Optimal load of robotic manipulator with joint elasticity using accuracy and actuator constraints

A computational technique for obtaining the maximum load-carrying capacity for a robotic manipulator with joint elasticity, subject to accuracy and actuator constraints, is described. Full load motions and increased productivity are linked in the industrial applications of many robotic manipulators; the maximum load carrying capacity which can be achieved by a manipulator during a given trajectory is limited by a number of factors. The dynamic properties of a manipulator, its actuator limitations, and joint elasticity (transmissions, reducers, and servo drive system) are probably the most important factors. This paper presents a strategy for determining dynamic load carrying capacity (DLCC), subject to both accuracy and actuator constraints, where a series of cubical bounds centred at the desired trajectory is used in the end-effector oscillation constraint while a typical d.c. motor speed-torque characteristics curve is used in the actuator constraint. The technique which considers the full nonlinear manipulator dynamics, actuator constraints, and accuracy constraints permits the manipulator user to specify the trajectory completely. Finally, a numerical example involving a two-link manipulator with joint flexibility using this method is presented and the results are discussed.     

Dynamic load-carrying capacity of mobile-base flexible joint manipulators

A computational technique for obtaining the maximum load-carrying capacity of robotic manipulators with joint elasticity is described while different base positions are considered. The maximum load-carrying capacity which can be achieved by a robotic manipulator during a given trajectory is limited by a number of factors. Probably the most important factors are the actuator limitations, joint elasticity (transmissions, reducers and servo drive system) and relative configuration of the robot with respect to its base. Therefore, both actuator torque capacity constraint considering typical torque-speed characteristics of DC motors and trajectory accuracy constraints considering a series of spherical bounds centred at each desired trajectory are applied as the main constraints. For the desired trajectory of load, different base locations are considered. It is seen that the load-carrying capacity at different base positions is different due to distinct dynamic effects of links and load motions on joint actuators. Then, a general computational algorithm for a multi-link case on a given trajectory and different base location is laid out in detail. Finally, two numerical examples involving a two-link manipulator and a PUMA robot using the method are presented. The obtained results illustrate the effect of base location, dual actuator torque and end effector precision constraints on load-carrying capacity on a given trajectory .     

The effect of base replacement on the dynamic load carrying capacity of robotic manipulators

The problem of establishing the load carrying capacity of mobile base manipulators operated by limited force or torque actuators is presented. It is shown the maximum allowable load on a given load trajectory, is a function of base position. The load workspace is defined as the union of places where the base can be located on them and it carries a load by the manipulator on a desired trajectory. The load workspace is discretised into some grid points, and the base is positioned on each grid point. The recursive Newton-Euler method is used to compute the dynamic effects of the load and manipulator on each joint actuator, then the load carrying capacity of the mobile manipulator at each base location is computed by considering the manipulator joints and actuator torque constraints. By applying a simple procedure, a smaller subspace of the load workspace is selected, so that the load carrying capacity is near to a maximum. This procedure is repeated until the optimum base location is found so that the load carrying of the manipulator is a global maximum in the load workspace for the desired dynamic trajectory. Finally, the effect of base mobility on optimising the dynamic load carrying capacity for different robotic arms is investigated in separate case studies.     

Optimal load of elastic joint mobile manipulators imposing an overturning stability constraint

Full load motion of mobile manipulators while carrying a load with pre-defined motion precision is an important consideration in their application. Therefore, in this paper a general formulation for finding the maximum load-carrying capacity of compliant joint mobile manipulators is presented. The overturning stability of the system and the precision of the motion on the given end effector trajectory are taken into account. The main constraints used for the algorithm presented are the actuator torque capacity, the limited error bound for the end effector and the overturning stability during motion on the given trajectory. This paper presents a strategy for determining the dynamic load-carrying capacity (DLCC), subject to overturning stability, accuracy and actuator constraints, in which a series of ball-type bounds centred at the desired trajectory is used in the end effector oscillation constraint, while a typical d.c. motor speed-torque characteristics curve is used in the actuator constraint. The technique, which considers the full nonlinear mobile manipulator dynamics, actuator constraint, overturning stability constraint, and accuracy constraint, permits the user to specify the trajectory completely. In order to verify the effectiveness of the algorithm presented, a simulation study considering a compliant joint two-link planar manipulator mounted on a differentially driven mobile base is given with details.     

Optimal load of elastic joint mobile manipulators imposing an overturning stability constraint

Full load motion of mobile manipulators while carrying a load with pre-defined motion precision is an important consideration in their application. Therefore, in this paper a general formulation for finding the maximum load-carrying capacity of compliant joint mobile manipulators is presented. The overturning stability of the system and the precision of the motion on the given end effector trajectory are taken into account. The main constraints used for the algorithm presented are the actuator torque capacity, the limited error bound for the end effector and the overturning stability during motion on the given trajectory. This paper presents a strategy for determining the dynamic load-carrying capacity (DLCC), subject to overturning stability, accuracy and actuator constraints, in which a series of ball-type bounds centred at the desired trajectory is used in the end effector oscillation constraint, while a typical d.c. motor speed-torque characteristics curve is used in the actuator constraint. The technique, which considers the full nonlinear mobile manipulator dynamics, actuator constraint, overturning stability constraint, and accuracy constraint, permits the user to specify the trajectory completely. In order to verify the effectiveness of the algorithm presented, a simulation study considering a compliant joint two-link planar manipulator mounted on a differentially driven mobile base is given with details.     

NEW APPROACHES FOR COMPUTING DYNAMIC LOAD-CARRYING CAPACITY OF MULTIPLE COOPERATING ROBOTIC MANIPULATORS

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Load carrying capacity of flexible joint manipulators with feedback linearization

A computational technique for obtaining the maximum load carrying capacity of robotic manipulators with joint elasticity, subject to accuracy and actuators constraints, is described herein. A feedback linearization technique is used to minimize end-effector deflection. An inversion algorithm is employed for the synthesis of a dynamic feedback control law that provides input-output decoupling and full state linearization. The linearizing input transformations and the corresponding state diffeomorphisms are presented. The proposed technique is then applied to a flexible joint robot. Linearizing control law is been expressed in terms of different sets of model variables and their derivatives. As a result, different tracking errors and torques are introduced in the robot-given trajectory and different load carrying capacities are obtained.     

Maximum allowable load of mobile manipulators for two given end points of end effector

The aim of this paper is the formulation and numerical solution for finding the maximum dynamic load of mobile manipulators for a given two-end-point task. In fixed-base classical robots, the maximum allowable load is limited mainly by their joint actuator capacity constraints. However, besides actuator capacity constraints, kinematic redundancy and non-holonomic constraints should be considered for finding maximum dynamic payload of mobile manipulators, both of which arise from base mobility. The extended Jacobian matrix concept is used to solve the redundancy resolution and non-holonomic constraints. The problem is formulated as a trajectory optimisation problem, which fundamentally is a constrained nonlinear optimisation problem. Then, the iterative linear programming (ILP) method is utilised to solve the optimisation problem. Finally, by a numerical example involving a two-link manipulator mounted on a differentially driven wheeled base, use of the method is presented and the results are discussed.     

Maximum allowable dynamic load of flexible mobile manipulators using finite element approach

In this paper a general formula for finding the maximum allowable dynamic load (MADL) of flexible link mobile manipulators is presented. The main constraints used for the proposed algorithm are the actuator torque capacity and the limited error bound for the end-effector during motion on a given trajectory. The accuracy constraint is taken into account with two boundary lines which are equally offset due to the given end-effector trajectory, while a speed-torque characteristics curve of a typical DC motor, is used for applying the actuator torque constraint. Finite element method (FEM), which is able to consider the full nonlinear dynamic of mobile manipulator is applied to derive the kinematic and dynamic equations. In order to verify the effectiveness of the presented algorithm, two simulation studies considering a flexible two-link planar manipulator mounted on a mobile base are presented and the results are discussed.     

Maximum allowable dynamic load of flexible mobile manipulators using finite element approach

In this paper a general formulation for finding the maximum allowable dynamic load (MADL) of flexible link mobile manipulators is presented. The main constraints used for the proposed algorithm are the actuator torque capacity and the limited error bound for the end-effector during motion on a given trajectory. The accuracy constraint is taken into account with two boundary lines which are equally offset due to the given end-effector trajectory, while a speed-torque characteristics curve of a typical DC motor is used for applying the actuator torque constraint. The finite element method (FEM), which is able to consider the full nonlinear dynamics of mobile manipulators, is applied to derive the kinematic and dynamic equations. In order to verify the effectiveness of the presented algorithm, two simulation studies considering a flexible two-link planar manipulator mounted on a mobile base are presented and the results are discussed.     

Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control

This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement.     

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations?? amplitudes and increasing stability.     

A robust real time adaptive controller design for robot manipulator with eight-joints based on DSPs

In this paper we propose a new technique to the design and real-time control of an adaptive controller for robotic manipulator based on digital signal processors. The Texas Instruments DSPs (TMS320C80) chips are used in implementing real-time adaptive control algorithms to provide enhanced motion control performance for robotic manipulators. In the proposed scheme, adaptation laws are derived from model reference adaptive control principle based on the improved Lyapunov second method. The proposed adaptive controller consists of an adaptive feed-forward and feedback controller and time-varying auxiliary controller elements. The proposed control scheme is simple in structure, fast in computation, and suitable for realtime control. Moreover, this scheme does not require any accurate dynamic modeling, nor values of manipulator parameters and payload. Performance of the proposed adaptive controller is illustrated by simulation and experimental results for robot manipulator with eight joints at the joint space and cartesian space.     

3自由度气动串联机械手的关节控制

3自由度气动机械手属关节串联式机器人,机械手在运动过程中,转动惯量、重力矩及关节间的耦合力矩等参数都会发生较大变化,影响了机械手末端的运动精度。针对这些问题,利用拉格朗日方程对机械手3关节进行动力学分析,得到多关节联动时单关节力矩方程。以腰部关节为例,通过对关节动力机构的数学模型线性化处理,采用状态反馈极点配置方法进行控制器设计,试验表明具有一定鲁棒性,但存在一定静态误差。分析产生误差的原因主要是干扰力矩的影响,根据单关节规划路径通过动力学模型得到补偿力矩,利用输入前馈对关节实施动态补偿。试验验证了方法的有效性,从结果可以看出,该组合控制策略抑制了扰动,提高了轨迹跟踪精度。     

太空机械臂带故障运行控制研究

为了对出现故障的太空机械臂进行控制,本文先对太空机械臂故障后行为进行动力学分析。在此基础上,得出了太空机械臂带故障运行的控制方案。本文所提出的新控制方案是基于自由转动关节的,也就是说,故障关节完全失去了驱动力矩。为了验证方案的可行性,我们还利用平面两连杆机械臂进行了动力学仿真。     

XML-based concurrent and integrated ergonomic analysis in PLM

In this paper, finding the maximum dynamic load carrying capacity of flexible joint manipulators in point-to-point motion is formulated as an optimal control problem. The computational methods are classified as indirect and direct methods. This work is based on the indirect solution method of optimal control problem. The application of Pontryagin’s minimum principle to this problem results in a two-point boundary value problem (TPBVP) solved numerically. Two algorithms are developed on the basis of the solution of the TPBVP. The first one is used to plan the optimal path for a given payload, and the other one is exploited to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories are obtained with different characteristics and different maximum payload. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to illustrate the power and efficiency of the proposed method in the presence of flexibility in joints, a number of simulation tests are performed for a two-link manipulator. Then, the effect of flexibility on the maximum payload value is investigated and compared with rigid one. Finally, for the sake of comparison with previous results in the literature, simulation is performed for a rigid-joint three-link manipulator, and a reasonable agreement is observed between the results.     

Optimization of manipulator point to point motion considering actuator output capability constraints

An optimization algorithm for planning minimum time cubic polynomial joint trajectory splines, is presented. In this optimization, constraints on manipulator joint kinematics and actuator output capabilities are enforced. The contribution of this paper to the algorithm is the incorporation of the actuator capability constraints in the optimization.

Manipulator tasks are specified as a sequence of required end effector locations and orientations, (task spaces). Continuous motion through the task spaces is achieved through use of cubic polynomial trajectory splines at the joint level. Movement times between task spaces are optimized off-line, using a direct search technique. Enforcement of the joint constraints is achieved by scaling infeasible manipulation kinematics and dynamics through expansion of the total motion time.

Example optimizations are included. It was found that trajectory optimization considering kinematic and dynamic constraints, will produce results superior to simple time scaling of a dynamically infeasible, kinematic optimum trajectory.     

Comparative study of tracking control for a mobile manipulator: Nonholonomic and dynamic cases

This paper gives an in-depth treatment of the modeling and control of a mobile manipulator which consists of a robotic manipulator mounted upon a mobile robot. By neglecting slip of the platform's tires, nonholonomic constraints are introduced into the equations of motion. By considering wheel slip, the assumption of nonholonomic motion is violated. Nonholonomic and dynamic models of a mobile manipulator are developed and compared using the Lagrange-d'Alembert formulation and the Newton-Euler method, respectively. The dynamic model which considers wheel slip incorporates a nonlinear tire friction model. The tracking problem is investigated by using imput-output linearization for the nonholonomic model. For the dynamic model, a robust control method based on a matching condition is developed to eliminate the harmful effects of wheel slip, which acts as a disturbance to the system. Then, the effect of wheel slip on the tracking of commanded motion is identified via simulation. The effectiveness of the proposed control algorithm is demonstrated through computer simulation.     

Design of magnetically suspended frictionless manipulator

Magnetically suspended frictionless manipulator is designed to improve the resolution and position accuracy. In order to increase the dynamic stability, the magnetically suspended manipulator is constructed using push-and-push forces. Using the force analysis, the design and modeling processes of the manipulator are achieved. The proposed modeling process is experimentally verified from free vibration of the manipulator. Comparison is made between the natural frequencies from the modeled dynamic equation and those from experimentally obtained.     

Optimal trajectory planning with application to industrial robots

A procedure is presented for planning optimal trajectories for application to industrial robots. First, trajectories are optimised by considering the nominal dynamics of a robot with rigid links and joints and with constraints on joint torque and speed. The minimum-time optimisation criterion is complemented by a miminal dynamic energy criterion that leads to smoother actuator inputs that do not excite joint vibrations. Weighting factors for these cost functions are then determined by trial simulations. By these means the effect of controller characteristics and elasticity, friction and backlash in the joints may be taken into account. A minimum-time movement for the real-world robot is obtained which displays the dynamical behaviour predicted in the planning procedure. Results from measurements and simulations for a PUMA 562 robot illustrate the approach. Further improvements may be achieved by a custom controller with the feedforward torques as shown in a comparison of trajectories executed with a VAL2 controller and a custom controller.