A constrained optimization approach to resolving manipulator redundancy

A redundant manipulator can achieve additional tasks by utilizing the degree of redundancy, in addition to a basic motion task. While some additional tasks can be performed by optimizing a proper objective function, other additional tasks can be performed by satisfying a set of kinematic inequality constraints. In this article, we reformulate a redundancy resolution problem with multiple criteria into a local equality and inequality constrained optimization problem, and propose a method to solve it at velocity level. The proposed method is efficient, especially when the number of additional tasks is larger than the degree of redundancy. It also systematically assigns the priorities between the additional tasks. Besides the computational efficiency, the method has a cyclic property. © 1996 John Wiley & Sons, Inc.     

基于梯度投影法与随机优化算法的约束优化方法

针对带有线性等式和不等式约束的无确定函数形式的约束优化问题,提出一种利用梯度投影法与遗传算法、同时扰动随机逼近等随机算法相结合的优化方法。该方法利用遗传算法进行全局搜索,利用同时扰动随机逼近算法进行局部搜索,算法在每次进化时根据线性约束计算父个体处的梯度投影方向,以产生新个体,从而能够严格保证新个体满足全部约束条件。将上述约束优化算法应用于典型约束优化问题,其仿真结果表明了所提出算法的可行性和收敛性。     

Control-Based Solution to Inverse Kinematics for Mobile Manipulators Using Penalty Functions

This study offers the solution at the control feedback level to the inverse kinematics problem subject to state equality and inequality constraints for mobile manipulators. Based on the Lyapunov stability theory, a class of controllers generating the mobile manipulator trajectory whose attractor attained in a finite time, fulfills the above state constraints. The problem of both holonomic manipulability enforcement and collision avoidance is solved here based on an exterior penalty function approach which results in continuous mobile manipulator velocities near obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a nonholonomic wheel and a holonomic manipulator of two revolute kinematic pairs, operating in both a constraint-free task space and task space including obstacles, illustrate the performance of the proposed controllers.     

快速连续反应-避障作业环境下的七自由度灵巧臂轨迹规划

人类经长期学习训练后能对高速物体 (如棒球、乒乓球等)具有快速连续反应作业的运动技能, 从深层次上揭示是由于人体在其训练过程中不断学习优选了相应手臂的动作轨迹, 并储存了丰富的经验和知识. 受人体手臂动作此行为机制启发, 本文提出一种 7-DOF灵巧臂快速连续反应-避障作业的轨迹规划方法. 该方法将灵巧臂对高速物体目标作业的轨迹规划问题转化为动作轨迹参数化优选问题, 考虑作业过程中灵巧臂的机构物理约束和障碍约束条件, 以灵巧臂目标可作业度指标构建适应度函数, 采用粒子群优化 (Particle swarm optimization, PSO)方法优选作业轨迹中的冗余参数; 在此基础上 利用灵巧臂动作轨迹参数化优选方法构建相应作业环境下的知识数据库, 实现灵巧臂对高速物体目标的快速连续反应作业. 以仿人机器人乒乓球对弈作业为例, 将该方法应用于 7-DOF灵巧臂乒乓球作业的轨迹规划中. 数值实验及实际对弈试验结果表明, 该方法不仅能使灵巧臂所规划的轨迹 满足灵巧臂机构物理约束与障碍约束条件, 同时能实现灵巧臂对乒乓球体的快速连续反应作业, 验证了该方法的有效性.     

Adaptive robust control and admittance control for contact-driven robotic surface conditioning

This work presents a hybrid position/force control of robots for surface contact conditioning tasks such as polishing, profiling, deburring, etc. The robot force control is designed using sliding mode ideas to benefit from robustness. On the one hand, a set of equality constraints are defined to attain the desired tool pressure on the surface, as well as to keep the tool orientation perpendicular to the surface. On the other hand, inequality constraints are defined to adapt the tool position to unmodeled features present in the surface, e.g., a protruding window frame. Conventional and non-conventional sliding mode controls are used to fulfill the equality and inequality constraints, respectively. Furthermore, in order to deal with sudden changes of the material stiffness, which are forwarded to the robot tool and can produce instability and bad performance, adaptive switching gain laws are considered not only for the conventional sliding mode control but also for the non-conventional sliding mode control. A lower priority tracking controller is also defined to follow the desired reference trajectory on the target surface. Moreover, the classical admittance control typically used in force control tasks is adapted for the proposed surface contact application in order to experimentally compare the performance of both control approaches. The effectiveness of the proposed method is substantiated by experimental results using a redundant 7R manipulator, whereas its advantages over the classical admittance control approach are experimentally shown.     

Humanoid robot arm performance optimization using multi objective evolutionary algorithm

As humanoid robots are expected to operate in human environments they are expected to perform a wide range of tasks. Therefore, the robot arm motion must be generated based on the specific task. In this paper we propose an optimal arm motion generation satisfying multiple criteria. In our method, we evolved neural controllers that generate the humanoid robot arm motion satisfying three different criteria; minimum time, minimum distance and minimum acceleration. The robot hand is required to move from the initial to the final goal position. In order to compare the performance, single objective GA is also considered as an optimization tool. Selected neural controllers from the Pareto solution are implemented and their performance is evaluated. Experimental investigation shows that the evolved neural controllers performed well in the real hardware of the mobile humanoid robot platform.     

MEC中资源分配与卸载决策联合优化策略

针对移动边缘计算(MEC)中用户任务处理时延与能耗过高的问题,提出了“云-边-端”三层MEC计算卸载结构下的资源分配与卸载决策联合优化策略。首先,考虑系统时延与能耗,将优化问题规划为系统总增益(任务处理时延与能耗相对减少的加权和)最大化问题;其次,为用户任务设置优先级,并根据任务数据量初始化卸载决策方案;然后,采用均衡传输性能的信道分配算法为卸载任务分配信道资源,对于卸载至同一边缘服务器上的任务以最大化资源收益为目标进行资源竞争,实现计算资源最优配置;最后,基于博弈论证明优化问题为关于卸载决策的势函数,即存在纳什均衡,并利用迭代增益值比较法得到了纳什均衡下的卸载决策方案。仿真结果表明,所提联合优化策略在满足用户处理时延要求的情况下最大化系统总增益,有效地提高了计算卸载的性能。     

基于改进梯度投影算法的移动机械臂轨迹规划研究

移动机械臂由移动平台和机械臂构成,是一种典型的冗余机械臂系统。其运动学和轨迹规划问题是研究热点。梯度投影法是求解该问题的一类常用算法,其应用难点主要集中在比例因子的选取上。极值法通过最优化方法求解比例因子,将比例因子作为目标函数,并基于关节速度极限、可优化度等设计约束条件。针对极值法存在使关节加速度超限的问题,提出一种考虑关节加速度约束的新算法,并通过仿真对比验证该算法的有效性。     

Kinematic modeling of mobile robots by transfer method of augmented generalized coordinates

A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc.     

Mobile manipulator path planning by a genetic algorithm

This article addresses the path-planning problem for a mobile manipulator system that is used to perform a sequence of tasks specified by locations and minimum oriented force capabilities. The problem is to find an optimal sequence of base positions and manipulator configurations for performing a sequence of tasks given a series of task specifications. The formulation of the problem is nonlinear. The feasible regions for the problem are nonconvex and unconnected. Genetic algorithms applied to such problems appear to be very promising while traditional optimization methods cause difficulties. Computer simulations are carried out on a three-degrees-of-freedom manipulator mounted on a two-degrees-of-freedom mobile base to search for the near optimal path-planning solution for performing the sequence of tasks. © 1994 John Wiley & Sons, Inc.     

A unified quadratic-programming-based dynamical system approach to joint torque optimization of physically constrained redundant manipulators

In this paper, for joint torque optimization of redundant manipulators subject to physical constraints, we show that velocity-level and acceleration-level redundancy-resolution schemes both can be formulated as a quadratic programming (QP) problem subject to equality and inequality/bound constraints. To solve this QP problem online, a primal-dual dynamical system solver is further presented based on linear variational inequalities. Compared to previous researches, the presented QP-solver has simple piecewise-linear dynamics, does not entail real-time matrix inversion, and could also provide joint-acceleration information for manipulator torque control in the velocity-level redundancy-resolution schemes. The proposed QP-based dynamical system approach is simulated based on the PUMA560 robot arm with efficiency and effectiveness demonstrated.     

Whole-body hierarchical motion and force control for humanoid robots

Robots acting in human environments usually need to perform multiple motion and force tasks while respecting a set of constraints. When a physical contact with the environment is established, the newly activated force task or contact constraint may interfere with other tasks. The objective of this paper is to provide a control framework that can achieve real-time control of humanoid robots performing both strict and non strict prioritized motion and force tasks. It is a torque-based quasi-static control framework, which handles a dynamically changing task hierarchy with simultaneous priority transitions as well as activation or deactivation of tasks. A quadratic programming problem is solved to maintain desired task hierarchies, subject to constraints. A generalized projector is used to quantitatively regulate how much a task can influence or be influenced by other tasks through the modulation of a priority matrix. By the smooth variations of the priority matrix, sudden hierarchy rearrangements can be avoided to reduce the risk of instability. The effectiveness of this approach is demonstrated on both a simulated and a real humanoid robot.     

Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots

A symmetry position/force hybrid control framework for cooperative object transportation tasks with multiple humanoid robots is proposed in this paper. In a leader-follower type cooperation, follower robots plan their biped gaits based on the forces generated at their hands after a leader robot moves. Therefore, if the leader robot moves fast (rapidly pulls or pushes the carried object), some of the follower humanoid robots may lose their balance and fall down. The symmetry type cooperation discussed in this paper solves this problem because it enables all humanoid robots to move synchronously. The proposed framework is verified by dynamic simulations.     

空间机器人最优能耗捕获目标的自适应跟踪控制

提出了一种能够引导末端执行器以期望速度跟踪目标的轨迹规划方法。该方法可以实现避障并满足关节限制要求。基于轨迹规划方法,设计了一种利用自由飘浮空间机器人跟踪与捕获章动自旋卫星的自适应控制策略。此外,该控制策略还考虑了最优能耗、测量误差和优化误差。首先,为了使执行器的跟踪误差和机械臂的能耗最小,将空间机器人的控制策略描述为一个关于关节速度、力矩和避障距离的不等式约束优化问题。然后,推导出一个系数为下三角矩阵的显式状态方程,并对目标函数进行解耦和线性化。设计了一种关节速度和力矩分段优化方法去代替传统的凸二次规划方法求解最优问题,这种方法具有较高的计算效率。最后,利用李雅普诺夫稳定性理论验证了所提控制方法的收敛性。     

Somatosensory computation for man-machine interface from motion-capture data and musculoskeletal human model

We discuss the computation of somatosensory information from motion-capture data. The efficient computational algorithms previously developed by the authors for multibody systems, such as humanoid robots, are applied to a musculoskeletal model of the human body. The somatosensory information includes tension, length, and velocity of the muscles, tension of the tendons and ligaments, pressure of the cartilages, and stress of the bones. The inverse dynamics of the musculoskeletal human model is formulated as an optimization problem subject to equality and inequality conditions. We analyzed the solutions obtained by linear and quadratic programming methods, and showed that linear programming has better performance. The technological development aims to define a higher dimensional man-machine interface and to open the door to the cognitive-level communication of humans and machines.     

A Study on Acquiring Underlying Behavioral Criteria for Manipulator Motion by Focusing on Learning Efficiency

Conventional humanoid robotic behaviors are directly programmed depending on the programmer's personal experience. With this method, the behaviors usually appear unnatural. It is believed that a humanoid robot can acquire new adaptive behaviors from a human, if the robot has the criteria underlying such behaviors. The aim of this paper is to establish a method of acquiring human behavioral criteria. The advantage of acquiring behavioral criteria is that the humanoid robots can then autonomously produce behaviors for similar tasks with the same behavioral criteria but without transforming data obtained from morphologically different humans every time for every task. In this paper, a manipulator robot learns a model behavior, and another robot is created to perform the model behavior instead of being performed by a person. The model robot is presented some behavioral criteria, but the learning manipulator robot does not know them and tries to infer them. In addition, because of the difference between human and robot bodies, the body sizes of the learning robot and the model robot are also made different. The method of obtaining behavioral criteria is realized by comparing the efficiencies with which the learning robot learns the model behaviors. Results from the simulation have demonstrated that the proposed method is effective for obtaining behavioral criteria. The proposed method, the details regarding the simulation, and the results are presented in this paper.     

一种仿人机械臂的运动学逆解的几何求解方法

运用几何方法求解一种具有7个旋转自由度的仿人机械臂的运动学逆解,并运用特定的寻优指标,搜索与指定末端位姿对应的关节角空间最优解.这种解法没有理论误差并且解算速度足够快,有利于在线实时控制机械臂的运动.     

Robot coordination using task-priority and sliding-mode techniques

In this work, an approach based on task-priority redundancy resolution and sliding mode ideas is proposed for robot coordination. In particular, equality and inequality constraints representing the coordination of the multi-robot system are considered as mandatory (for instance, rigid-body manipulation constraints to distance between the end-effectors of several robot arms, or other inequality constraints guaranteeing safe operation of a robotic swarm or confining the robot's workspace to avoid collision and joint limits). Besides the mandatory constraints, other constraints with lower priority are considered for the tracking of the workspace reference and to achieve secondary goals. Thus, lower-priority constraints are satisfied only in the null space of the higher-priority ones. The fulfillment of the constraints is achieved using geometric invariance and sliding mode control theory. The validity and effectiveness of the proposed approach are substantiated by 2D and 3D simulation results using two 3R planar robots and two 6R PUMA-762 robots, respectively.     

Collision-free and smooth joint motion planning for six-axis industrial robots by redundancy optimization

Planning collision-free and smooth joint motion is crucial in robotic applications, such as welding, milling, and laser cutting. Kinematic redundancy exists when a six-axis industrial robot performs five-dimensional tasks, and there are infinite joint configurations for a six-axis industrial robot to realize a cutter location data of the tool path. The robot joint motion can be optimized by taking advantage of the kinematic redundancy, and the collision-free joint motion with minimum joint movement is determined as the optimal. However, most existing redundancy optimization methods do not fully exploit the redundancy of the six-axis industrial robots when they conduct five-dimensional tasks. In this paper, we present an optimization method to solve the problem of inverse kinematics for a six-axis industrial robot to synthesize the joint motion that follows a given tool path, while achieving smoothness and collision-free manipulation. B-spline is applied for the joint configuration interpolation, and the sum of the squares of the first, second, and third derivatives of the B-spline curves are adopted as the smoothness indicators. Besides, the oriented bounding boxes are adopted to simplify the shape of the robot joints, robot links, spindle unit, and fixtures to facilitate collision detections. Dijkstra's shortest path technique and Differential Evolution algorithm are combined to find the optimal joint motion efficiently and avoid getting into a local optimal solution. The proposed algorithm is validated by simulations on two six-axis industrial robots conducting five-axis flank milling tasks respectively.     

基于粒子群优化的刚柔混合机械臂振动抑制规划

提出基函数叠加与粒子群优化(PSO)相结合的振动抑制轨迹规划方法.首先推导了各关节变量与模态坐标的关系,采用正弦-梯形函数作为基函数构造各关节的角速度,其中基函数的系数和幅值为待定参数;然后将末端振动最小化轨迹规划转换为待定参数的优化问题,并采用PSO算法获得待定参数的最优值;最后以双杆刚柔混合机械臂为例开展仿真研究.仿真结果表明,所提出的方法大大减小了机械臂末端的残留振动.