Analytical Inverse Kinematics Solver for Anthropomorphic 7-DOF Redundant Manipulators with Human-Like Configuration Constraints

It is a common belief that service robots shall move in a human-like manner to enable natural and convenient interaction with a human user or collaborator. In particular, this applies to anthropomorphic 7-DOF redundant robot manipulators that have a shoulder-elbow-wrist configuration. On the kinematic level, human-like movement then can be realized by means of selecting a redundancy resolution for the inverse kinematics (IK), which realizes human-like movement through respective nullspace preferences. In this paper, key positions are introduced and defined as Cartesian positions of the manipulator’s elbow and wrist joints. The key positions are used as constraints on the inverse kinematics in addition to orientation constraints at the end-effector, such that the inverse kinematics can be calculated through an efficient analytical scheme and realizes human-like configurations. To obtain suitable key positions, a correspondence method named wrist-elbow-in-line is derived to map key positions of human demonstrations to the real robot for obtaining a valid analytical inverse kinematics solution. A human demonstration tracking experiment is conducted to evaluate the end-effector accuracy and human-likeness of the generated motion for a 7-DOF Kuka-LWR arm. The results are compared to a similar correspondance method that emphasizes only the wrist postion and show that the subtle differences between the two different correspondence methods may lead to significant performance differences. Furthermore, the wrist-elbow-in-line method is validated as more stable in practical application and extended for obstacle avoidance.     

A biomimetic approach to inverse kinematics for a redundant robot arm

Redundant robots have received increased attention during the last decades, since they provide solutions to problems investigated for years in the robotic community, e.g. task-space tracking, obstacle avoidance etc. However, robot redundancy may arise problems of kinematic control, since robot joint motion is not uniquely determined. In this paper, a biomimetic approach is proposed for solving the problem of redundancy resolution. First, the kinematics of the human upper limb while performing random arm motion are investigated and modeled. The dependencies among the human joint angles are described using a Bayesian network. Then, an objective function, built using this model, is used in a closed-loop inverse kinematic algorithm for a redundant robot arm. Using this algorithm, the robot arm end-effector can be positioned in the three dimensional (3D) space using human-like joint configurations. Through real experiments using an anthropomorphic robot arm, it is proved that the proposed algorithm is computationally fast, while it results to human-like configurations compared to previously proposed inverse kinematics algorithms. The latter makes the proposed algorithm a strong candidate for applications where anthropomorphism is required, e.g. in humanoids or generally in cases where robotic arms interact with humans.     

仿人足底肌电特征的机器人行走规划

模仿人类行走规律是规划双足机器人运动的基础.以往模仿人类步态主要通过视觉方法或惯性模块测量(Inertia measurement unit, IMU)方法捕捉人体特征点轨迹.这些方法不考虑零力矩点(Zero moment point, ZMP)的相似性.为解决该问题,本文提出了一种基于足底肌电信号(Electromyography, EMG)和惯性模块测量信号的混合运动规划方法.该方法通过测量足底肌电信号计算出足底压力中心的位置以及踝关节扭矩,结合惯性模块所测量的人体躯干和双足轨迹,来规划双足机器人的步态.首先,用肌电仪测量足底肌电信号,用惯性测量模块测量人体各肢体部分的姿态轨迹,经数据标定后作为仿人机器人的运动参考; 然后,通过预观控制输出稳定的步态.为确保仿人行走的效果,基于人体相似性对运动数据进行了步态优化.实验验证和分析表明, EMG信号超前ZMP约160ms,利用这个特性实现了对压力点位置的有效预测,提高了机器人在线模仿人类行走的稳定性.     

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.     

The handwriting problem [man-machine motion analogy in robotics]

Two approaches are proposed to model and control a human-like motion of robot arms. The first, which is based on the concept of distributed positioning (DP), is suggested as a good model of arm motion in the phase where fatigue does not appear. The prescribed motion of the end-effector is distributed to a redundant number of arm joints in accordance to their acceleration capabilities. For the phase where fatigue appears, the concept of virtual fatigue is proposed. This artificial variable, which is based on robot dynamics, emulates the progress of biological fatigue. The human handwriting task is chosen for the simulation. The DP concept is tested first by modeling nonfatigued motion. The justification of the usual inclination of letters is presented, and the relation between the inclination, legibility, and a secondary objective (finger involvement, energy consumption, motor thermal load) is discussed. It is found that, for some prescribed level of legibility, the individual optima of all the secondary cost functions are quite near to each other. Writing in the presence of fatigue is also analyzed, applying the method of the so-called "virtual fatigue".     

Generating human-like soccer primitives from human data

Recently, interest in analysis and generation of human and human-like motion has increased in various areas. In robotics, in order to operate a humanoid robot, it is necessary to generate motions that have strictly dynamic consistency. Furthermore, human-like motion for robots will bring advantages such as energy optimization.This paper presents a mechanism to generate two human-like motions, walking and kicking, for a biped robot using a simple model based on observation and analysis of human motion. Our ultimate goal is to establish a design principle of a controller in order to achieve natural human-like motions. The approach presented here rests on the principle that in most biological motor learning scenarios some form of optimization with respect to a physical criterion is taking place. In a similar way, the equations of motion for the humanoid robot systems are formulated in such a way that the resulting optimization problems can be solved reliably and efficiently.The simulation results show that faster and more accurate searching can be achieved to generate an efficient human-like gait. Comparison is made with methods that do not include observation of human gait. The gait has been successfully used to control Robo-Erectus, a soccer-playing humanoid robot, which is one of the foremost leading soccer-playing humanoid robots in the RoboCup Humanoid League.     

Position referenced force augmentation in teleoperated hydraulic manipulators operating under delayed and lossy networks: A pilot study

Position error between motions of the master and slave end-effectors is inevitable as it originates from hard-to-avoid imperfections in controller design and model uncertainty. Moreover, when a slave manipulator is controlled through a delayed and lossy communication channel, the error between the desired motion originating from the master device and the actual movement of the slave manipulator end-effector is further exacerbated. This paper introduces a force feedback scheme to alleviate this problem by simply guiding the operator to slow down the haptic device motion and, in turn, allows the slave manipulator to follow the desired trajectory closely. Using this scheme, the master haptic device generates a force, which is proportional to the position error at the slave end-effector, and opposite to the operator’s intended motion at the master site. Indeed, this force is a signal or cue to the operator for reducing the hand speed when position error, due to delayed and lossy network, appears at the slave site. Effectiveness of the proposed scheme is validated by performing experiments on a hydraulic telemanipulator setup developed for performing live-line maintenance. Experiments are conducted when the system operates under both dedicated and wireless networks. Results show that the scheme performs well in reducing the position error between the haptic device and the slave end-effector. Specifically, by utilizing the proposed force, the mean position error, for the case presented here, reduces by at least 92% as compared to the condition without the proposed force augmentation scheme. The scheme is easy to implement, as the only required on-line measurement is the angular displacement of the slave manipulator joints.     

Implementation of the velocities of the end-effector with the distributed arithmetic architecture

The fast implementation of the linear and of the angular velocities of the end-effector of robotic manipulators, using the distributed arithmetic technique is described. The linear and angular velocities of the end-effector as well as the positional and the orientational jacobian matrices is calculated by a cascade configuration of two pipelined arrays. The building blocks of the arrays are the distributed arithmetic-based circuits that implement the matrix-vector multiplications involved in the calculations. The digit-serial configuration of the proposed implementation of the linear and angular velocities of the end-effector is described, while the serial and the parallel configurations may result as special cases of the digit-serial configuration. The proposed distributed arithmetic computer architecture may be used in the real-time operation of the robot control system that requires the on-line computation of the position, of the linear and angular velocities of the end-effector and of the Jacobian matrix.     

Internal Redundancy – the Way to Improve Robot Dynamics and Control Performances

The research follows the concept of variable geometry. The concept was originally introduced for general mechanical system in order to improve its dynamic behaviour [14]. Here, we apply the concept to robots. It can be shown that enhancement of robot dynamic performances is achieved. In this paper variation of geometry is considered equally as the motion in robot joints. Thus, a new set of degrees of freedom is introduced. This leads to redundancy – different internal motions are possible for the given external motion of the end-effector. However, there is an important difference from the usual notion of redundancy. Here, the additional joints do not influence the external motion and accordingly cannot improve the end-effector ability for maneuvering. For this reason the new notion is defined the internal redundancy.Although variation of geometry is treated equally with the motion in robot joints, there is still a difference in the aim of these new degrees of freedom. They should contribute to overcoming the limits of robot actuators, achieving better static compensation, etc. One might say that internal redundancy improves the robot dynamic capabilities. In this paper the mathematical formulation of kinematics and dynamics of robots with internal redundancy is carried out. A case study is presented in order to support the main idea.     

Optimization of layout and path planning of surgical robotic system

Positioning a surgical robot for optimal operation in a crowded operating room is a challenging task. In the robotic-assisted surgical procedures, the surgical robot’s end-effector must reach the patient’s anatomical targets because repositioning of the patient or surgical robot requires additional time and labor. This paper proposes an optimization algorithm to determine the best layout of the operating room, combined with kinematics criteria and optical constraints applied to the surgical assistant robot system. A new method is also developed for trajectory of robot’s end-effector for path planning of the robot motion. The average deviations obtained from repeatability tests for surgical robot’s layout optimization were 1.4 and 4.2 mm for x and y coordinates, respectively. The results of this study show that the proposed optimization method successfully solves the placement problem and path planning of surgical robotic system in operating room.

     

An obstacle avoidance algorithm for robot manipulators based on decision-making force

Obstacle avoidance is a significant skill not only for mobile robots but also for robot manipulators working in unstructured environments. Various algorithms have been proposed to solve off-line planning and on-line adaption problems. However, it is still not able to ensure safety and flexibility in complex scenarios. In this paper, a novel obstacle avoidance algorithm is proposed to improve the robustness and flexibility. The method contains three components: A closed-loop control system is used to filter the preplanned trajectory and ensure the smoothness and stability of the robot motion; the dynamic repulsion field is adopted to fulfill the robot with primitive obstacle avoidance capability; to mimic human’s complex obstacle avoidance behavior and instant decision-making mechanism, a parametrized decision-making force is introduced to optimize all the feasible motions. The algorithms were implemented in planar and spatial robot manipulators. The comparative results show the robot can not only track the task trajectory smoothly but also avoid obstacles in different configurations.     

A Dynamic Motion Control Technique for Human-like Articulated Figures

This paper presents a dynamic motion control technique for human-like articulated figures in a physically based character animation system. This method controls a figure such that the figure tracks input motion specified by a user. When environmental physical input such as an external force or a collision impulse are applied to the figure, this method generates dynamically changing motion in response to the physical input. We have introduced comfort and balance control to compute the angular acceleration of the figure's joints. Our algorithm controls the several parts of a human-like articulated figure separetely through the minimum number of degrees-of-freedom. Using this approach, our algorithm simulates realistic human motions at efficient computational cost. Unlike existing dynamic simulation systems, our method assumes that input motion is already realistic, and is aimed at dynamically changing the input motion in real-time only when unexpected physical input is applied to the figure. As such, our method works efficiently in the framework of current computer games.     

Asymmetric Velocity Moderation for human-safe robot control

With the increasing physical proximity of human–robot interaction, ensuring that robots do not harm surrounding humans has become crucial. Therefore, we propose asymmetric velocity moderation as a low-level controller for robotic systems to enforce human-safe motions. While our method prioritizes human safety, it also maintains the robot’s efficiency. Our proposed method restricts the robot’s speed according to (1) the displacement vector between human and robot, and (2) the robot’s velocity vector. That is to say, both the distance and the relative direction of movement are taken into account to restrict the robot’s motion. Through real-robot and simulation experiments using simplified HRI scenarios and dangerous situations, we demonstrate that our method is able to maintain the robot’s efficiency without undermining human safety.     

Interaction rule learning with a human partner based on an imitation faculty with a simple visuo-motor mapping

Imitation has been receiving increasing attention from the viewpoint of not simply generating new motions but also the emergence of communication. This paper proposes a system for a humanoid who obtains new motions through learning the interaction rules with a human partner based on the assumption of the mirror system. First, a humanoid learns the correspondence between its own posture and the partner’s one on the ISOMAPs supposing that a human partner imitates the robot motions. Based on this correspondence, the robot can easily transfer the observed partner’s gestures to its own motion. Then, this correspondence enables a robot to acquire the new motion primitive for the interaction. Furthermore, through this process, the humanoid learns an interaction rule that control gesture turn-taking. The preliminary results and future issues are given.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

Describing Upper-Body Motions Based on Labanotation for Learning-from-Observation Robots

We have been developing a paradigm that we call learning-from-observation for a robot to automatically acquire a robot program to conduct a series of operations, or for a robot to understand what to do, through observing humans performing the same operations. Since a simple mimicking method to repeat exact joint angles or exact end-effector trajectories does not work well because of the kinematic and dynamic differences between a human and a robot, the proposed method employs intermediate symbolic representations, tasks, for conceptually representing what-to-do through observation. These tasks are subsequently mapped to appropriate robot operations depending on the robot hardware. In the present work, task models for upper-body operations of humanoid robots are presented, which are designed on the basis of Labanotation. Given a series of human operations, we first analyze the upper-body motions and extract certain fixed poses from key frames. These key poses are translated into tasks represented by Labanotation symbols. Then, a robot performs the operations corresponding to those task models. Because tasks based on Labanotation are independent of robot hardware, different robots can share the same observation module, and only different task-mapping modules specific to robot hardware are required. The system was implemented and demonstrated that three different robots can automatically mimic human upper-body operations with a satisfactory level of resemblance.     

遥控作业移动机器人环境建模方法研究

本文介绍了用于遥控机器人作业虚拟环境生成的建模方法，重点研究了基于人机交互的双目立体视觉和多视点建模方法，以克服视觉自动建模方法计算复杂、鲁棒性差的缺点，给出了环境建模的实验系统和实验结果。     

Optimal Collision Free Path Planning for Non-Synchronized Motions

This paper treats the path finding problem for robots whose joints cannot be controlled in such a way that the end-effector follows a prespecified trajectory. Hence, if two or more joints are moving at the same time during the motion, the relative positions for the joints, i.e. the exact positions of the end-effector, are not known. This may be due to the low level control of the robot (for example, with heavy load robots), or due to a complicated kinematic structure. For such mechanisms a motion is specified by certain intermediate positions (values for all joints) along a desired path. These intermediate positions (synchronization points) and the requirement that the motions in the single joints are monotonous between consecutive synchronization points guarantee a certain structure of a path. We develop a new algorithm that determines paths for such mechanisms, i.e., a respective sequence of intermediate positions, such that the path is collision free and is shortest with respect to different optimality criteria.     

Coupled dynamical system based arm–hand grasping model for learning fast adaptation strategies

Performing manipulation tasks interactively in real environments requires a high degree of accuracy and stability. At the same time, when one cannot assume a fully deterministic and static environment, one must endow the robot with the ability to react rapidly to sudden changes in the environment. These considerations make the task of reach and grasp difficult to deal with. We follow a Programming by Demonstration (PbD) approach to the problem and take inspiration from the way humans adapt their reach and grasp motions when perturbed. This is in sharp contrast to previous work in PbD that uses unperturbed motions for training the system and then applies perturbation solely during the testing phase. In this work, we record the kinematics of arm and fingers of human subjects during unperturbed and perturbed reach and grasp motions. In the perturbed demonstrations, the target’s location is changed suddenly after the onset of the motion. Data show a strong coupling between the hand transport and finger motions. We hypothesize that this coupling enables the subject to seamlessly and rapidly adapt the finger motion in coordination with the hand posture. To endow our robot with this competence, we develop a coupled dynamical system based controller, whereby two dynamical systems driving the hand and finger motions are coupled. This offers a compact encoding for reach-to-grasp motions that ensures fast adaptation with zero latency for re-planning. We show in simulation and on the real iCub robot that this coupling ensures smooth and “human-like” motions. We demonstrate the performance of our model under spatial, temporal and grasp type perturbations which show that reaching the target with coordinated hand–arm motion is necessary for the success of the task.     

A compliant end-effector coupling for vertical assembly: design and evaluation

Many manipulation tasks require compliance, i.e. the robot's ability to comply with the environment and accomplish force as well as position control. Examples are constrained motion tasks and tasks associated with touch or feel in fine assembly. Few compliance-related tasks have been automated, and usually by active means of active compliance control: the need for passive compliance offered by the manipulator itself has been recognized and has led to the development of compliant end-effectors and/or wrists. In this paper we present a novel passively compliant coupling, the compliant end-effector coupling (CEEC), which aids automated precision assembly. It serves as a mechanical interface between the end of the robot arm and the end-effector. The coupling has 6 degrees of freedom. The design of the coupling is based on a “lock and free” assembly idea. The coupling is locked and behaves like a stiff member during robot motion, and is free (compliant) during constrained motion. It features an air bearing, a variable stiffness air spring and a center-locking mechanism. The end-effector assembly, being centrally unlocked, will float within the designed compliance limits assisted by the air bearing. These frictionless and constraint-free conditions facilitate a fast correction of any initial lateral and angular misalignments. In a peg insertion assembly, such accommodation is possible provided that the tip of the peg is contained within the chamfer of the hole. A variable stiffness air spring was incorporated in the design to allow variable and passive vertical compliance. This vertical compliance allows the accommodation of angular and vertical errors. The center-locking mechanism will return the end-effector assembly to its initial position upon an error correction. In a robot application program, the CEEC can be locked during rapid motion to securely transport a part or be set free during assembly or disassembly processes when the motions are constrained.