot׳s manipulator end effector. The search algorithm gradually approaches the desired configuration by selecting and evaluating a number of alternative robot׳s configurations. A grid of the robot׳s alternative configurations is constructed using a set of parameters which are reducing the search space to minimize the computational time. In the evaluation of the alternatives, multiple criteria are used in order for the different requirements to be fulfilled. The alternative configurations are generated with emphasis being given to the robot׳s joints that mainly affect the position of the end effector. Grid resolution and size parameters are set on the basis of the desired output. High resolution is used for a smooth path and lower for a rough estimation, by providing only a number of the intermediate points to the goal position. The path derived is a series of robot configurations. This method provides an inexperienced robot programmer with flexibility to generate automatically a robotic path that would fulfill the desired criteria without having to record intermediate points to the goal position.