Robot path planning in a constrained workspace by using optimal control techniques

Robot manipulators are programmable mechanical systems designed to execute a great variety of tasks in a repetitive way. In industrial environment, while productivity increases, cost reduction associated with robotic operation and maintenance can be obtained as a result of decreasing the values of dynamic quantities such as torque and jerk, with respect to a specific task. Furthermore, this procedure allows the execution of various tasks that require maximum system performance. By including obstacle avoidance ability to the robot skills, it is possible to improve the robot versatility, i.e., the robot can be used in a variety of operating conditions. In the present contribution, a study concerning the dynamic characteristics of serial robot manipulators is presented. An optimization strategy that considers the obstacle avoidance ability together with the dynamic performance associated with the movement of the robot is proposed. It results an optimal path planning strategy for a serial manipulator over time varying constraints in the robot workspace. This is achieved by using multicriteria optimization methods and optimal control techniques. Numerical simulation results illustrate the interest of the proposed methodology and the present techniques can be useful for the design of robot controllers. Commemorative contribution.     

Design parameter evaluation based on human operation for tip mechanism of forceps manipulator using surgical robot simulation

We proposed a design method for pediatric surgical robots that evaluates the workspace and view information in computer simulator before the actual robot is developed. In this study, we investigated a suturing task in a virtual environment using forceps manipulators with different mechanical parameters. We reproduced the surgical workspace for congenital esophageal atresia and measured the working volume and invisible area to obtain suitable parameters for the suturing task. We also calculated the suitable mechanical parameters using Pareto optimal solution method and verified the mechanical parameters in Pareto optimal solution. We verified from the experimental results that there is a trade-off between the working volume and invisible area during the suturing task. Moreover, we determined from the calculation results that the mechanical design of the forceps manipulator is influenced by the invisible area during the suturing task. Finally, we confirmed that it is possible to obtain suitable parameters for surgical robots using the proposed method.     

Vision-Based Task-Level Control of a Flexible-Link Manipulator

This paper discusses a vision-based approach to implement task-level control in flexible-link manipulators. The proposed approach emphasizes the advantage of using vision in the control of flexible manipulators. It is pointed out that taking advantage of the inherent robustness, implementation of an image-based visual servo can be regarded as a synthetic solution to precise task-level control of flexible manipulators. This approach is implemented in a three-dimensional flexible-link manipulator. The implementation makes good use of filters in decoupling task-level control and vibration suppression control. Moreover, we point out that although the robustness of the approach can help to overcome the difficulty in control resulting from the complex measurement of the link's elastic deformation, it lacks in capability of tip trajectory specification. This problem is analyzed in this research and it leads to the proposal for the integration of the image interpolation technique. This technique makes the proposed approach adequate for tasks involved with complex tip trajectories. For flexible-link manipulators, the proposed approach with the remedy is the first vision-based synthetic solution that attempts to make a flexible manipulator usable for a practical task.     

Task-Space Modular Dynamics for Dual-Arms Expressed through a Relative Jacobian

This paper presents modular dynamics for dual-arms, expressed in terms of the kinematics and dynamics of each of the stand-alone manipulators. The two arms are controlled as a single manipulator in the task space that is relative to the two end-effectors of the dual-arm robot. A modular relative Jacobian, derived from a previous work, is used which is expressed in terms of the stand-alone manipulator Jacobians. The task space inertia is expressed in terms of the Jacobians and dynamics of each of the stand-alone manipulators. When manipulators are combined and controlled as a single manipulator, as in the case of dual-arms, our proposed approach will not require an entirely new dynamics model for the resulting combined manipulator. But one will use the existing Jacobians and dynamics model for each of the stand-alone manipulators to come up with the dynamics model of the combined manipulator. A dual-arm KUKA is used in the experimental implementation.     

Lookup table control method for vibration suppression of a flexible manipulator with optimization of the minimum settling time and energy consumption

Active vibration suppression of flexible manipulators is important in many engineering applications, such as robot manipulators and high‐speed flexible mechanisms. The demand for a short settling time and low energy consumption of vibration suppression requires consideration of optimal control. Under a wide range of operating conditions, however, the fixed optimal parameters determined for a control algorithm might not produce the best performance. Therefore, to enhance performance, this paper suggests a lookup table control method for a flexible manipulator. This method can tune itself to the optimal parameters on the basis of initial maximum responses to the controlled system. In this study, a multi‐objective genetic algorithm is used to search for optimal parameters with regard to positive position feedback to the control algorithm. In turn, with the optimal parameters, the multi‐objective functions of the settling time and energy consumption during the vibration control of a flexible manipulator can be minimized. The simulation and experimental results both indicate that the energy consumption can be reduced significantly if the settling time is slightly increased. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

冗余机械臂运动学优化设计

该文主要从机械臂运动学的角度,定义了故障容错机械臂,巧妙地论证了冗余故障容错机械臂应该具备的自由度数,以及针对不同的任务要求,设计故障容错机械臂的方法。通过将任务空间抽象简化为一系列的特征点,建立机械臂参数与理想值相关的罚函数,选择有效的优化算法,设计出了通用一阶故障容错平面位置机械臂,通用一阶故障容错空间位置机械臂,以及特定任务一阶故障容错平面位置机械臂。建立起完整的故障容错机械臂的设计方法。     

Design and Control of a Hydraulic Simulator for a Flexible-Joint Robot

For the first time, a novel experimental hydraulic system that simulates joint flexibility of a single-rigid-link flexible-joint robot manipulator, with the ability of changing the joint flexibility's parameters, was designed and implemented in this study. Such a system could facilitate future control studies of robot manipulators by reducing investigation time and implementation cost of research. It could also be used to test the performance of different strategies to control the movement of flexible-joint manipulators. A hydraulic rotary servo motor was used to simulate the action of a flexible-joint robot manipulator, which was a challenging task, since the control of angular acceleration was required. In this study, a single-rigid-link elastic-joint robot manipulator was mathematically modeled and implemented in which joint flexibility parameters such as stiffness and damping could be easily changed. This simulation is referred to as a 'function generator' to drive a hydraulic robot manipulator. In this study the desired angular acceleration of the manipulator was used as the input to the hydraulic rotary motor and the objective was to make the hydraulic system follow the desired acceleration in the frequency range specified. A hydraulic actuator robot was built and tested. The results indicated that if the input signal had a frequency in the range of 5–15 Hz and damping ratio of 0.1 (typical values for flexible joints), the experimental setup was able to reproduce the input signal with acceptable accuracy. Owing to the inherent noise associated with the measurement of acceleration and some severe nonlinearities in the rotary motor, control of the experimental test system using classical methods was a challenging task that had not been anticipated.     

冗余机器人的双向自运动路径规划

冗余机器人的自运动路径规划是在保持手端任务向量不变的情况下,在关节空间内寻找一条连接机器人初始关节构形和期望关节构型的几何路径.本文给出一种双向自运动路径规划算法,其基本思想是使位于初始关节构形的真实机器人和位于期望关节构形的虚拟机器人在自运动流形上运动并收敛到同一关节构形,从而得到一条连接初始和期望关节构形的自运动几何路径.该算法克服了以往算法容易陷入局部极小构形的缺陷.仿真结果证实了算法的有效性.     

Time-optimal trajectory planning in cable-based manipulators

In this paper, the trajectory planning of high-speed cable-based parallel manipulators is studied for a given geometrical path. The time-optimal trajectory-planning technique is adapted for these manipulators in which cable forces must be maintained tensile. This condition is represented as a constraint on the acceleration of the end-effector along the path. The results of this technique are evaluated experimentally on DeltaBot, a cable-based manipulator developed at the University of Waterloo. The performance of the time-optimal technique is examined both for the moving time of the manipulator and the computational time of the trajectory generation.     

Robust Shape Control of Deformable Objects Using Model-Based Techniques

Shape control of a deformable object by a robotic system is a challenging problem because of the difficulty of imposing shape change by a finite number of actuation points to an essentially infinite-dimensional object. In this paper, a new approach to shape changing of deformable objects by a system of manipulators is presented. First, an integrated dynamic equation of motion for a system of multiple manipulators handling a deformable object is developed. A shape correspondence between the initial contact points of the multiple manipulators on a deformable object and a two-dimensional curve that represents the final desired shape is determined. A shape Jacobian that contains the local shape information of the desired shape of the object is formulated and is introduced into the control law. We develop a shape estimator with a second-order dynamics that is used to estimate the curve parameters corresponding to the end-effector position in each time step as the initial object is deformed to its desired final shape. Finally, we design a robust controller for the shape changing task that can work in the presence of modeling uncertainty. The simulation results demonstrate the efficacy of the proposed method.     

A global approach for the optimal path generation of redundant robot manipulators

In this article the optimal path generation of redundant robot manipulators is considered as an optimization problem, with given kinematics and subject to the robot requirements and a singularities avoidance constraint. This problem is formulated as a constrained continuous optimal control problem, which allows to consider joints and velocities constraints and/or manipulator dynamics. This approach is exemplified for a planar redundant manipulator and the resultant state constrained problem is solved by an efficient iterative numerical technique.     

An efficient local approach for the path generation of robot manipulators

In this article an efficient local approach for the path generation of robot manipulators is presented. The approach is based on formulating a simple nonlinear programming problem. This problem is considered as a minimization of energy with given robot kinematics and subject to the robot requirements and a singularities avoidance constraint. From this formulation a closed form solution is derived which has the properties that allows to pursue both singularities and obstacle avoidance simultaneously; and that it can incorporate global information. These properties enable the accomplishment of the important task that while a specified trajectory in the operational space can be closely followed, also a desired joint configuration can be attained accurately at a given time. Although the proposed approach is primarily developed for redundant manipulators, its application to nonredundant manipulators is examplified by considering a particular commercial manipulator.     

Design of reconfigurable coupled-serial-chain-based manipulation assistive aids

Our goal is to design a reconfigurable single degree-of-freedom (dof) articulated manipulation assistive aid, whose end-effector is required to closely approximate a series of constrained planar paths. To this end, we investigate the viability of the coupled-serial-chain configuration manipulator design created by constraining the relative rotations of a revolute-jointed serial-chain manipulator with linear cable–pulley couplings. The forward kinematics equations take the form of a finite trigonometric series in terms of the input crank rotations. Our proposed Fourier-based synthesis method exploits this special structure to facilitate the design synthesis of such manipulators. We then examine design enhancements, to permit this manipulator to be reconfigured for multiple sets of constrained end-effector tasks, by controlled variation of the principal structural parameters. Particular attention is paid to the creation of a physical prototype, which facilitates such reconfiguration.     

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.     

Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method

Hyper redundancy, high reliability, and high task repeatability are the main advantages of binary manipulators over conventional manipulators with continuous joints, especially when manipulators are operated under tough and complex work conditions. The precise and complex movement of a binary manipulator necessitates many modules. In this case, numerically efficient inverse kinematics algorithms for binary manipulators usually require impractically large memory size for the real-time calculation of the binary states of all joints. To overcome this limitation by developing a new inverse kinematics algorithm is the objective of this research. The key idea of the proposed method is to formulate the inverse kinematics problem of a binary manipulator as an optimization problem with real design variables, in which the real variables are forced to approach the permissible binary values corresponding to two discrete joint displacements. Using the proposed optimization method, the inverse kinematics of 3-D binary manipulators with many modules can be solved almost in real time (say, less than a second for up to 16 modules) without requiring a large memory size. Furthermore, some manipulation considerations, such as operation power minimization, can be easily incorporated into the proposed formulation. The effectiveness of the proposed method is verified through several numerical problems, including 3-D inverse kinematics problems.     

Editorial

A fundamental physical understanding of the properties and structure of dynamic robot models is the basis of controller design for robotic manipulators. This paper focuses on the estimation of different parameters which appear in the dynamics models of robots. By introducing candidate functions and a statistical approach to analyze these functions it is possible to identify the significant parameters in the dynamics model of the manipulator. This generalized method is also capable of considering Coloumb and viscous friction effects. Modeling based on candidate functions does not require symbolic calculation for the dynamics of the manipulator and can easily be applied to manipulators with more than 6 d.o.f. Parameter estimation is especially appropriate for modeling manipulators with many degrees of freedom prior to developing control algorithms, where otherwise the computation of such models is overwhelming. It is also demonstrated that this type of modeling is equivalent to the conventional symbolic calculation of dynamics of manipulators.     

A new approach to improve absolute positioning accuracy of robot manipulators

This article describes a new calibration system for robot manipulators which improves their absolute positioning accuracy by using parameter-estimation algorithms based on the Newton method. When 3D position data of the specified points on a manipulator and the joint encoder values are input to the calibration system, the system estimates the offset values of joint encoders, link lengths, and position and orientation of the manipulator base coordinate system with respect to the world coordinate system which is difficult to obtain by conventional calibration methods. This calibration system can be applied to various manipulator types by just changing the basic kinematic equations. The system employs an algebraic programming system called REDUCE to automatically reduce the manipulator kinematic equation and partial differential calculus in the Newton method. For efficiency, first only the arm part with three degrees of freedom and then the hand part are calibrated. The experimental results demonstrate the effectiveness of this system by reducing the robot's absolute positioning errors to the order of repeatability errors.     

A kinetostatic index to measure the task-executing ability of robotic manipulators with limit-driven characteristics of actuators

Dexterity is an important issue for the design, trajectory planning and control of robotic manipulators. However, even though a lot of robot manipulators are driven by DC motors, no dexterity measures were introduced to evaluate how efficient a manipulator system is for performing a required task in the case of taking the limit-driven characteristics of the DC motor into consideration. In this study, we introduce a new kinetostatic dexterity index to measure the task-executing ability of robotic manipulators where the possible maximum velocity and force of the required task are derived subject to the heat-converted power limit of the DC motor. The measure is to evaluate how efficient a manipulator system is to execute a required task, while the limit-driven characteristics of its actuators are taken into consideration. Two examples are used to show that the proposed dexterity index is task-dependent and changed due to the tasks.     

Suboptimal control of industrial manipulators with a weighted minimum time-fuel criterion

Even if a manipulator does not have to follow a prespecified path (i.e., a time history of position and velocity) due to the complexity and nonlinearity of the manipulator dynamics, control of manipulators has been conventionally divided into two subproblems, namely path planning and path tracking, which are then separately and independently solved. This may result in mathematically tractable solutions but cannot offer a solution that utilizes manipulators' maximum capabilities (e.g., operating them at their maximum speed). To combat this problem, we have developed a suboptimal method for controlling manipulators that provides improved performance in both their operating speed and use of energy. The nonlinearity and the joint couplings in the manipulator dynamics-a major hurdle in the design of robot control-are handled by a new concept of averaging the dynamics at each sampling interval. With the averaged dynamics, we have derived a feedback controller which has a simple structure allowing for on-line implementation with inexpensive mini- or microcomputers, and offers a near minimum time-fuel (NMTF) solution, thus enabling manipulators to perform nearly up to their maximum capability and efficiency. As a demonstrative example, we have simulated the proposed control method with a dynamic model of the Unimation PUMA 600 series manipulator on a DEC VAX-11/780. The simulation results agree with the expected high performance nature of the control method.