Task-space Errors Research Articles

Task Space Compliant Control and Six-Dimensional Force Regulation Toward Automated Robotic Ultrasound Imaging

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Objective:</i> We propose a general control framework for task space compliant motion and six-dimensional (6-D) force regulation towards automated robotic ultrasound (US) imaging. The framework endows a position-controlled robotic manipulator with the capability of accurate compliant motion in free space and accurate force control in motion-constrained environment. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Methods:</i> An intuitive six degree-of-freedom (6-DoF) admittance control model expressed in an arbitrary Cartesian body frame is mathematically derived with closed-form task space error mapping. Its practical implementation on widely-used collaborative manipulators is proposed to achieve full task space compliant behaviors and accurate 6-D force control. A hybrid control law is presented to achieve good motion accuracy in free space and improved coupled stability in motion-constrained environment. The coupled model of physical human-robot interaction is established and the reason for the improved coupled stability is analyzed through simulation. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Results:</i> Evaluation experiments on the proposed control framework were performed to show the effectiveness. The mean error of compliant trajectory following was less than 0.30 mm in free space. The mean relative force and moment control accuracy in three orthogonal directions was better than 0.5% and 0.8%, respectively. The improved coupled stability under the same model parameters was also confirmed by human-robot interaction experiments. Finally, an automated robotic US imaging experiment on a human volunteer in a real clinical scenario was carried out to show the potential application of our proposed framework. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Conclusion:</i> Experimental results have shown the advantages of the control framework, including satisfied force control accuracy, high accuracy of compliant motion, improved coupled stability, and system effectiveness on a human volunteer. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper was motivated by the increasing needs of automated ultrasound (US) scanning for both diagnostic and interventional purpose. Clinical sonographers suffer from repeated workload when performing diagnostic US imaging, which could benefit from automated robotic scanning. Robotic US imaging involves physical interaction between the robot end-effector (i.e., US transducer) and the human body. The dynamics of the interaction is regulated by the control law to guarantee the contact of the US transducer and the safety of the procedure. Most existing works have focused on regulating in-plane contact force in terms of the position without considering the compliance in other dimensions. However, it is not a trivial work to extend the positional compliance to six degree-of-freedom (6-DoF) compliance. As the prevalence of low-cost collaborative robotic arms in medical scenarios, how to perform 6-DoF compliant trajectory following and accurate six-dimensional (6-D) force control on these robotic arms becomes increasingly important. This paper gives a complete general solution to achieve 6-DoF compliant control and 6-D force regulation with accurate kinematics on a position-controlled robotic arm. A hybrid control law is proposed to switch the government of “instantaneous model” and “theoretical model” to achieve compliant motion accuracy in free space and improved coupled stability in motion-constrained environment. No expensive torque sensors and torque control interface are required. And no prior geometric knowledge about the scanning object is needed. We have demonstrated the application for robotic US imaging in a real clinical scenario.

Hierarchical control of manipulator with null-space compliance at the kinematic level

This article proposes a hierarchical control framework with null-space impedance at the kinematic level. The proposed framework aims to overcome the limitations of the prior methods for null-space compliance which rely on the dynamics of the manipulator. Two task-space control laws and a null-space control law at the kinematic level are designed to improve task-space errors and exhibit compliant joint motion behavior. The task-space’s end-effector force tracking uses an adaptive variable impedance control approach to enhance tracking performance. Experimental results conducted on a 7R manipulator demonstrate that the proposed control framework is capable of improving task performance when interaction forces act on the manipulator body.

A Cerebellum-Inspired Network Model and Learning Approaches for Solving Kinematic Tracking Control of Redundant Manipulators

Tracking control of redundant manipulators is always a basic and important issue in robotics. Existing studies have indicated that the pivotal region of the brain associated with human motion control is the cerebellum. This motivates us to devise a model-based cerebellum-inspired (MBCI) scheme and a model-free cerebellum-inspired (MFCI) scheme for the tracking control of redundant manipulators in this article. The MBCI scheme solves the inverse kinematics problem with a cerebellum model. By using the parameters and Jacobian matrix of the manipulator, the task space error is transformed into joint space error, which is taken as the teaching signal to train the cerebellum model designed based on the echo state network. The MFCI scheme is formed by coupling a cerebellum model and a multilayer perceptron (MLP). The MLP is able to generate approximate joint angle commands to the manipulator and the cerebellum model is utilized to fine-tune the MLP controller, thereby improving the tracking accuracy. In addition, leaky integrator neurons (LINs) are integrated into the cerebellum model to further improve the performance of the proposed schemes. Finally, comparative simulations and physical experiments on different types of redundant manipulators are conducted to verify the efficacy and merits of the proposed cerebellum-inspired schemes.

Two model-free schemes for solving kinematic tracking control of redundant manipulators using CMAC networks

Kinematic tracking control of robotic manipulators is a basic and vital issue in robotics. However, how to achieve the control of robotic manipulators with unknown kinematic models remains challenging. Existing studies show that cerebellum, a pivotal region of brain, plays a major role in human motion control, which motivates us to devise two schemes based on cerebellum model articulation controller (CMAC) for the tracking control of redundant manipulators with unknown kinematic models in this article. The first scheme is based on a CMAC network and a gradient neural dynamics (GND) algorithm. The CMAC network is utilized to generate approximate joint angle commands for the manipulator. By using the Jacobian matrix of the manipulator which is estimated by the GND algorithm, task space error is transformed into joint space error, which is taken as the teaching signal for training the CMAC. For the second scheme, another CMAC network replaces the GND algorithm to achieve the estimation of the Jacobian matrix of the manipulator. The effectiveness and robustness of the proposed control schemes are verified by both simulations and physical experiments.

Adaptive robust synchronized control for cooperative robotic manipulators with uncertain base coordinate system

In this paper, cooperative robotic manipulators under uncertain base coordinate are investigated. The coordinate uncertainties result in biases of cooperative robotic dynamics, which involve horizontal and vertical translational errors in the task space and rotational errors in the joint space. To the best of our knowledge, uncertainties in the base coordinate system of cooperative robotic manipulators have drawn little attention in existing literature. To solve this problem, this paper presents an adaptive robust controller for the synchronized control of two cooperative robotic manipulators. An adaptive neural network associated with base coordinate parameter adaption law is proposed to estimate the cooperative system parameters given unknown system dynamics and base coordinate uncertainties. A synchronization-factor-based robust slide mode controller is then derived to stabilize the target position and internal force between the cooperative manipulators. Mathematical proof and numerical experiments under various conditions are conducted. The results demonstrate the satisfactory and effective convergences of both the cooperative robotic trajectory and internal force despite of uncertainties in the base coordinate system.

Force, orientation and position control in redundant manipulators in prioritized scheme with null space compliance

This paper addresses the problem of executing multiple prioritized tasks for robot manipulators with compliant behavior in the remaining null space. A novel controller–observer is proposed to ensure accurate accomplishment of various tasks based on a predefined hierarchy using a new priority assignment approach. Force control, position control and orientation control are considered. Moreover, a compliant behavior is imposed in the null space to handle physical interaction without using joint torque measurements. Asymptotic stability of the task space error and external torque estimation error during executing multiple tasks are shown. The performance of the proposed approach is evaluated on a 7R light weight robot arm by several case studies.

Hierarchical tracking task control in redundant manipulators with compliance control in the null-space

In this paper, a new approach for dealing with multiple tracking tasks during physical interaction is proposed. By using this method, multiple tasks are accomplished based on the assigned priority in addition to a compliant behavior in the null-space of the main tasks. This issue is critical when robots are employed for complex manipulation in unknown environments and in the presence of human. During the manipulation in the dynamic environments, different objects may collide with the robot body and disturb its manipulation. In these cases, the robot is expected to continue execution of the tasks, accurately. Meanwhile, the robot should be compliant to ensure the safety during the interaction. A nonlinear controller-observer is proposed for tracking the desired trajectory based on a preallocated hierarchy. The suggested controller-observer estimates the external torques applied to the robot body without using joint torque measurements and compensates its projection on the task spaces. Asymptotic stability of the task space errors, the null-space velocity and the external interaction estimation error during accomplishing multiple tracking tasks are shown analytically. Finally, the algorithm performance is shown through experiments on a 7-DOF KUKA LWR robot arm.

Task-Space Control of Robot Manipulators With Null-Space Compliance

In this paper, the problem of controlling a robot manipulator in task space, while guaranteeing a compliant behavior for the redundant degrees of freedom, is considered. This issue may arise in the case where the robot experiences an interaction on its body, especially in the presence of humans. The proposed approach guarantees correct task execution and compliance of the robot's body during intentional or accidental interaction in the null space of the main task, simultaneously. The asymptotic stability of the task-space error is ensured by using suitable observers to estimate and compensate the generalized forces acting on the task variables, without using joint torque measurements. Two different controller-observer algorithms are designed, and they are based on the task-space error and on the generalized momentum of the robot, respectively. The performance of the proposed algorithms is verified in experiments on a 7R lightweight robot arm.

Continuous and Discrete Time Domain Stability Analysis of Composite Weighted Least Norm Solution in Redundancy Resolution

Stability aspects of redundancy resolution both in velocity and acceleration level have been investigated for a method which augments the weighted least norm solution by weighted residual of the current joint rate and preferred pose rate in null space. While doing this the first and second order inverse kinematics solutions with redundancy have been re-casted as a feedback control problem, with the classical Close Loop Inverse Kinematics (CLIK) both for range space and null space and its stability conditions are derived for continuous and discrete time domains using Lyapunov and non Lyapunov based stability criteria. The non Lyapunov based analysis is based on the exponential convergence of the task space error system in discrete time domain. For generality the stability conditions of regularized version of CWLS has been analyzed considering the null space contribution which will provide the information of feasible and unfeasible directions that is especially important in near singularity configuration. General Terms Inverse Kinematics, Stability.

Are muscle synergies useful for neural control?

The observation that the activity of multiple muscles can be well approximated by a few linear synergies is viewed by some as a sign that such low-dimensional modules constitute a key component of the neural control system. Here, we argue that the usefulness of muscle synergies as a control principle should be evaluated in terms of errors produced not only in muscle space, but also in task space. We used data from a force-aiming task in two dimensions at the wrist, using an electromyograms (EMG)-driven virtual biomechanics technique that overcomes typical errors in predicting force from recorded EMG, to illustrate through simulation how synergy decomposition inevitably introduces substantial task space errors. Then, we computed the optimal pattern of muscle activation that minimizes summed-squared muscle activities, and demonstrated that synergy decomposition produced similar results on real and simulated data. We further assessed the influence of synergy decomposition on aiming errors (AEs) in a more redundant system, using the optimal muscle pattern computed for the elbow-joint complex (i.e., 13 muscles acting in two dimensions). Because EMG records are typically not available from all contributing muscles, we also explored reconstructions from incomplete sets of muscles. The redundancy of a given set of muscles had opposite effects on the goodness of muscle reconstruction and on task achievement; higher redundancy is associated with better EMG approximation (lower residuals), but with higher AEs. Finally, we showed that the number of synergies required to approximate the optimal muscle pattern for an arbitrary biomechanical system increases with task-space dimensionality, which indicates that the capacity of synergy decomposition to explain behavior depends critically on the scope of the original database. These results have implications regarding the viability of muscle synergy as a putative neural control mechanism, and also as a control algorithm to restore movements.

Approximation of Jacobian Inverse Kinematics Algorithms: Differential Geometric vs. Variational Approach

This paper addresses the approximation problem of Jacobian inverse kinematics algorithms for redundant robotic manipulators. Specifically, we focus on the approximation of the Jacobian pseudo inverse by the extended Jacobian algorithm. The algorithms are defined as certain dynamic systems driven by the task space error, and identified with vector field distributions. The distribution corresponding to the Jacobian pseudo inverse is non-integrable, while that associated with the extended Jacobian is integrable. Two methods of devising the approximating extended Jacobian algorithm are examined. The first method is referred to as differential geometric, and relies on the approximation of a non-integrable distribution (in fact: a codistribution) by an integrable one. As an alternative, the approximation problem has been formulated as the minimization of an approximation error functional, and solved using the methods of the calculus of variations. Performance of the obtained extended Jacobian inverse kinematics algorithms has been compared by means of computer simulations involving the kinematics model of the 7 dof industrial manipulator POLYCRANK. It is concluded that the differential geometric method offers a rapid, while the variational method a systematic tool for solving inverse kinematic problems.

A prescribed performance referential control for human-like reaching movement of redundant arms

A novel and low-complexity dynamical approach for controlling reaching movements of redundant manipulators is proposed achieving preset performance attributes on the task space error. The iCub platform is used to compare its performance against a multi-referential solution. Simulation results for a 4 degrees of freedom (dof) planar robot are also provided comparing the proposed approach to another velocity based controller. The proposed scheme is shown to exhibit quasi-straight line paths and bell-shaped velocity profiles as well as path and joint configuration consistency in cyclic movements outperforming alternative solutions.

On the Stability of Closed-Loop Inverse Kinematics Algorithms for Redundant Robots

The purpose of this paper is to provide a convergence analysis of classical inverse kinematics algorithms for redundant robots, whose stability is usually proved only in the continuous-time domain, thus neglecting limits of the actual implementation in the discrete time, whereas the convergence analysis carried out in this paper in the discrete-time domain provides a method to find bounds on the gain of the closed-loop inverse kinematics algorithms in relation to the sampling time. It also provides an estimation of the region of attraction (without resorting to Lyapunov arguments), i.e., upper bounds on the initial task space error. Simulations on an 11-degree-of-freedom manipulator are performed to show how the found bounds on the gain are not too restrictive.

準静的に獲得した関節軌道を利用して動的な類似運動を逐次的に学習する方法

We propose a new supervised learning and synthesis framework for fast, complex motor tasks for redundant robots. A statics-based task-space controller acts not only as a full-body motion control module, but also as a module to generate synergistic joint motion patterns for redundant systems. Similar, but faster motions are incrementally synthesized by superposing the task-space controller output and stiffness around the joint trajectories with the modified speed, while iteratively learning the dynamics and joint stiffness according to the L2 norm of the task-space error. We demonstrate the proposed framework by simulating a balanced fast squat on a simple humanoid model.

Compensation of velocity and/or acceleration joint saturation applied to redundant manipulator

The article describes a new method for velocity/acceleration redistribution in order to compensate joint velocity and/or acceleration saturation. The method is designed for redundant manipulators. When some of the joint velocities/accelerations are in saturation other joints compensate for the lack of the velocity and the velocity in the task space remains unchanged. Without the compensation the task space error would appear. Using the compensation method we can achieve maximal velocity/acceleration in the task space while preserving joint velocity/acceleration within limits. The method is also appropriate to compensate a torque saturation. Additionally, we have introduced a condition that shows if the compensation is kinematically and mathematically possible or not.

An experimental investigation into the fault-tolerant control of an autonomous underwater vehicle

Autonomous underwater vehicles (AUVs) are expected to function in an unstructured underwater environment. One of the main requirements for effective operation in such an environment is to accommodate faults. In this paper, we have investigated a new approach to the allocation of thruster forces of an autonomous underwater vehicle under thruster faults. Generally, an AUV is equipped with more thrusters than what is minimally required to produce the desired motion. The proposed framework exploits the excess number of thrusters to accommodate thruster faults during operation. First, a redundancy resolution scheme is presented that considers the presence of excess number of thrusters along with any thruster faults and determines the reference thruster forces to produce the desired motion. These reference thruster forces are then utilized in the thruster controller to generate the required motion. This approach resolves the thruster redundancy in the Cartesian space and allows the AUV to track the task-space trajectories with asymptotic reduction of the task-space errors. Results from actual underwater experiments are provided to demonstrate the viability of the proposed scheme.

Fault-tolerant control of an autonomous underwater vehicle under thruster redundancy

A novel approach to the allocation of thruster forces of an autonomous underwater vehicle (AUV) is investigated. Generally, the number of thrusters in an AUV is more than what is minimally required to produce the desired motion. We investigate how to exploit the excess number of thrusters to accommodate thruster faults during operation. First, a redundancy resolution scheme is presented that takes into account the presence of excess number of thrusters along with any thruster faults and determines the reference thruster forces to produce the desired motion. These reference thruster forces are utilized in the controller to generate the required motion. This approach resolves the thruster redundancy in the Cartesian space and allows the AUV to track the task-space trajectories with asymptotic reduction of the task-space errors. Results from computer simulations are presented to demonstrate the viability of the proposed scheme.

Stability analysis of a joint space control law for a two-manipulator system

The control problem for a truly cooperative manipulator system cannot be regarded as a simple extension of single manipulator control since additional complexity arises from the need for ensuring coordinated motion of the system. Recently, we have proposed a control strategy based on two stages, namely, kinematic inversion of a set of cooperative task variables and a joint space control law with kinetostatic filtering of cooperative task space errors; this strategy avoids some of the drawbacks of other approaches. In this paper, the stability analysis for the joint space control law is provided and asymptotic stability of a set of equilibrium points is demonstrated. The case of imperfect compensation of the gravity terms has been analyzed. The addition of a force loop to achieve internal force regulation is also discussed.

Optimal joint trajectory planning for coordinated point-to-point motion of two-arm manipulators

This paper addresses the area of trajectory planning for point-to-point motion of two-arm manipulators. This type of motion is very suitable and sufficient for many industrial applications, where motion trajectories are planned for joint displacements (or velocities). In our previous paper we had introduced a position control scheme, which accepts preplanned motion joint trajectories as inputs to the controllers. This algorithm monitors the task space trajectory of the object carried by the two-arm manipulator, using a position control module, and re-computes some intermediate joint configurations in order not to drop (or excessively squeeze) the object. In this paper we present an off-line trajectory planning algorithm, which minimizes the probability of encountering excessive task space errors that would require the position control module to re-compute joint configurations. The proposed methods uses cubic polynomials for all joint trajectories as means of obtaining continuous velocities and accelerations throughout the motion. A two-loop multi-variable optimization algorithm is carried out to obtain optimal joint trajectories. The main objective of the optimization is: to minimize the number of intermediate joint configurations, to be used in fitting cubic splines to joint displacements, thus reducing computational burden during the real-time control of the arm. The primary constraint of the optimization problem is: to determine joint trajectories such that task space errors remains under specified tolerance values.

Position control of two‐arm manipulators for coordinated point‐to‐point motion

AbstractA trajectory planning and motion control algorithm is; presented for the point‐to‐point (PTP) motion of two‐arm manipulators cooperating on a task. The proposed method considers the multi‐arm manipulator as a system when formulating its kinematic model and obtains a global solution to the system, as opposed to individual arm solutions. For PTP motion control between two arm configurations, a simple trajectory is first assumed by defining joint velocity profiles and maximum allowable task space errors between the two end effectors of the manipulator. The task space errors during the motion are then continuously monitored to take corrective action when necessary to prevent those errors from exceeding the given tolerance limits. The main objective of this method is to reduce the number of inverse kinematics solutions during the real‐time control of the two‐arm system. The algorithm is illustrated by a numerical example for an eight degree‐of‐freedom kinematically redundant planar two‐arm system.