A novel end-effector upper limb rehabilitation robot: Kinematics modeling based on dual quaternion and low-speed spiral motion tracking control

For patients with upper limb dysfunction after stroke, robot-assisted rehabilitation training plays an important role in functional recovery. The existing upper limb rehabilitation robots have some problems, such as complex mechanisms, insufficient compliance, and can only realize the rehabilitation training of shoulder and elbow joints in the horizontal plane. This research proposes a novel end-effector upper limb rehabilitation robot with three degrees of freedom. Two horizontal rotation freedoms are driven by motors and one vertical translation freedom is driven by a pneumatic cylinder. So it can realize the spatial rehabilitation training of shoulder and elbow joints. The rotation and translation transformation of the robot can be represented by a dual quaternion, which is concise in form and clear in the physical meaning. Therefore, this article adopts dual quaternions to complete the robot’s kinematics modeling, inverse kinematics calculation, and terminal spiral motion trajectory planning. To improve the low-speed moving performance of the spiral motion, a sliding mode control strategy plus feedforward compensation is employed to control the displacement of the cylinder. Experiments show that the robot can realize proximal joints training and has good position tracking accuracy (tracking error is within 2 mm) with smoothness under the proposed control strategy, which can guarantee the accuracy and comfort of passive rehabilitation training, contributing to restoring the function of the impairment upper limbs.

Recreating the Motion Trajectory of a System of Articulated Rigid Bodies on the Basis of Incomplete Measurement Information and Unsupervised Learning

Re-creating the movement of an object consisting of articulated rigid bodies is an issue that concerns both mechanical and biomechanical systems. In the case of biomechanical systems, movement re-storation allows, among other things, introducing changes in training or rehabilitation exercises. Motion recording, both in the case of mechanical and biomechanical systems, can be carried out with the use of sensors recording motion parameters or vision systems and with hybrid solutions. This article presents a method of measuring motion parameters with IMU (Inertial Measurement Unit) sensors. The main assumption of the article is to present the method of data estimation from the IMU sensors for the given time moment on the basis of data from the previous time moment. The tested system was an industrial robot, because such a system allows identifying the measurement errors from IMU sensors and estimating errors basing on the reference measurements from encoders. The aim of the research is to be able to re-create the movement parameters of an object consisting of articulated rigid bodies on the basis of incomplete measurement information from sensors. The developed algorithms can be used in the diagnostics of mechanical systems as well as in sport or rehabilitation. Limiting sensors will allow, for example, athletes defining mistakes made during training only on the basis of measurements from one IMU sensor, e.g., installed in a smartphone. Both in the case of rehabilitation and sports, minimizing the number of sensors allows increasing the comfort of the person performing a given movement as part of the measurement.

Algorithmic approach to geometric solution of generalized Paden–Kahan subproblem and its extension

Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems—opposite to conventional Denavit–Hartenberg approach, where at least n + 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit–Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden–Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden–Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden–Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

Motion mapping of the heterogeneous master–slave system for intuitive telemanipulation

Heterogeneous master–slave robots are widely used as both the assistive robot system for the elder/disabled people and the teleoperation robot system in dangerous environments. For the sake of intuitive teleoperation, motion mapping should be applied to keep the slave arm possessing the similar configuration of the master arm in the whole course of telemanipulation. We propose a motion mapping on the joint analog level based on unit dual quaternions (UDQs) for the telecontrol of a heterogeneous slave robot arm via the motion of human master arm. First, we analogize the links of the slave robot to the links of the human master arm, and accordingly group the slave arm joints into “shoulder,” “elbow,” and “wrist” joint analog sets. Then, we capture the motion of the human master arm via a wearable motion capture system and take it as the motion order of the slave arm. Finally, we solve the motion of slave robot arm’s joint via UDQ-based 1-, 2-, and 3-Degree of freedom (DOF) orientation error UDQ decomposition algorithms that are suit for solving a typical class of robotic slave arms. As a result, the operator can manipulate the heterogeneous robot system intuitively and conveniently, and the fatigue degree and error rate of the user can be significantly reduced, and thus the safety of teleoperation in an unstructured and constrained environment can be significantly improved.

Improved Inverse Kinematics Algorithm Using Screw Theory for a Six-DOF Robot Manipulator

Based on screw theory, a novel improved inverse-kinematics approach for a type of six-DOF serial robot, “Qianjiang I”, is proposed in this paper. The common kinematics model of the robot is based on the Denavit-Hartenberg (D-H) notation method while its inverse kinematics has inefficient calculation and complicated solution, which cannot meet the demands of online real-time application. To solve this problem, this paper presents a new method to improve the efficiency of the inverse kinematics solution by introducing the screw theory. Unlike other methods, the proposed method only establishes two coordinates, namely the inertial coordinate and the tool coordinate; the screw motion of each link is carried out based on the inertial coordinate, ensuring definite geometric meaning. Furthermore, we adopt a new inverse kinematics algorithm, developing an improved sub-problem method along with Paden-Kahan sub-problems. This method has high efficiency and can be applied in real-time industrial operation. It is convenient to select the desired solutions directly from among multiple solutions by examining clear geometric meaning. Finally, the effectiveness and reliability performance of the new algorithm are analysed and verified in comparative experiments carried out on the six-DOF serial robot “Qianjiang I”.

Motion Control of a Quadrotor Aircraft via Singular Perturbations

In this paper, a new motion controller for a quadrotor aircraft is introduced. A reformulation of the control inputs of the dynamic model is discussed and then the control algorithm is given in a constructive form. The stability proof of the state space origin of the overall closed-loop system relies on the theory of singularly perturbed systems. Numerical simulations corroborate the viability of the proposed control scheme and the conclusions concerning stability. A set of simulations under practical conditions is also presented, where the system is affected by different types of disturbances and nonlinearities such as noise and actuator saturation.

Collaborative Simulation and Experimentation on the Dental Arch Generator of a Multi-manipulator Tooth-arrangement Robot

In the orthodontic treatment and manufacture of complete dentures, the most important steps are designing and generating a dental arch curve which adapts to the requirements of the patient according to their jaw arch form. The traditional way of acquiring the dental arch curve form is based on manual operation, which will randomly generate a lot of errors caused by human factors. The purpose of this paper is to automatically acquire the dental arch curve and implement the coordinated control of the dental arch generator of the multi-manipulator tooth-arrangement robot, which can be used in full denture manufacturing. According to the work principle, motion planning method of the dental arch generator will be analysed. A collaborative simulation of the dental arch generator is realized based on Matlab and ADAMS. Controlled experimentation of the dental arch generator and preliminary tooth-arrangement experimentation are performed using the multi-manipulator tooth-arrangement robot system in order to verify the feasibility of the motion planning method and the technical route. It will lay an important theoretical foundation for quantitative research on oral restoration and also provide a way to standardize the manufacturing process of full dentures and orthodontic treatments.