End-effector Trajectory Research Articles

Variable impedance interaction and demonstration interface design based on measurement of arm muscle co-activation for demonstration learning

Learning from Demonstration (LfD) is a good way for robots to learn some complex tasks from human tutors, but the ordinary demonstration mode of LfD is unsuitable for learning interaction tasks that require the robot to run under the variable impedance control mode. In this study, we develop a variable impedance physical human–robot interaction (pHRI) interface and LfD mode for human motion skill transport based on surface electromyography (sEMG) signal and kinesthetic teaching. The pHRI interface and LfD mode developed in this study have the following advantages: 1) they can provide intuitive and pleasing variable impedance interaction effect for kinesthetic teaching on the basis of human arm stiffness estimation using sEMG signal. 2) They can simultaneously provide the expected motion data (expected end-effector trajectory and impedance gain scheduling) of tutors for demonstration learning, and these motion data can be used for learning complex interaction tasks under robot variable impedance control mode. 3) Kinesthetic teaching can provide tutor haptic feedback, which conforms to the human–human teaching mode, thereby reducing professional knowledge requirements and energy consumption of the tutor and improving teaching effect and efficiency. The pHRI interface and LfD mode are experimentally tested by two interaction and demonstration experiments. Results show that the proposed interface and mode have better dynamic interaction characteristic and performance than the constant impedance gain control LfD mode. Moreover, the tutor can be rapidly familiarized with this interface and mode and finish the demonstration with low energy consumption.

A process account of the uncontrolled manifold structure of joint space variance in pointing movements

In many situations, the human movement system has more degrees of freedom than needed to achieve a given movement task. Martin et al. (Neural Comput 21(5):1371–1414, 2009) accounted for signatures of such redundancy like self-motion and motor equivalence in a process model in which a neural oscillator generated timed end-effector virtual trajectories that a neural dynamics transformed into joint virtual trajectories while decoupling task-relevant and task-irrelevant combinations of joint angles. Neural control of muscle activation and the biomechanical dynamics of the arm were taken into account. The model did not address the main signature of redundancy, however, the UCM structure of variance: Many experimental studies have shown that across repetitions, variance of joint configuration trajectories is structured. Combinations of joint angles that affect task variables (lying in the uncontrolled manifold, UCM) are much more variable than combinations of joint angles that do not. This finding has been robust across movement systems, age, and tasks and is often preserved in clinical populations as well. Here, we provide an account for the UCM structure of variance by adding four types of noise sources to the model of Martin et al. (Neural Comput 21(5):1371–1414, 2009). Comparing the model to human pointing movements and systematically examining the role of each noise source and mechanism, we identify three causes of the UCM effect, all of which, we argue, contribute: (1) the decoupling of motor commands across the task-relevant and task-irrelevant subspaces together with “neural” noise at the level of these motor commands; (2) “muscle noise” combined with imperfect control of the limb; (3) back-coupling of sensed joint configurations into the motor commands which then yield to the sensed joint configuration within the UCM.

Learning based end effector tracking control of a mobile manipulator for performing tasks on an uneven terrain

A Mobile manipulator (MM) combines the ability to move on an uneven terrain and perform a desired task using the manipulator arm, like drilling, welding, pick and place, etc. However, due to slip, modeling and sensor errors during motion, the MM tends to deviate from the desired end effector path. The MM considered in this paper consists of a 10 DOF vehicle and a 4 DOF arm. As the system is redundant, the standard jacobian based pseudo inverse methods for finding the inverse kinematics solution cannot be used in real time and are very complex. Therefore, a learning based method using a two stage KSOM network has been used to learn the inverse kinematics solution and also track the end effector during motion. In the first stage the KSOM performs the redundancy resolution of the system and in the second stage it corrects the error during the actual motion. The forward kinematics model of the mobile manipulator is used to train the KSOM network, with the manipulability measure of the arm, joint angles of the system and the wheel terrain contact as constraints. Once the network is trained for a particular terrain, the corresponding joint angles and wheel velocities for tracking a desired end effector trajectory can be found in real time. Simulation and experimental results for tracking different end effector trajectories on an uneven terrain, proves the efficiency of the proposed method. The experimental results prove that the proposed method could track the end effector trajectory with an average error of less than 2 cm.

Virtual Reality-Based Time-Delayed Haptic Teleoperation Using Point Cloud Data

This paper presents a methodology for bilateral teleoperation of robots based on the use of point cloud data obtained with an RGB-D camera for providing haptic feedback, as well as a virtual robot workspace that allows the user to interact with the teleoperated robot and the environment, regardless of the time-delay between the master device and the slave robot. The robot movements are executed first in the Virtual Workspace and then in the real one. The Virtual Workspace is created using point cloud data, and the haptic feedback is calculated directly using this data. The proposed methodology was validated in 2D and 3D trajectory-following experiments with 20 volunteers each teleoperating a KUKA industrial robot. In addition, we studied two inverse kinematic teleoperation modes: “Proportional Workspace” and “Delta end-effector movements”, with the objective of determining which one is more suitable for the haptic teleoperation methodology proposed. The results obtained confirm that the proposed haptic teleoperation methodology enhances the precision of the operator by reducing the average error between the robot end-effector trajectory and the goal trajectory. Furthermore, the likelihood that the end-effector will collide with objects in the environment is reduced. The methodology also diminishes the time that it takes to complete the trajectory-following task in an unknown workspace. The inverse kinematic teleoperation mode with the better results is the “Proportional Workspace”, which is more intuitive for operators (users).

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.

Human-Robot Interaction and Demonstration Learning Mode Based on Electromyogram Signal and Variable Impedance Control

In this research, properties of variable admittance controller and variable impedance controller were simulated by MATLAB firstly, which reflected the good performance of these two controllers under trajectory tracking and physical interaction. Secondly, a new mode of learning from demonstration (LfD) that conforms to human intuitive and has good interaction performances was developed by combining the electromyogram (EMG) signals and variable impedance (admittance) controller in dragging demonstration. In this learning by demonstration mode, demonstrators not only can interact with manipulator intuitively, but also can transmit end-effector trajectories and impedance gain scheduling to the manipulator for learning. A dragging demonstration experiment in 2D space was carried out with such learning mode. Experimental results revealed that the designed human-robot interaction and demonstration mode is conducive to demonstrators to control interaction performance of manipulator directly, which improves accuracy and time efficiency of the demonstration task. Moreover, the trajectory and impedance gain scheduling could be retained for the next learning process in the autonomous compliant operations of manipulator.

Understanding the True Dynamics of Space Manipulators from Air-Bearing Based Ground Testing

A space manipulator can easily handle a large payload having a much larger mass than its own mass. However, physical test of such a manipulator handling a large-mass payload in 3D space on the ground is almost impossible due to gravity effect. A commonly used test method is to support the manipulator with air-bearing pads on a horizontal granite surface so that the robot can freely maneuver on the 2D surface as it were floating in a 2D microgravity environment. However, such a test method suffers a major problem: the air-bearing based support equipment is large and massive when the manipulator is long (e.g., 10 m or longer) and/or its payload is heavy (e.g., 500 kg or heavier), which adds significant inertial loading to the robot when it maneuvers. As a result, the manipulator has to make much more effort on a test than it would need in space. This paper describes a study for understanding the true dynamics of a space manipulator from such an air-bearing supported test. A test-data analysis method is developed, which can decouple and remove the dynamics effect of the air-bearing support equipment from tested manipulator system. With such an approach, the true joint torques for the space manipulator to produce a prescribed end-effector motion trajectory can be determined, although the manipulator has to be constrained to a massive air-bearing based support equipment for the testing. The method has been experimentally validated by a specially designed experiment facility.

Perceptual Validation for the Generation of Expressive Movements from End-Effector Trajectories

Endowing animated virtual characters with emotionally expressive behaviors is paramount to improving the quality of the interactions between humans and virtual characters. Full-body motion, in particular, with its subtle kinematic variations, represents an effective way of conveying emotionally expressive content. However, before synthesizing expressive full-body movements, it is necessary to identify and understand what qualities of human motion are salient to the perception of emotions and how these qualities can be exploited to generate novel and equally expressive full-body movements. Based on previous studies, we argue that it is possible to perceive and generate expressive full-body movements from a limited set of joint trajectories, including end-effector trajectories and additional constraints such as pelvis and elbow trajectories. Hence, these selected trajectories define a significant and reduced motion space, which is adequate for the characterization of the expressive qualities of human motion and that is both suitable for the analysis and generation of emotionally expressive full-body movements. The purpose and main contribution of this work is the methodological framework we defined and used to assess the validity and applicability of the selected trajectories for the perception and generation of expressive full-body movements. This framework consists of the creation of a motion capture database of expressive theatrical movements, the development of a motion synthesis system based on trajectories re-played or re-sampled and inverse kinematics, and two perceptual studies.

Coordinated Control of Aerial Robotic Manipulators: Theory and Experiments

This brief presents a three-layer control architecture for coordinated control of multiple unmanned aerial vehicle manipulators (UAVMs): the centralized top layer plans the end-effector desired trajectories of each UAVM; the middle layer, local to each vehicle, computes the corresponding motion references; the bottom layer is a low level dynamic motion controller, which tracks the motion references. At second layer, the overall mission is hierarchically decomposed in a set of elementary behaviors, which are combined together, via the null space-based behavioral approach, into more complex compound behaviors. For each UAVM, the suitable compound behavior to be executed is selected by a supervisor. The proposed framework has been tested through an experimental campaign.

Toward Motion Coordination Control and Design Optimization for Dual-Arm Concentric Tube Continuum Robots

Dual-arm continuum robots have been considered mainly for teleoperation, where human perception and cognition permitted coordination, and collision-free motions. This letter describes theoretical investigations on automation of dual-arm robots constituted of two concentric tube continuum manipulators. An optimization algorithm is developed in order to improve triangulation ability of the robot and thus enhance the arms’ collaborative operation. This a priori knowledge provides design directives in order to fulfill integration, reachability, and collaboration requirements. Further, automatic control is assigned to perform online safe collaboration tasks. Our initial exploration is validated with numerical simulations using robot designs based on the optimization algorithm output. The control algorithm—based on the relative Jacobian and Cosserat rod modeling—performs simultaneously with less than 1% of the total robot's length of accuracy for both relative end-effector distance control and trajectory tracking.

Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.

Adaptive motion/force control of uncertain nonholonomic mobile manipulator with estimation of unknown external force

This paper describes a stable adaptive motion/force control of uncertain nonholonomic mobile manipulator with the consideration of external force. As it is well known, unexpected external force makes the motion of the system unstable since there are no fixed points in the stationary coordinate. Here, a novel adaptive control scheme is utilized to estimate and compensate the unknown external force exerted to the end-effector even if the parameters of the system are uncertain. The important advantages of this approach are to achieve estimation without the requirement of force-sensing feedback and the knowledge of the system dynamic model. The update laws for the force and the parameters are derived from a Lyapunov function to guarantee the control system stability. Furthermore, a unified operational space dynamic formulation is presented to solve the problem of redundancy. As a result, the desired end-effector and platform trajectories are simultaneously tracked with a perfect coordination between the two subsystems. Therefore, the proposed controller proves that it can not only guarantee the stability, but also the tracking performance of the system in the task space. The effectiveness of the proposed algorithm is evaluated through extensive simulations and they demonstrate the stability, tracking trajectories and feasibility in estimating the external force and the dynamic uncertainties.

Dynamically Feasible Periodic Trajectories for Generic Spatial Three-Degree-of-Freedom Cable-Suspended Parallel Robots1

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to be varied, thus providing more latitude in the trajectory definition. We finally study transition trajectories to move the robot from an initial state of rest (within the static workspace) to the elliptical trajectory (and vice versa) or to connect two identical ellipses having different centers.

Optimal trajectory planning considering optimal torque distribution of redundantly actuated parallel mechanism

Previous studies on the optimal operation planning of redundantly actuated parallel mechanisms have focused on optimal torque distribution for a predefined trajectory. However, the optimized result obtained for a predefined trajectory cannot guarantee an optimal operation plan, because the torque distribution ability of a redundantly actuated parallel mechanism is highly dependent on the shape of the end-effector trajectory. Therefore, we can expect the redundantly actuated parallel mechanism performance to be enhanced when both the trajectory and torque distribution are optimized during the optimal operation planning stage. We propose a novel redundantly actuated parallel mechanism optimization procedure that can optimize both the end-effector trajectory and torque distribution. The proposed procedure is composed of two stages of optimizers, i.e. upper- and lower-level optimizers that generate the end-effector trajectory and distribute the torques along the generated trajectory, respectively. Composition of these two stages of the optimization procedure allows optimization of both the trajectory and torque distribution, despite the correlation between them. The proposed optimization procedure is simulated using two types of cost functions. All the simulation results show that the proposed procedure facilitates optimization of the end-effector trajectory and the torque distribution concurrently. Also, the cost function value is minimized to a greater extent than in the result with the optimal torque distribution along the initial trajectory.

Workspace Limiting Strategy for 6 DOF Force Controlled PKMs Manipulating High Inertia Objects

This article describes an efficient and effective strategy for limiting the workspace of a six degrees of freedom parallel manipulator, with challenging motion smoothness requirements due to both the high inertia objects carried by the end effector and the pose references coming from a force feedback loop. Firstly, a suitable formulation of the workspace is studied, distinguishing between different conventions and procedures. Thereafter a discrete and analytical formulation of the workspace is obtained and developed in order to suit this application. Having obtained the limits, a methodology to evaluate the robot pose is discussed, taking into account the reference pose buffering technique and the real time pose estimation through the numeric solution of the nonlinear forward kinematics equations. The safety algorithm designed checks the actual robot pose and future poses to be commanded, and takes control of the reference pose generation process, if an exit of the safety workspace is detected. The result obtained is a soft compliant surface within which the robot is free to move, but outside of which a “force field” pushes the robot end-effector to return smoothly. To reach this objective, the control deflects the end effector trajectory safely and smoothly and moves it back to within the workspace limits. Nevertheless, this preserves the continuity of the velocity and controls the acceleration, to avoid dangerous vibrations and shocks. Simulation and experimental result tests are conducted to verify the algorithm effectiveness and the efficient implementation.

Path Planning and Collision Avoidance for a Multi-Arm Space Maneuverable Robot

In this paper, a path planning algorithm for a multi-arm space robot is proposed. The robot is capable of maneuvering on the exterior of a large space station. Based on the maneuver strategy, continuous and smooth trajectories of the manipulator end effectors are first determined via the polynomial interpolation method. Then, the kinematics describing the relation between the end effector and the joint angles as well as the platform are formulated. A Moore–Penrose pseudoinverse solution of the joint trajectories is calculated to describe the motion of the manipulators, particularly, considering the singularity avoidance. In addition, a collision detection algorithm is developed to estimate the security during operation. Constraints are formulated by considering collision avoidance, based on which a collision-free trajectory is optimized through the multiplier-penalty method. The numerical results of a triple-arm space robotic system are given to demonstrate the effectiveness of the proposed algorithms.

Programming by Demonstration Using Two-Step Optimization for Industrial Robot.

The paper presents programming by demonstration approach for industrial robots that uses two steps trajectory optimization. On the first stage, optimization is done by statistical methods, on the second stage, the robot end-effector trajectory is obtained based on minimization of energy consumption and task execution time criteria. We verified our approach using 7 degree-of-freedom redundant robot KUKA iiwa and Microsoft Kinect 2.0 motion capture system.

Constraint-Based Cooperative Control of Multiple Aerial Manipulators for Handling an Unknown Payload

This paper presents the planning and control synthesis of cooperative aerial manipulators to carry an unknown object together. The online parameter estimation algorithm is designed to estimate the unknown physical parameters of the common payload such as mass and moment of inertia, without the need of multiaxis force/torque sensors. Based on the augmented adaptive sliding mode controller with the estimated physical parameters, the desired trajectory of each aerial manipulator is generated to track the desired trajectory of corresponding end effector. In order to carry an unknown object safely considering the actuation limit of the hexacopter, we use the task priority to satisfy the unilateral constraints determined by the allowable flight envelope. To validate our approach, the experimental result on a successful transportation by using multiple custom-made aerial manipulators is shown. This result suggests that the proposed approach can be utilized for safe cooperative aerial transportation.

A TE-E Optimal Planning Technique Based on Screw Theory for Robot Trajectory in Workspace

In the previous study, the minimum time and energy have been both considered to improve the efficiency and reliability of the manipulator operations. For further guaranteeing the tracking precision of end effector, a TE-E optimal planning technique is presented in this paper to optimize the trajectory of end effector. TE-E means two optimization objectives and one constraint condition: T is the total motion time, the first E is the total kinetic energy consumption and the second E is the motion error due to trajectory planning. In this technique, a local optimization process is completed to find a time-energy optimal trajectory, which could improve the movement efficiency and reliability. In this local process, the screw theory is used to obtain the forward and inverse kinematic models for simplifying the computation. The multi-solution situation in inverse kinematic is considered. The modified cubic spline interpolation is applied in the joint space to obtain the good motion stability. The objective function is defined as the weighted sum of two optimization objectives. The local optimal trajectory is obtained by using the particle swarm optimization (PSO) algorithm. Finally, the motion errors are considered as a condition to determine the number of the path points and obtain the final optimal trajectory that has good tracking precision. The simulation experiment for QJ-1 welding manipulator is completed to verify the reliability and validity of this technique. In the optimal trajectory, the relationships between the motion time and parameters for each joint show a good performance in the motion. The comparison of motion errors obtained by using the previous and presented methods proves the validity of this presented technique.

Cognitive learning and its future in urology

The aim of this study is to provide an overview of the current status of novel cognitive training approaches in surgery and to investigate the potential role of cognitive training in surgical education. Kinematics of end-effector trajectories, as well as cognitive state features of surgeon trainees and mentors have recently been studied as modalities to objectively evaluate the expertise level of trainees and to shorten the learning process. Virtual reality and haptics also have shown promising in research results in improving the surgical learning process by providing feedback to the trainee. 'Cognitive training' is a novel approach to enhance training and surgical performance. The utility of cognitive training in improving motor skills in other fields, including sports and rehabilitation, is promising enough to justify its utilization to improve surgical performance. However, some surgical procedures, especially ones performed during human-robot interaction in robot-assisted surgery, are much more complicated than sport and rehabilitation. Cognitive training has shown promising results in surgical skills-acquisition in complicated environments such as surgery. However, these methods are mostly developed in research groups using limited individuals. Transferring this research into the clinical applications is a demanding challenge. The aim of this review is to provide an overview of the current status of these novel cognitive training approaches in surgery and to investigate the potential role of cognitive training in surgical education.