Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

In cable-driven parallel manipulators (CPMs), cables can perform only under tension, and therefore, redundant actuation, which can be provided by redundant limbs, is needed to maintain the cable tensions. By optimizing the distribution of the forces in the cables and the redundant limbs, the average size of actuators can be reduced resulting in lower cost. Optimizing the force distribution in CPMs requires consideration for the inequality constraints imposed on the cable forces as a result of the unilateral driving property of the cables. In this study, a projection method is presented to calculate optimum solutions for the actuators force distribution in CPMs. Two solutions are presented: 1) a minimum-norm solution that minimizes the 2-norm of all forces in the cables and redundant limbs and 2) a solution that minimizes the 2-norm of the forces in the cables only. The optimization problem is formulated as a projection on an intersection of convex sets and the Dykstra's projection method is used to obtain the solutions. This method is successfully applied to a 3-DOF CPM.     

Static analysis of spatial parallel manipulators by means of the principle of virtual work

It is presented a comprehensive approach for the static analysis of spatial parallel manipulators using the principle of virtual work, equipped with a recursive and systematic formulation, which is intended for conducting an efficient manipulation of the kinematics associated with the problem. Thus, it is possible omitting all internal forces and nonworking external constraint forces in the problem formulation. As a result, the actuator drive forces and/or torques can be directly related with the external loads supported by the manipulator, including the weight of the mobile platform and also the weight of the links of the connecting legs. A thorough understanding of these forces and/or torques is important for proper sizing of actuators at the design stage. In order to prove the feasibility and the validity of the proposed method, two fully detailed examples are presented.     

The NIST robocrane

The Robot Systems Division of the National Institute of Standards and Technology (NIST) has been experimenting for several years with new concepts for robot cranes. These concepts utilize the basic idea of the Stewart platform parallel link manipulator. The unique feature of the NIST approach is to use cables as the parallel links and to use winches as the actuators. As long as the cables are all in tension, the load is kinematically constrained and the cables resist perturbing forces and moments with equal stiffness to both positive and negative loads. The result is that the suspended load is constrained with a mechanical stiffness determined by the elasticity of the cables, the suspended weight, and the geometry of the mechanism. Based on these concepts, a revolutionary new type of robot crane, the NIST ROBOCRANE, has been developed that can control the position, velocity, and force of tools and heavy machinery in all six degrees of freedom (x, y, z, roll, pitch, and yaw). Depending on what is suspended from its work platform, the ROBOCRANE can perform a variety of tasks. Examples are: cutting, excavating and grading, shaping and finishing, lifting, and positioning. A 6-m version of the ROBOCRANE has been built and critical performance characteristics analyzed.     

Optimal custom design of both symmetric and unsymmetrical hexapod robots for aeronautics applications

The Stewart parallel mechanism is used in various applications due to its high load-carrying capacity, accuracy and stiffness, such as flight simulation, spaceship aligning, radar and satellite antenna orientation, rehabilitation applications, parallel machine tools. However, the use of such parallel robots is not widespread due to three factors: the limited workspace, the singularity configurations existing inside the workspace, and the high cost. In this work, an approach to support the design of a cost-effective Stewart platform-based mechanism for specific applications and to facilitate the choice of suitable components (e.g., linear actuators and base and mobile plates) is presented. The optimal design proposed in this work has multiple objectives. In detail, it intends to maximize the payload and minimize the forces at each leg needed to counteract external forces applied to the mobile platform during positioning or manufacturing, or, in general, during specific applications. The approach also aims at avoiding reduction of the robot workspace through a kinematic optimization. Both symmetric and unsymmetrical geometries have been analysed to show how the optimal design approach can lead to effective results with different robot configurations. Moreover, these objectives are achieved through a dynamic optimization and several optimization algorithms were compared in terms of defined performance indexes.     

Optimal design of multi-stage structures: a nested decomposition approach

A new approach to the optimal design of multi-stage structures is presented. The problem considered is that of optimal sizing and configurations for minimal weight, using limit analysis under a single loading condition. It is formulated as a large-scale linear program with the staircase structure. Using the technique of nested decomposition, design problems too large for conventional methods can be solved. Computational results are reported on examples in planar truss design.     

Impedance Compensation of SUBAR for Back-Drivable Force-Mode Actuation

The Sogang University biomedical assistive robot (SUBAR), which is an advanced version of the exoskeleton for patients and the old by Songang (EXPOS) is a wearable robot developed to assist physically impaired people. It provides a person with assistive forces controlled by human intentions. If a standard geared dc motor is applied, however, the control efforts will be used mainly to overcome the resistive forces caused by the friction, the damping, and the inertia in actuators. In this paper, such undesired properties are rejected by applying a flexible transmission. With the proposed method, it is intended that an actuator exhibits zero impedance without friction while generating the desired torques precisely. Since the actuation system of SUBAR has a large model variation due to human–robot interaction, a control algorithm for the flexible transmission is designed based on a robust control method. In this paper, the mechanical design of SUBAR, including the flexible transmission and its associated control algorithm, are presented. They are also verified by experiments.      

Automated optimal design of double-layer latticed domes using particle swarm optimization

Most of the conventional design methods of large-scale domes need deep engineering insight; furthermore, they hardly give the most economical solutions. Therefore, in this paper, a new practical design algorithm is presented to automate optimal geometry and sizing design of the latticed space domes through the idea of using parametric mathematical functions. Moreover, a simple approach is developed for the optimal sizing design of trusses with outsized number of elements. The robust technique of particle swarm optimization is employed to find the solution of the propounded optimization problem. Some numerical examples on the minimum weight design of several famous domes are provided to demonstrate the efficiency of the proposed design algorithm.     

A general solution for the position,velocity, and acceleration of hyperredundant planar manipulators

A new approach for the solution of the position, velocity, and acceleration of hyperredundant planar manipulators following any twice‐differentiable desired path is presented. The method is singularity free, and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers, and dividing them into virtual/real three‐link or four‐link subrobots. It starts by solving the inverse kinematic problem for the subrobot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the subrobots located in the upper virtual layers. An algorithm is developed that provides a singularity‐free solution up to the full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the subrobots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach, and it is shown that the value of the configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish their tasks. Computer simulations of several hyperredundant manipulators using the proposed method are presented as numerical examples. © 2002 John Wiley & Sons, Inc.     

Object-oriented modelling for spacecraft dynamics: Tools and applications

The development process for spacecraft control systems relies heavily on modelling and simulation tools for spacecraft dynamics. For this reason, there is an increasing need for adequate design tools in order to cope efficiently with tightening budgets for space missions. The paper discusses the main issues related to the modelling and simulation of satellite dynamics for control purposes, and then presents an object-oriented modelling framework, implemented as a Modelica library. The proposed approach allows a unified approach to a range of problems spanning from initial mission design and actuator sizing phases, down to detailed closed-loop simulation of the control system, including realistic models of sensors and actuators. It also promotes the reuse of modelling knowledge among similar missions, thus minimizing the design effort for any new project. The proposed framework and the Modelica library are demonstrated by several illustrative case studies.     

Development of an Intelligent Wheelchair Using Computer Graphics Animation and Simulation

A new robot simulator JC-1 is used as a control software development tool in a project in progress where an intelligent wheelchair for a blind user is being developed. The intelligent wheelchair is planned to be able to fulfill simple symbolic commands like "follow wall" or "follow object" and using the JC-1 simulator an evaluation team which includes e.g. the user, a rehabilitation engineer and a software engineer, can check control algorithms and user interface routines before constructing a real wheelchair prototype. The JC-1 simulator models the environment using simplified boundary- representation where objects, robot sensors and actuators are presented as symbolic objects in the graphics data-base of the simulator. In the JC-1 simulator a robot controller under development controls the motion of the graphical model of the robot while simulator commands or other robot controllers can be used to control the movement of disturbing obstacles. Computer graphics animation and simulation help to find fundamental design errors at an early design stage and as this paper suggests, enable the user of the final product to take part in to the designing process of the robot controller. Benefits and difficulties of using computer graphics simulation in the wheelchair development process are discussed.     

Grasp capability analysis of multifingered robot hands

This paper addresses the problem of grasp capability analysis of multifingered robot hands. The aim of the grasp capability analysis is to find the maximum external wrench that the multifingered robot hands can withstand, which is an important criterion in the evaluation of robotic systems. The study of grasp capability provides a basis for the task planning of force control of multifingered robot hands. For a given multifingered hand geometry, the grasp capability depends on the joint driving torque limits, grasp configuration, contact model and so on. A systematic method of the grasp capability analysis, which is in fact a constrained optimization algorithm, is presented. In this optimization, the optimality criterion is the maximum external wrench, and the constraints include the equality constraints and the inequality constraints. The equality constraints are for the grasp to balance the given external wrench, and the inequality constraints are to prevent the slippage of fingertips, the overload of joint actuators, the excessive forces over the physical limits of the object, etc. The advantages of this method are the ability to accomodate diverse areas such as multiple robot arms, intelligent fixtures and so on. The effectiveness of the proposed method is confirmed with a numerical example of a trifingered grasp.     

Development of micro-robot system for playing soccer games

This paper surveys recent trends in developing a micro-robot soccer system, and presents a design procedure for soccer-playing robots, focusing on our system based on the centralized approach. The robot soccer game has a lot of challenging problems, such as coordination between robots, motion planning of robots, visual recognition of objects, and so on. Considering the results of the MIROSOT contests, the centralized approach may be more powerful than the distributed approach in order to implement such functions. Our attempt was to develop a micro-robot system with a remote-brainless control architecture. After that, new techniques were applied to the chasis design, the actuators, the radio link, the vision system software, and the control strategy software. Using a fast vision system, we obtain the configuration of each robot, and then the host computer computes the desired motion and commands each robot directly via RF communication. We describe in detail some technical tips for developing the robots, and explain our strategy for obtaining the scores. This article also includes the most recent improvements in robot hardware and software. This work was presented, in part, at the Third International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–21, 1998     

SMA驱动的微型平面关节机器人的研究

近年来，利用形状记忆合金（ＳＭＡ）的形状记忆效应原理制作的驱动器已在机器人领域中得到应用，ＳＭＡ驱动器以其重量轻、结构紧凑、易控制等优点，大大推动了微型机器人的发展．本课题使用所研制的推挽式直线位移型和旋转关节型ＳＭＡ驱动器代替传统的伺服驱动系统，研制了一台三自由度（两个旋转自由度和一个直线自由度）且带末端夹持器的微型平面关节机器人．本文将介绍该机器人的结构设计，控制系统及其软件设计．     

Design of a robot that walks in any direction

In this article the design of a six-legged walking robot is presented. The design consists of two triangular body halves joined by actuators. Each body half has three legs attached to it. By shifting one of the halves with respect to the other the robot can walk in any direction. The design of the robot is explained in detail and a final prototype is presented. © 1998 John Wiley & Sons, Inc. 15: 75–83, 1998     

Synthesis and analysis of a flexible elephant trunk robot

This paper presents a novel synthesis and analysis of a flexible elephant trunk robot (biological continuum–style manipulator). The robot includes eight flexible segments, although it can be extended to more segments as necessary. In this study the gravity of the springs is neglected due to the fact that the manipulation force is much larger than these gravity forces. This mechanism exhibits a wide range of maneuverability and has a large number of degrees of freedom. Each segment is designed using a novel flexible mechanism based on the loading of a compression spring in both transverse and axial directions, and using cable–conduit systems. The rotational motion is transformed to tendon-like behavior, which enables the location of the actuators away from the trunk (e.g. at the end of the trunk). The forward kinematics of the mechanism is also presented and lends itself well to computer control. It is shown that the solution of the transverse deflection of each segment is obtained in a general form, while the stiffness coefficients are obtained in closed form from a two-dimensional model (small and large deflection angles) and from a three-dimensional model used in a finite element method to verify results. The friction in the analysis between the cable and the conduit is neglected in the analysis. A prototype trunk segment is experimentally tested, the results are verified and the elephant trunk robot is built. A bench-top actuation system has been developed and a control scheme used in prosthetic hand control has been implemented to control the mechanism.     

Biologically inspired design of a parallel actuated humanoid robot

This paper presents the comparison for the role of bi-articular and mono-articular actuators in human and bipedal robot legs, in particular the hip and knee joint, for driving the design of a humanoid robot with inspirations from the biological system. The various constraints driving the design of both systems are also compared. Additional factors particular to robotic system are identified and incorporated in the design process. To do this, a dynamic simulation is used to determine loading conditions and the forces and power produced by each actuator under various arrangements. It is shown that while the design principles of humans and humanoids are similar, other constraints ensure that robots are still merely inspired by humans, and not direct copies. A simple design methodology that captures the complexity and constraints of such a system in this paper is proposed. Finally, a full-size humanoid robot that demonstrates the newfound principle is highlighted.     

The Effect of Snake Muscular System on Actuators’ Torque

Most of the research conducted on snake robots has been on movement, control or dynamics. There is only some research dealing with the reduction of actuators’ sizes. Actuator size usually depends on the force/torque it can provide. Small actuators imply a more efficient, long lasting, lighter and more flexible robot. The required force/torque and energy consumption consequently is directly affected by the mechanism design. Mother nature has always presented optimum systems and has inspired engineers. In this paper, we have adopted the snake anatomy to design a snake robot. The results show a reduction in torque demand. This robot is an extension of our previous research on building a snake without including the anatomy. The new robot weighs about only one-third of the previous version.     

Design,modelling and validation of a novel extra slender continuum robot for in-situ inspection and repair in aeroengine

In-situ aeroengine maintenance works are highly beneficial as it can significantly reduce the current maintenance cycle which is extensive and costly due to the disassembly requirement of engines from aircraft. However, navigating in/out via inspection ports and performing multi-axis movements with end-effectors in constrained environments (e.g. combustion chamber) is fairly challenging. A novel extra-slender (diameter-to-length ratio  < 0.02) dual-stage continuum robot (16 degree-of-freedom) is proposed to navigate in and out confined environments and perform required configuration shapes for repair operations. Firstly, the robot design presents several innovative mechatronic solutions: (i) dual-stage tendon-driven structure with bevelled disks to perform required shapes and to provide selective stiffness for carrying high payloads; (ii) various rigid-compliant combined joints to enable different flexibility and stiffness in each stage; (iii) three commanding cables for each 2-DoF section to minimise the number of actuators with precise actuation. Secondly, a segment-scaled piecewise-constant-curvature-theory based kinematic model and a Kirchhoff-elastic-rod-theory based static model are established by considering the applied forces/moments (friction, actuation, gravity and external load), where the friction coefficient is modelled as a function of bending angle. Finally, experiments were carried out to validate the proposed static modelling and to evaluate the robot capabilities of performing the predefined shape and stiffness.     

Dynamic modeling,stability and energy consumption analysis of a realistic six-legged walking robot

This paper deals with a detailed analysis on kinematics, dynamics, stability and energy consumption of a realistic six-legged robot. The aim of this study is to extend a previous work of Roy et al. [1], in order to estimate optimal feet forces and joint torques of the six-legged robot generating wave-gaits with four different duty factors and deal with its stability issues. Two different approaches are developed to determine optimal feet forces. In the first approach, minimization of the norm of feet forces is carried out using a least square method, whereas minimization of the norm of joint torques is performed in the second approach. The second approach is found to be more energy efficient compared to the first one. The maximum values of feet forces and joint torques are seen to decrease with the increase of duty factor. The effects of walking parameters, namely velocity, stroke and duty factors have been studied on energy consumption and stability of the robot. The variations of average power consumption and specific energy consumption with the velocity and stroke are compared for four different duty factors. Wave gait with a low duty factor is found to be more energy-efficient compared to that with a high duty factor at the highest possible velocity.