Smooth trajectory planning for a parallel manipulator with joint friction and jerk constraints

In order to achieve better tracking accuracy effectively, a new smooth and near time-optimal trajectory planning approach is proposed for a parallel manipulator subject to kinematic and dynamic constraints. The complete dynamic model is constructed with consideration of all joint frictions. The presented planning problem can be solved efficiently by formulating a new limitation curve for dynamic constraints and a reduced form for jerk constraints. The motion trajectory is planned with quartic and quintic polynomial splines in Cartesian space and septuple polynomial splines in joint space. Experimental results show that smaller tracking error can be obtained. The developed method can be applied to any robots with analytical inverse kinematic and dynamic solutions.     

增强现实应用中基于三维模型的手形追踪

本文介绍了一种基于三维模型的分步迭代法来实现对全局和局部手运动的估计追踪。手部位置由ICP(Iterative Closed point)算法和因式分解法求得的掌形近似。结合自然手运动限制，本文采用基于序列的Monte Carlo算法追踪手指运动。最后采用在姿态估计和手指关节追踪之间的迭代算法得到一个精确的结构估计。实验证实本方法对自然手势运动具有较好的精确性和鲁棒性。     

平面复杂边缘的双机器人协调跟踪运动规划研究

研究双机器人协调跟踪平面复杂边缘所涉及的问题.在笛卡儿空间内对跟踪任务进行协调分解,并分析双机器人的位置约束关系,采用双曲线函数规划双机器人基于关节空间的运动轨迹,以满足位置、速度以及加速度等平滑运动的约束条件,采用基于曲线极大值的分段跟踪算法扩展平面复杂曲线的一般性.仿真实验和应用均表明了所研究内容的可行性和正确性.     

基于加速度计的手指运动姿态检测

针对动态测量手指关节角度的需要,设计了一种基于MEMS加速度计的手指运动姿态检测方法。在该方法中,通过固定于手指上的三轴加速度计ADXL330的各个敏感轴感受到的重力加速度分量的大小来检测手指的关节角度。为了验证该方法的可行性,设计了一步进电机控制的能在竖直平面内转动的装置,通过同步检测传感器的输出和电机转动的角度,评估传感器在动态条件下的测量精度,结果表明:在动态条件下,其绝对误差为1°～2.5°,相对误差为3%～6%。在此基础上,将传感器用于测量手指关节的运动姿态,采集手指敲击键盘时传感器的输出,通过数据处理获得食指MCP关节、PIP关节和DIP关节随时间的变化关系。实验结果表明:加速度计可以有效地检测手指的运动姿态。     

Predicting Articulated Human Motion from Spatial Processes

We present a probabilistic interpretation of inverse kinematics and extend it to sequential data. The resulting model is used to estimate articulated human motion in visual data. The approach allows us to express the prior temporal models in spatial limb coordinates, which is in contrast to most recent work where prior models are derived in terms of joint angles. This approach has several advantages. First of all, it allows us to construct motion models in low dimensional spaces, which makes motion estimation more robust. Secondly, as many types of motion are easily expressed in spatial coordinates, the approach allows us to construct high quality application specific motion models with little effort. Thirdly, the state space is a real vector space, which allows us to use off-the-shelf stochastic processes as motion models, which is rarely possible when working with joint angles. Fourthly, we avoid the problem of accumulated variance, where noise in one joint affects all joints further down the kinematic chains. All this combined allows us to more easily construct high quality motion models. In the evaluation, we show that an activity independent version of our model is superior to the corresponding state-of-the-art model. We also give examples of activity dependent models that would be hard to phrase directly in terms of joint angles.     

Analyzing and capturing articulated hand motion in image sequences

Capturing the human hand motion from video involves the estimation of the rigid global hand pose as well as the nonrigid finger articulation. The complexity induced by the high degrees of freedom of the articulated hand challenges many visual tracking techniques. For example, the particle filtering technique is plagued by the demanding requirement of a huge number of particles and the phenomenon of particle degeneracy. This paper presents a novel approach to tracking the articulated hand in video by learning and integrating natural hand motion priors. To cope with the finger articulation, this paper proposes a powerful sequential Monte Carlo tracking algorithm based on importance sampling techniques, where the importance function is based on an initial manifold model of the articulation configuration space learned from motion-captured data. In addition, this paper presents a divide-and-conquer strategy that decouples the hand poses and finger articulations and integrates them in an iterative framework to reduce the complexity of the problem. Our experiments show that this approach is effective and efficient for tracking the articulated hand. This approach can be extended to track other articulated targets.     

On inverse kinematics with inequality constraints: new insights into minimum jerk trajectory generation

The problem of inverse kinematics is revisited in the present paper. The paper is focusing on the problem of solving the inverse kinematics problem while minimizing the jerk of the joint trajectories. Even though the conventional inverse kinematics algorithms have been proven to be efficient in many applications, it has been proven that constraints on the accelerations or the jerk cannot be guaranteed, and even yields to divergence or makes the problem unsolvable. The proposed algorithm yields smooth velocity and acceleration trajectories, which are highly desired features for industrial robots. The algorithm uses the joint jerk as the control parameter instead of the classical use of the joint velocity as result constraints on the jerk function can be easily incorporated. To validate the proposed approach, we have conducted several simulations scenarios. The simulation results have revealed that the proposed method can efficiently solve the inverse kinematics problem while considering constraints on the joint acceleration and jerk.     

Control of biomimetic robots based on analysis of human arm trajectories in 3D movements

In this study, a biomimetic robot arm with joint redundancy movable in a three-dimensional space is taken into consideration. The basic trajectories for controlling all joints are formulated under the minimum angular jerk criterion. Then, a time adjustment of the joint motion of the elbow relative to the shoulder is provided for representing specific properties of joint angular trajectories during a movement. Here, a systematical scheme for formulating the human-like trajectory has been developed by use of a direct kinematics. As the angular trajectories of all joints can be formulated in the proposed manner, the hand trajectory can be uniquely produced once the initial and final postures of the arm and a movement duration are given. The trajectories under the proposed scheme are produced by utilizing the same movement conditions observed by experiments. Then, performance for reproducing human-like trajectories has been evaluated under the comparative analysis between the observed and the produced trajectories.     

Hard disk drive seeking profile optimisation via linear programming

In this article we develop an approach to design track-seeking controller for hard disk drive. We convert the current multi-sine seek approach to an equivalent linear programming problem that can be solved efficiently and accurately. We demonstrate the efficacy of this approach by numerical case studies that are otherwise infeasible in the current approach. We further derive the time optimal track seeking as a three-piece constant control. Our approach can also be extended to deal with other sophisticated requirements on smoothness, jerk and resonance.     

Time-optimal parabolic interpolation with velocity,acceleration, and minimum-switch-time constraints

Time-optimal trajectories with bounded velocities and accelerations are known to be parabolic, i.e. piecewise constant in acceleration. An important characteristic of this class of trajectories is the distribution of the switch points – the time instants when the acceleration of any robot joint changes. When integrating parabolic trajectory generation into a motion planning pipeline, especially one that involves a shortcutting procedure, resulting trajectories usually contain a large number of switch points with a dense distribution. This high frequency acceleration switching intensifies joint motor wear as well as hampers the robot performance. In this paper, we propose an algorithm for planning parabolic trajectories subject to both physical bounds, i.e. joint velocity and acceleration limits, and the minimum-switch-time constraint. The latter constraint ensures that the time duration between any two consecutive switch points is always greater than a given minimum value. Analytic derivations are given, as well as comparisons with other methods to demonstrate the efficiency of our approach.     

在线考虑运动学限制的最小加速度的轨迹规划

提出了一种基于简化运动规划的机器人轨迹规划新方法,可用于多自由度的机器人操作臂系统。关键问题是找到最小加速度的轨迹规划,来优化操作臂的运动以减少抖动。此外,给出了轨迹规划的解存在的充分必要条件,并考虑了所有的关节位置、角速度、加速度、加加速度等运动学限制。而且这种方法能够在线应用,适合任意非零的关节初始状态和目标状态,以便使机器人能够在运动过程中进行实时路径修正。最后提出的方法应用于一个七自由度的仿人机器人手臂来验证方法的有效性。     

Extended impedance control of redundant manipulators based on weighted decomposition of joint space

In this work, impedance control approach based on an extended task space formulation is addressed to control the kinematically redundant manipulators. By defining a weighted inner product in joint space, a minimal parameterization of the null space is achieved, and we can visualize the null space motion explicitly. Moreover, it is shown that careful choice of the weighting matrix gives physically consistent and inertially decoupled dynamics. By augmenting this minimal null motion parameter with a forward kinematic relation, a new extended task space formulation can be obtained. Based on this formulation, we propose two control methods, a kinematically decomposed impedance controller and an inertially decoupled impedance controller, to control the motion of the end-effector as well as the internal motion expanding the conventional impedance control. We also show the relationship with the previous dynamic controllers of a redundant manipulator. Some numerical simulations are given to demonstrate the performance of the proposed control methods. © 1998 John Wiley & Sons, Inc.     

Operating robot manipulators through kinematic singularities using a continuously sliding mode control

Planning the motion of end-effectors of robot manipulators can be carried out more directly in the Cartesian space compared to the joint space. Yet, Cartesian paths may include singular configurations where conventional control schemes suffer from excessive joint velocities and loss of tracking accuracy. The difficulties arise because the Jacobian matrix that is used to establish a linear relation between the velocities in the task and joint spaces loses rank at singularities. The problem can be resolved by using a local second-order approximation of robot kinematics for the joint velocities, which is called Resolved Motion Quadratic Rate Control. In this article, we present a control strategy based on this approach and a recently developed variable structure control scheme. The controller receives Cartesian inputs whenever the manipulator is outside the singular domain. Otherwise, it uses resolved motion quadratic rate control to compute the required joint inputs. Numerical simulation is performed to show that the proposed control scheme provides accurate tracking of the desired motion without inducing excessive control activity when operating robot manipulators through singular configurations. © 1994 John Wiley & Sons, Inc.     

A finger motion model for reach and grasp

This study aimed to develop a model that describes human finger motion for simulation of reach and grasp for selected objects and tasks. Finger joint angles and timing of their changes were measured for six subjects as they reached 20-40 cm and grasped cylindrical handles (1.3-10.2 cm D) of varying orientation (vertical/axial). The empirical results from multiple regression analyses served as inputs to allow a fourth order polynomial to predict motion of each finger joint. The proposed model showed good fit with observations, with high coefficients of determination from 0.54 to 1 and reasonable errors from 0.04° to 5.44° for all conditions considered. The proposed finger motion model was implemented in an existing kinematic hand model to employ a contact algorithm for refined prediction of grip posture and to illustrate its predictive power by graphically displaying the opening and closing of the hand.

Relevance to industry

Finger joint motions during reach and grasp are needed for prediction of (1) tendon excursions for study of work-related musculoskeletal disorders, (2) required space for the hand, (3) finger locations on work objects, and (4) hand grip postures and strength.     

钢丝绳传动机器人运动学的支路分析方法

通过研究分析一类[N+1]条钢丝绳驱动[N]个自由度机器人的运动学,其运动学可通过推导移去钢丝绳后开环链机器人关节空间与笛卡尔空间之间的运动学关系和关节空间与驱动空间之间的运动学关系来完成。在基本回路、共轴条件和传动线运动学分析的基础上,提出了用支路矩阵和等效半径矩阵描述钢丝绳传动机器人运动学的支路分析方法。根据钢丝绳传动原理,通过观察法可直接列写支路矩阵和驱动空间等效半径矩阵,从而得到了驱动空间与关节空间之间的运动学映射关系,解耦了由于钢丝绳传动导致机器人关节间的运动耦合。结合传统机器人运动学,实现了驱动空间、关节空间和笛卡尔空间完整运动学映射关系,加快和简化了钢丝绳传动机器人运动学建模和分析过程。以Stanford/JPL手指为例进行了运动学分析和仿真,验证了用支路矩阵和等效半径矩阵描述钢丝绳传动机器人运动学支路分析方法的正确性,为钢丝绳传动机构的设计、运动学分析与控制奠定了基础。     

Natural metrics and least-committed priors for articulated tracking

In articulated tracking, one is concerned with estimating the pose of a person in every frame of a film. This pose is most often represented as a kinematic skeleton where the joint angles are the degrees of freedom. Least-committed predictive models are then phrased as a Brownian motion in joint angle space. However, the metric of the joint angle space is rather unintuitive as it ignores both bone lengths and how bones are connected. As Brownian motion is strongly linked with the underlying metric, this has severe impact on the predictive models. We introduce the spatial kinematic manifold of joint positions, which is embedded in a high dimensional Euclidean space. This Riemannian manifold inherits the metric from the embedding space, such that distances are measured as the combined physical length that joints travel during movements. We then develop a least-committed Brownian motion model on the manifold that respects the natural metric. This model is expressed in terms of a stochastic differential equation, which we solve using a novel numerical scheme. Empirically, we validate the new model in a particle filter based articulated tracking system. Here, we not only outperform the standard Brownian motion in joint angle space, we are also able to specialise the model in ways that otherwise are both difficult and expensive in joint angle space.     

带滑移铰空间机械臂的非完整运动规划遗传算法

本文讨论带滑移铰空间机械臂非完整运动规划的最优控制问题。利用系统的非完整特性,将带滑移铰空间机械臂运动规划转化为非线性系统最优控制问题。提出基于遗传算法的非完整运动规划最优控制方法。通过仿真计算,验证了该方法的有效性和可行性。     

Latent motion spaces for full-body motion editing

We explore an approach to full-body motion editing with linear motion models, prioritized constraint-based optimization and latent-space interpolation. By exploiting the mathematical connections between linear motion models and prioritized inverse kinematics (PIK), we formulate and solve the motion editing problem as an optimization function whose differential structure is rich enough to efficiently optimize user-specified constraints within the latent motion space. Performing motion editing within latent motion spaces has the advantage of handling pose transitions and consequently motion flow by construction from single key-frame editing. To handle motion adjustments from multiple key-frame and trajectory constraints, we developed a latent-space interpolation technique by exploiting spline functions. Such an approach handles per-frame adjustments generating smooth animations, while avoiding the computational expense of joint space interpolations. We demonstrate the usefulness of this approach by editing and generating full-body reaching and walking jump animations in challenging environment scenarios.     

Jerk-level synchronous repetitive motion scheme with gradient-type and zeroing-type dynamics algorithms applied to dual-arm redundant robot system control

Dual-arm redundant robot systems are usually required to handle primary tasks, repetitively and synchronously in practical applications. In this paper, a jerk-level synchronous repetitive motion scheme is proposed to remedy the joint-angle drift phenomenon and achieve the synchronous control of a dual-arm redundant robot system. The proposed scheme is novelly resolved at jerk level, which makes the joint variables, i.e. joint angles, joint velocities and joint accelerations, smooth and bounded. In addition, two types of dynamics algorithms, i.e. gradient-type (G-type) and zeroing-type (Z-type) dynamics algorithms, for the design of repetitive motion variable vectors, are presented in detail with the corresponding circuit schematics. Subsequently, the proposed scheme is reformulated as two dynamical quadratic programs (DQPs) and further integrated into a unified DQP (UDQP) for the synchronous control of a dual-arm robot system. The optimal solution of the UDQP is found by the piecewise-linear projection equation neural network. Moreover, simulations and comparisons based on a six-degrees-of-freedom planar dual-arm redundant robot system substantiate the operation effectiveness and tracking accuracy of the robot system with the proposed scheme for repetitive motion and synchronous control.