Two recurrent neural networks for local joint torque optimizationof kinematically redundant manipulators

This paper presents two neural network approaches to real-time joint torque optimization for kinematically redundant manipulators. Two recurrent neural networks are proposed for determining the minimum driving joint torques of redundant manipulators for the eases without and with taking the joint torque limits into consideration, respectively. The first neural network is called the Lagrangian network and the second one is called the primal-dual network. In both neural-network-based computation schemes, while the desired accelerations of the end-effector for a specific task are given to the neural networks as their inputs, the signals of the minimum driving joint torques are generated as their outputs to drive the manipulator arm. Both proposed recurrent neural networks are shown to be capable of generating minimum stable driving joint torques. In addition, the driving joint torques computed by the primal-dual network are shown never exceeding the joint torque limits.     

Improving local torque optimization techniques for redundant robotic mechanisms

Two techniques that improve existing local torque optimization methods for redundant robotic mechanisms are proposed. The first technique is based on a balancing scheme, which balances a joint torque norm against a norm of joint accelerations. Expressions have been derived utilizing the Lagrangian multipliers method. The other technique is based on a torque optimization method which minimizes torques through accelerations, obtained from the null-space of the Jacobian matrix. These accelerations are balanced against the minimum-norm acceleration component in order to improve the performance. Numerical simulations have been carried out which in most cases illustrate good performance capability from the viewpoint of torque optimization and global stability.     

Force polytope and force ellipsoid for redundant manipulators

Evaluation of force/motion capabilities for a manipulator is useful both in the design phase and in the operational phase. Manipulability ellipsoids and polytopes are well-known tools used to represent these capabilities graphically. This article focuses on the evaluation of force capabilities for redundant manipulators, for which additional constraints must be imposed on the available joint torques to satisfy the static assumption. An algorithm to correctly evaluate the task space force polytope is given and a new definition of the force ellipsoid is proposed. The obtained results can be applied also to nonredundant manipulators in singular configurations. Numerical results are provided in the case of a planar redundant arm. ©1997 John Wiley & Sons, Inc.     

Static modeling and control of redundant manipulators

This paper develops unified static models for control of a redundant manipulator. We introduce the Premultiplier Diagram to describe the static behavior of a redundant manipulator. This diagram provides insight into the algebra and physics related to redundant manipulators. We derive redundancy expressions for the joint displacement, joint torque and joint stiffness matrix. These redundancy expressions are composed of a particular (net) part and a homogeneous (null) part. Based on the orthogonality property between the net and the null components, we propose an extension of the stiffness control scheme for redundant manipulators. We also show how the decomposed and decoupled static behavior of redundant manipulators can be used to derive an optimal control strategy.     

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

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.     

A balancing technique to stabilize local torque optimization solution of redundant manipulators

A technique that stabilizes the existing local torque optimization solutions for redundant manipulators is proposed in this article. The technique is based on a balancing scheme, which balances a solution of joint torque-minimization against a solution of joint velocity-minimization. Introducing the solution of joint velocity-minimization in the approach prevents occurrence of high joint velocities, and thus results in stable optimal arm motions and guarantees the joint velocities at end of motion to be near zero. Computer simulations were executed on a three-link planar rotary manipulator to verify the performance of the proposed local torque optimization technique and to compare its performance with existing ones for various straight line trajectories. © 1996 John Wiley & Sons, Inc.     

柔性冗余度机器人力矩优化的研究

本文首先应用模态理论，对柔性冗余度机器人振动的控制问题的原理与策略进行了研究．在此基础上通过对满足抑振要求的自运动的选取进行分析，指出柔性冗余度机器人在通过优化其自运动实现振动抑制的同时还具有二次优化的能力，并给出了在满足抑振的前提下实现关节力矩优化的方法．最后对一个末杆为柔杆的平面三杆机械手的振动控制与力矩优化进行了仿真，结果验证了该方法的可行性．     

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.     

A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation

The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit–Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant manipulators. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation satisfies the equivalent DAEs.     

Near Time-Optimal Control of Redundant Manipulators along a Specified Path with Jerks Constraint

A time-optimal control scheme for a general type of closed-chain manipulator is proposed. The considered manipulator is composed of multiple serial manipulators that are connected to each other and single manipulators may be kinematically redundant. Also, the limit on the actuator torques and actuator jerks are considered. The jerk constraints create a smooth trajectory for reducing strain on robot actuators and satisfy torque limitations of industrial actuators. Inclusion of the jerk constraints increases the traversal time, hence, a method is introduced to optimize this time. To this end, a simple method to find switching points is investigated.     

A local solution with global characteristics for the joint torque optimization of a redundant manipulator

In this article, a stable local solution with global characteristics is developed for the joint torque optimization problem in redundant robotic manipulators. It is shown that the local optimization of the inertia inverse weighted dynamic torque corresponds to the global kinetic energy minimization problem. The proposed local-global alternative to the joint torque optimization problem is compared for stability and torque optimality with five different methods used for redundancy resolution of robotic manipulators at the acceleration level. The proposed local-global solution has been implemented and tested on a planar four-DOF kinematically redundant lab robot which was designed and built at Southwest Research Institute (SWRI). Several numerical simulations confirm the positive advantages of solutions which have a local as well as a global interpretation. In addition, a “dynamic manipulation index” is introduced to monitor the stability of an optimization problem in a kinematically redundant robot.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

Force Transmissibility Performance of Parallel Manipulators

In this paper, a new force transmission index called the mean force transmission index (MFTI) is proposed, and the force transmissibility analysis procedure is established for parallel manipulators. The MFTI is an extended definition of the force transmission index (FTI) introduced by the authors previously. It is shown that the FTI is a function of the input velocity ratio (IVR) for a multi‐DOF mechanism of the same configuration. To represent the force transmissibility by a definite value, the MFTI is defined as the mean value of the normalized FTIs function over the whole range of the IVR. The force transmissibility analysis of two planar parallel manipulators is illustrated using the MFTI method. The result is compared with that of the Jacobian matrix method and the joint force index (JFI) method. It shows that, especially for symmetric parallel manipulators, an approximate inverse‐proportionality relationship exists between the JFI and MFTI, and between the maximum input torque/force and MFTI. It is concluded that the MFTI can be used as a quantitative measure of the force transmissibility performance for parallel manipulators. In the end, a design optimization problem is studied by taking the global force transmission index as the objective function. © 2003 Wiley Periodicals, Inc.     

机器人自适应PID饱和输出反馈控制

针对机器人系统在仅有位置传感、驱动器饱和、存在建模不确定性及干扰等条件下的轨迹跟踪控制问题,提出了一种新的自适应PID控制方案。采用高精度滤波器估计机器人关节速度,采用带饱和函数的控制器限制输出力矩,采用自适应PID控制器补偿建模不确定性和干扰。通过Lyapunov直接法,证明系统的稳定性。最后以两关节机器人为例,给出仿真实验结果,验证了算法的有效性。     

Extended impedance control of redundant manipulators based on weighted decomposition of joint space

In this work, impedance control approach based on an extended task space formulation is addressed to control the kinematically redundant manipulators. By defining a weighted inner product in joint space, a minimal parameterization of the null space is achieved, and we can visualize the null space motion explicitly. Moreover, it is shown that careful choice of the weighting matrix gives physically consistent and inertially decoupled dynamics. By augmenting this minimal null motion parameter with a forward kinematic relation, a new extended task space formulation can be obtained. Based on this formulation, we propose two control methods, a kinematically decomposed impedance controller and an inertially decoupled impedance controller, to control the motion of the end-effector as well as the internal motion expanding the conventional impedance control. We also show the relationship with the previous dynamic controllers of a redundant manipulator. Some numerical simulations are given to demonstrate the performance of the proposed control methods. © 1998 John Wiley & Sons, Inc.     

Hierarchical control of end-point impedance and joint impedance forredundant manipulators

This paper proposes an impedance control method for redundant manipulators, which can control not only the end-point impedance using one of the conventional impedance control methods, but the joint impedance which has no effects on the end-point impedance. First, a sufficient condition for the joint impedance controller is derived. Then, the optimal controller for a given desired joint impedance is designed using the least squares method. Finally, computer simulations and experiments using a planar direct-drive robot are performed in order to confirm the validity of the proposed method     

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.     

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.     

Force,orientation and position control in redundant manipulators in prioritized scheme with null space compliance

This paper addresses the problem of executing multiple prioritized tasks for robot manipulators with compliant behavior in the remaining null space. A novel controller–observer is proposed to ensure accurate accomplishment of various tasks based on a predefined hierarchy using a new priority assignment approach. Force control, position control and orientation control are considered. Moreover, a compliant behavior is imposed in the null space to handle physical interaction without using joint torque measurements. Asymptotic stability of the task space error and external torque estimation error during executing multiple tasks are shown. The performance of the proposed approach is evaluated on a 7R light weight robot arm by several case studies.     

Joint trajectory generation for redundant robots in an environment with obstacles

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.