Force and acceleration sensor fusion for compliant manipulation control in 6 degrees of freedom

This paper focusses on sensor fusion in robotic manipulation: six-dimensional (6-D) force/torque signals and 6-D acceleration signals are used to extract forces and torques caused by inertia. As result, only forces and torques established by environmental contact(s) remain. Apart from an improvement of hybrid force/pose control behavior, an additional major benefit is that regular resetting/zeroing of force/torque sensors before free space/contact transitions can be omitted. All essential equations, transformations and calculations that are required for this 6-D fusion approach are derived. To highlight the meaning for practical implementations, numerous experiments with a six-joint Staeubli RX60 industrial manipulator are presented and the achieved results are discussed.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Feedback control for robotic manipulator with an uncertain Jacobian matrix

In most applications of robots, a desired path for the end‐effector is usually specified in task space such as Cartesian space. One way to move the robot along this path is to solve the inverse kinematics problem to generate the desired angles in joint space. However, it is a very time consuming task to solve the inverse kinematics problem. Furthermore, in the presence of uncertainty in kinematics, it is impossible to derive the desired joint angle from the desired end‐effector path and the Jacobian matrix of the mapping from joint space to task space. In this article, a feedback control law using an uncertain Jacobian matrix is proposed for setpoint control of robots. Sufficient conditions for the bound of the estimated Jacobian matrix and stability conditions for the feedback gains are presented to guarantee the stability and passivity of the robots. A gravity regressor with an uncertain Jacobian matrix is also proposed for gravitational force compensation when the gravitational force is uncertain. Simulation results are presented to illustrate the performance of the proposed controllers. ©1999 John Wiley & Sons, Inc.     

Two-stage adaptive robot position/force control using fuzzy reasoning and neural networks

Many studies have been performed on the position/force control of robot manipulators. Since the desired position and force required to realize certain tasks are usually designated in the operational space, the controller should adapt itself to an environment and generate the control force vector in the operational space. On the other hand, the friction of each joint of a robot manipulator is a serious problem since it impedes control accuracy. Therefore, the friction should be effectively compensated for in order to realize precise control of robot manipulators. Recently, soft computing techniques (fuzzy reasoning, neural networks and genetic algorithms) have been playing an important role in the control of robots. Applying the fuzzy-neuro approach (a combination of fuzzy reasoning and neural networks), learning/adaptation ability and human knowledge can be incorporated into a robot controller. In this paper, we propose a two-stage adaptive robot manipulator position/force control method in which the uncertain/unknown dynamic of the environment is compensated for in the task space and the joint friction is effectively compensated for in the joint space using soft computing techniques. The effectiveness of the proposed control method was evaluated by experiments.     

Robust motion control with the consideration algorithm of joint torque saturation for a redundant manipulator

As each joint actuator of a robot manipulator has a limit value of torque, the motion control system should consider the torque saturation. In order to consider the torque saturation in a transient state, this paper proposes a new redundant motion control system using the autonomous consideration algorithm on torque saturation. A Jacobian matrix of a redundant robot manipulator can select the optimal one considering its motion energy in the steady state. When the motion control system carries out fast motion and quick disturbance suppression, a high joint torque is required in a transient state. In the experimental results, under the condition of having a large payload torque and a fast motion reference, the proposed redundant manipulator control realizes the quick robot motion robustly and smoothly.     

Muscle force distribution for adaptive control of a humanoid robot arm with redundant bi-articular and mono-articular muscle mechanism

Robot arms driven by bi-articular and mono-articular muscles have numerous advantages. If one muscle is broken, the functionality of the arm is not influenced. In addition, each joint torque is distributed to numerous muscles, and thus the load of each muscle can be relatively small. This paper addresses the problem of muscle control for this kind of robot arm. A relatively mature control method (i.e. sliding mode control) was chosen to get joint torque first and then the joint torque was distributed to muscle forces. The muscle force was computed based on a Jacobian matrix between joint torque space and muscle force space. In addition, internal forces were used to optimize the computed muscle forces in the following manner: not only to make sure that each muscle force is in its force boundary, but also to make the muscles work in the middle of their working range, which is considered best in terms of fatigue. Besides, all the dynamic parameters were updated in real-time. Compared with previous work, a novel method was proposed to use prediction error to accelerate the convergence speed of parameter. We empirically evaluated our method for the case of bending-stretching movements. The results clearly illustrate the effectiveness of our method towards achieving the desired kinetic as well as load distribution characteristics.     

Final-state control of a two-link cat robot

In this study, we deal with the twisting motion of a falling cat robot by means of two torque inputs around her waist. The cat robot consists of two rigid columns and has two internal actuators at the joint to generate torque inputs around normal coordinates. This system is a nonholonomic system whose angular momentum is conserved. We formulate the state equation that has torque inputs to the joint by using the nonholonomic constraint and the Lagrange-d'Alembert principle. Then, we transform the system into a linear parameter varying system. In order to improve error learning of a final-state control method, we provide the initial inputs in order to determine the appropriate rotation direction in the early stage of the twisting motion. Next, we introduce the method of the artificial potential function to the final-state control in order to make the maximum bending angle small. The feedforward torque inputs can be obtained by the final-state control in order to bring the system from the initial state to the final state in the desired time. In simulations, we also demonstrate that the twolink cat robot can land on her feet by using the 2-d.o.f. control system even when her waist damping coefficient varies.     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

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.     

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。     

The jacodian matrix for a flexble manipulator

This article develops the exact first-order endpoint Jacobian matrix for a general n-degrees of freedom tree-like robot with flexible links. The Jacobian is developed in terms of the joint axes, the link deformations, and the relative position vectors using cross products. To have the correct first-order endpoint Jacobian matrix, the second-order kinematics is used to describe a flexible link. Using two local Jacobian matrices enables to write the endpoint Jacobian sub-matrix associated to a flexible link, which is similar to the column of the Jacobian associated to a joint. An example with a one-link flexible arm rotating in a vertical plane illustrates the usefulness of the endpoint Jacobian in calculating the torque required to apply an endpoint force and the link deformation resulting from this force. An experimental verification proves the validity of the developed Jacobian and suggests that using only first-order kinematics results in serious errors in the prediction of the beam's curvatures and deformations © 1995 John Wiley & Sons, Inc.     

Motion teaching method for complex robot links using motor current

Conventional robot motion teaching methods use a teaching pendant or a motion capture device and are not the most convenient or intuitive ways to teach a robot sophisticated and fluid movements such as martial arts motions. Ideally, a robot could be set up as if it were a clothing mannequin that has light limbs and flexible yet frictional joints which can be positioned at desirable shape and hold all the positions. To do the same with a robot, an operator could pull or push the links with minor forces until the desired robot posture is attained. For this, a robot should measure the applied external force by using torque sensors at the robot joints. However, torque sensors are bulky and expensive to install in every DOF joints while keeping a compact design, which is essential to humanoid robots. In this paper, we use only motor current readings to acquire joint torques. The equations used to compensate for the effect of gravity on the joint torques and the self-calibration method to earn link parameters are presented. Additionally, kinematic restrictions can be imposed on the robot’s arms to simplify the motion teaching. Here, we teach the Kendo training robot with this method and the robot’s learnt martial art motions are demonstrated.     

Robust trajectory planning for robotic manipulators under payload uncertainties

A number of trajectory planning algorithms are available for determining the joint torques, positions, and velocities required to move a manipulator along a given geometric path in minimum time. These schemes require knowledge of the robot's dynamics, which in turn depend upon the characteristics of the payload which the robot is carrying. In practice, the dynamic properties of the payload will not be known exactly, so that the dynamics of the robot, and hence the required joint torques, must be calculated for a nominal set of payload characteristics. But since these trajectory planners generate nominal joint torques which are at the limits of the robot's capabilities, moving the robot along the desired geometric path at speeds calculated for the nominal payload may require torques which exceed the robot's capabilities. In this paper, bounds on joint torque uncertainties are derived in terms of payload uncertainties. Using these bounds, a new trajectory planner is developed to incorporate payload uncertainties such that all the trajectories generated can be realized with given joint torques. Finally, the trajectory planner is applied to the first three joints of the Bendix PACS arm, a cylindrical robot to demonstrate its use and power.     

An Experimental Study on Cartesian Impedance Control for a Joint Torque-Based Manipulator

The purpose of this paper is to present our results on experimental investigations on Cartesian impedance control and nonlinearity compensation for our harmonic drive robot based on joint torque sensors. The imperfection of the cubic model for harmonic drive friction is detected according to friction identification experiments. In addition, five different Cartesian impedance control schemes are considered and four of them are tested by corresponding experiments with/without friction compensation. Experimental results tell us that the force-based impedance control strategy is more suitable than the position-based strategy for the harmonic drive robot based on joint torque feedback.     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

机器人在任务空间的变结构跟踪控制

本文提出了一种面向任务空间的机器人变结构控制算法.该算法不需要从任务空间到关 节空间的坐标变换,直接利用任务坐标计算控制力矩.变结构控制的主要思想在于将复杂的 切换条件问题离线进行,从而庞复的动力学实时控制的计算问题可以迎刃而解.     

Balancing of humanoid robot using contact force/moment control by task-oriented whole body control framework

Balancing control of humanoid robots is of great importance since it is a necessary functionality not only for maintaining a certain position without falling, but also for walking and running. For position controlled robots, the for-ce/torque sensors at each foot are utilized to measure the contact forces and moments, and these values are used to compute the joint angles to be commanded for balancing. The proposed approach in this paper is to maintain balance of torque-controlled robots by controlling contact force and moment using whole-body control framework with hierarchical structure. The control of contact force and moment is achieved by exploiting the full dynamics of the robot and the null-space motion in this control framework. This control approach enables compliant balancing behavior. In addition, in the case of double support phase, required contact force and moment are controlled using the redundancy in the contact force and moment space. These algorithms are implemented on a humanoid legged robot and the experimental results demonstrate the effectiveness of them.     

Torque Distribution in a Six-Legged Robot

In this paper, distribution of required forces and moments to the supporting legs of a six-legged robot is handled as a torque-distribution problem. This approach is comparatively contrasted to the conventional approach of tip-point force distribution. The formulation of dynamics is performed by using the joint torques as the primary variables. The sum of the squares of the joint torques on the supporting legs is considered to be proportional to the dissipated power. The objective function is constructed as this sum, and the problem is formulated as to minimize this quadratic objective function with respect to linear equality and inequality constraints. It is demonstrated that the torque-distribution scheme results in a much more efficient distribution compared with the conventional scheme of force distribution. In contrast to the force distribution, the torque-distribution scheme makes good use of interaction forces and friction in order to minimize the required joint torques     

A Position and Torque Switching Control Method for Robot Collision Safety

With the increasing number of human-robot interaction applications, robot control characteristics and their effects on safety as well as performance should be taken account into the robot control system. In this paper, a position and torque switching control method was proposed to improve the robot safety and performance, when robots and humans work in the same space. The switching control method includes two modes, the position control mode using a proportion-integral (PI) algorithm, and the torque control mode using sliding mode control (SMC) algorithm for eliminating swing. Under the normal condition, the robot works in position control mode for trajectory tracking with quick response. Once the robot and human collide, the robot will switch to torque control mode immediately, and the impact force will be restricted within a safe range. When the robot and human detach, the robot will resume to position control mode automatically. Moreover, for a better performance, the joint torque is detected from direct-current (DC) motor’s current rather than the torque sensor. The experiment results show that the proposed approach is effective and feasible.     

机器人多指操作的递阶控制

为机器人多指协调操作建立一递阶控制系统.给定一操作任务,任务规划器首先生 成一系列物体的运动速度;然后,协调运动规划器根据期望的物体运动速度生成期望的手指 运动速度和期望的抓取姿态变化;同时,抓取力规划器为平衡作用在物体上的外力,根据当前 的抓取姿态,生成各手指所需的抓取力;最后,系统将手指的期望运动速度与为实现期望抓取 力而生成的顺应速度合并,并通过手指的逆雅可比转化为手指关节运动速度后,由手指的关 节级运动控制器实现手指的运动和抓取力的控制.该控制方法已成功应用于香港科技大学 (HKUST)灵巧手控制系统的开发.实验证明该方法不仅能完成物体轨迹的跟踪控制任务, 而且能完成物体对环境的力控制和力与速度的混合控制.