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.     

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 .     

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.     

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.     

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 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.     

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.     

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.     

关节速度约束下六轴机械臂空间运动轨迹规划方法

六轴机械臂在空间运动时,极易因速度和加速度突变导致运动轨迹出现随机波动,无法做连续性的运动。基于此,提出一种关节速度约束下机械臂空间运动轨迹规划方法。从运动学正解和逆解2个方面对机械臂建模,利用上关节D-H法分析同一位姿下,基座与末端执行器间的总变换过程。将不同的关节转角组合,辅助后续最优轨迹规划。利用三次和五次多项式插值构建末端执行器的插值函数,以执行器在不同坐标下关节角度为参考变量,求得角度、角速度和角加速度的值,完成运动轨迹规划。仿真实验表明,所提方法的运动轨迹可保证机器人平稳运行,连续性得到提高,从起始点至终止点整个过程中都没有出现明显震动情况。     

纳米级精度柔性机器人的设计方法及实现研究

从材料、几何结构、柔性铰链、驱动器、运动与负载及加工等几个方面总结了面向精密作业的柔性机器人设计准则。对柔性机器人的设计方法进行了探讨。以精密作业中的具体应用为例，依据这些设计方法与准则，从机械本体和驱动器控制2个方面详细描述了可实现纳米级精度的3自由度柔性机器人样机设计的具体实现过程，设计结果满足任务要求。     

Configuration dependent stiffness of the PUMA 560 manipulator: Analytical and experimental results

Joint stiffness of three PUMA 560 manipulators has been measured experimentally. Results of these studies indicate that stiffness data for joints 1, 2 and 3 are similar between PUMA 560 manipulators. Nonlinear relationships between end effector load, end effector displacement and joint configuration are explained. Because mass and inertia data has already been determined, complete dynamic models of the PUMA 560 manipulator which include joint compliance data, are now possible. Using linearized equilibrium equations, static, compliant, configuration dependent joint deflections are determined and compared with experimental results.     

Optimal actuator sizing and end point deformation for mobile robotic manipulators with elastic joint based on load criteria

Application of a numerical method to determine the maximum dynamic load carrying capacity (DLCC) for a robotic manipulator carrying an automobile petrol tank with joint elasticity subject to accuracy and actuator constraints is described in this paper. The maximum DLCC which can be achieved by a manipulator during a given trajectory is limited by a number of factors. The most important of which are the dynamic specification of the manipulator, the actuator limitations, and the elasticity of the joints such as reducers and servo drive system. Initially, the kinematic equations for carrying the automobile petrol tank by the robotic arm with 6 degrees of freedom (DOF) were calculated. The mechanical modeling was achieved via software programming. Dynamic modeling of the flexible joints manipulator was done simply for the three major axes. A method for determination of the dynamic load capacity with specific reference to both accuracy and actuator constraints is explained. The results obtained indicate the importance of both constraints and which constraint is more critical for accuracy and tracking.     

Stable joint torque optimization for multiple cooperating redundant manipulator system

In this paper, joint torque optimization for multiple cooperating redundant manipulators rigidly handling a common object is considered. This work focuses on finding the optimal and stable distribution of the operational forces of a multiple redundant manipulator system to the individual manipulators. Two joint torque optimization schemes (local joint torque minimization and natural joint motion) are formulated and compared. When a redundant manipulator with its joints free is driven by its tip, a naturally inducing joint motion can be called ‘natural joint motion’. From the simulation results of a system of three cooperating redundant manipulators, the natural joint motion scheme is shown to be better than the local joint torque minimization scheme with regard to global torque minimization capability and the resulting stability of motion. However, in order to guarantee the stability, the null space damping method is required for the both schemes. The effectiveness of the null space damping method is demonstrated by simulation. Additionally, the condition for the distribution of the operational forces required to drive the given system along a natural joint motion trajectory is addressed.     

基于DSP的机械臂约束预测控制系统设计

针对机械臂的实时控制问题,基于约束预测控制,提出了一种机械臂实时运动控制方法。介绍了机械臂动力学模型并进行了线性化处理,以降低算法复杂度、保证实时性。设计了轨迹跟踪控制器和约束预测控制器,其中轨迹跟踪控制器采用最优反馈控制律,可确保机械臂按参考轨迹运动;而约束预测控制器则在考虑机械臂物理约束的情况下,为跟踪控制器提供最优参考轨迹。以DSP作为核心控制器,搭建了机械臂控制系统,同时给出了硬件和软件设计方法。以梯形和三次多项式轨迹为例,进行了系统功能测试,测试结果表明了所述控制系统的可行性和有效性。     

Inverse kinematic and dynamic analyses of 6-DOFPUS type parallel manipulators

This paper presents inverse kinematic and dynamic analyses of HexaSlide type six degree-of-freedom parallel manipulators. The HexaSlide type parallel manipulators (HSM) can be characterized as an architecture with constant link lengths that are attached to moving sliders on the ground and to a mobile platform. In the inverse kinematic analyses, the slider and link motion (position, velocity, and acceleration) is computed given the desired mobile platform motion. Based on the inverse kinematic analysis, in order to compute the required actuator forces given the desired platform motion, inverse dynamic equations of motion of a parallel manipulator is derived by the Newton-Euler approach. In this derivation, the joint friction as well as all link inertia are included. Relative importance of the link inertia and joint frictions on the computed torque is investigated by computer simulations. It is expected that the inverse kinematic and dynamic equations can be used in the computed torque control and model-based adaptive control strategies.     

Collision-free control of mobile manipulators in a task space

This work offers the solution at the control feed-back level of the end-effector trajectory tracking problem for mobile manipulators subject to state equality and/or inequality constraints, suitably transformed into control dependent ones. Based on the Lyapunov stability theory, a class of controllers fulfilling the above constraints and generating a collision-free mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. The problem of collision avoidance is solved here based on an exterior penalty function approach which results in continuous and bounded mobile manipulator controls even near boundaries of obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a non-holonomic unicycle and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained task space and task space including the obstacles, illustrate the performance of the proposed controllers.     

空间2自由度冗余驱动并联机构运动学性能分析

面向建筑机器人领域的高性能机械臂需求,提出了一种空间2旋转自由度的3-UPS&U冗余驱动并联机构。基于螺旋理论和修正的G-K公式对机构的整体自由度进行分析,确定了其围绕恰约束支链万向副旋转的运动特性。建立驱动参数与末端参数之间的映射关系,得到其工作空间模型。通过主驱动并联、从动约束串联的独立建模,构造了该并联机构完整的广义雅可比矩阵,进一步得到动平台末端中心点线速度与驱动关节速度之间的无量纲化雅可比矩阵,并据此建立了特定工作空间下机构的灵巧度、承载能力和刚度性能评价指标。最后结果表明,3-UPS&U冗余驱动并联机构进行较高频次上下摆动作业时,在约束支链所布置的对应转轴方向上,具有更佳的综合运动学性能,且能大大降低性能衰减的幅度。     

Compound Impedance Control of a Hydraulic Driven Parallel 3UPS/S Manipulator

The hydraulic parallel manipulator combines the high-power density of the hydraulic system and high rigidity of the parallel mechanism with excellent load-carrying capacity. However, the high-precision trajectory tracking control of the hydraulic parallel manipulator is challenged by the coupling dynamics of the parallel mechanism and the high nonlinearities of the hydraulic system. In this study, the trajectory control of a 3-DOF symmetric spherical parallel 3 UPS/S manipulator is evaluated. Focusing on the highly coupling and nonlinear system dynamics, a compound impedance control method for a hydraulic driven parallel manipulator is proposed, which combines impedance control with the spatial motion characteristics of a parallel manipulator. The control strategy is divided into the inner and outer loops. The inner loop controls the impedance of the actuator in the joint space, and the outer loop controls the impedance of the entire platform in the task space to compensate the coupling of the actuators and improve the tracking accuracy of the moving platform. Compound impedance control does not require force or pressure sensors and is less dependent on modeling precision. The experimental results show that the compound impedance control e ectively improves the tracking accuracy of the moving platform. This research proposes a compound impedance control strategy for a 3-DOF hydraulic parallel manipulator, which has high tracking precision with a simple and cheap system configuration.     

角度与运动约束下串联式机械臂工作空间求解与结构优化

深水作业机械臂通常采用串联式结构,机械臂每个关节的转动角度与长度会受到相应的限制,这些参数会直接影响到机械臂的运动轨迹规划和作业效率。机械臂的有效工作空间的求解是一个多目标多约束的优化问题。通过数学分析建立机械臂的运动学模型,分析影响有效工作空间的相关参数,利用图解法来分析机械臂工作空间的边界曲线,得到机械臂的有效工作空间的截面。针对机械臂有效工作空间的截面积建立数学解析模型,最后运用遗传算法求得满足约束条件下的机械臂有效工作空间最优解和能够实现高效作业的最优结构参数。仿真结果表明,该模型能够有效求解角度与运动约束下的串联式机械臂结构优化问题。     

Evolutionary collision-free optimal trajectory planning for intelligent robots

This paper presents optimization procedures based on evolutionary algorithms such as the elitist non-dominated sorting genetic algorithm (NSGA-II) and differential evolution (DE) for solving the trajectory planning problem of intelligent robot manipulators with the prevalence of fixed, moving, and oscillating obstacles. The aim is the minimization of a combined objective function, with the constraints being actuator constraints, joint limits, and the obstacle avoidance constraint by considering dynamic equations of motion. Trajectories are defined by B-spline functions. This is a non-linear constrained optimization problem with six objective functions, 31 constraints, and 42 variables. The combined objective function is a weighted balance of transfer time, the mean average of actuator efforts and power, penalty for collision-free motion, singularity avoidance, joint jerks, and joint accelerations. The obstacles are present in the workspace of the robot. The distance between potentially colliding parts is expressed as obstacle avoidance. Further, the motion is represented using translational and rotational matrices. The proposed optimization techniques are explained by applying them to an industrial robot (PUMA 560 robot). Also, the results obtained from NSGA-II and DE are compared and analyzed. This is the first research work which considers all the decision criteria for the trajectory planning of industrial robots with obstacle avoidance. A comprehensive user-friendly general-purpose software package has been developed using VC++ to obtain the optimal solutions using the proposed DE algorithm.