A Reduced and Linearized High Fidelity Waveboard Multibody Model for Stability Analysis

In this paper, the stability of a waveboard, a human propelled two-wheeled vehicle consisting in two rotatable platforms, joined by a torsion bar and supported on two caster wheels, is analysed. A multibody model with holonomic and nonholonomic constraints is used to describe the system. The nonlinear equations of motion, which constitute a Differential-Algebraic system of equations (DAE system), are linearized along the steady forward motion resorting to a recently validated linearization procedure, which allows the maximum possible reduction of the linearized equations of motion of constrained multibody systems. The approach enables the generation of the Jacobian matrix in terms of the geometric and dynamic parameters of the multibody system, and the eigenvalues of the system are parameterized in terms of the design parameters. The resulting minimum set of linear equations leads to the elimination of spurious null eigenvalues, while retaining all the stability information in spite of the reduction of the Jacobian matrix. The linear stability results of the waveboard obtained in previous work are validated with this approach. The procedure shows an excellent computational efficiency with the waveboard, its utilization being highly advisable to linearize the equations of motion of complex constrained multibody systems.

Dynamics of moving-object grasped by a hybrid hand

When a heavy object is cooperatively grasped to move by several fingers of the robot hybrid hand, the inertial properties and the mass distribution of the object must influence largely on the operation precision, grasping stability, and the safety of both the hybrid hand and the object. Hence, it is an important and significant issue to establish and analyze the dynamics model of the moving-object cooperatively grasped by the hybrid hand in order to ensure the safety and grasping stability of the hybrid hand and the object. However, this research has not been conducted. In this paper, a dynamics model of the moving-object grasped by the hybrid hand is established, and its dynamics is studied and analyzed. First, a three-dimensional model of a hybrid hand formed by a novel parallel manipulator and three fingers is designed for cooperatively grasping object. Second, the kinematic formulas for solving the Jacobian matrices, the Hessian matrices, the general velocity/acceleration of the moving platform, and four active limbs of the parallel manipulator are derived. Third, the composite Jacobian matrix and the composite Hessian matrix of the hybrid hand are derived, and the general velocity/acceleration of the moving-object grasped by the hybrid hand is derived. Fourth, dynamics model of the hybrid hand is established, the formulas for solving the dynamic actuation forces of the three fingers and the dynamic actuation forces/torque and constrained forces of the parallel manipulator are derived. Finally, the theoretical solutions of the dynamics model of the moving-object grasped by the hybrid hand are verified by its simulation mechanism.

Image-based visual servoing with depth estimation

For the depth estimation problem in the image-based visual servoing (IBVS) control, this paper proposes a new observer structure based on Kalman filter (KF) to recover the feature depth in real time. First, according to the number of states, two different mathematical models of the system are established. The first one is to extract the depth information from the Jacobian matrix as the state vector of the system. The other is to use the depth information and the coordinate point information of the two-dimensional image plane as the state vector of the system. The KF is used to estimate the unknown depth information of the system in real time. And an IBVS controller gain adjustment method for 6-degree-of-freedom (6-DOF) manipulator is obtained using fuzzy controller. This method can obtain the gain matrix by taking the depth and error information as the input of the fuzzy controller. Compared with the existing works, the proposed observer has less redundant motion while solving the Jacobian matrix depth estimation problem. At the same time, it will also be beneficial to reducing the time for the camera to reach the target. Conclusively, the experimental results of the 6-DOF robot with eye-in-hand configuration demonstrate the effectiveness and practicability of the proposed method.

Forward Kinematic and Jacobian Matrix for the Prosthetic Human Finger Actuated by Links

The most important function of a prosthetic hand is their ability to perform tasks in a manner similar to a natural hand, so it is necessary to perform kinematic analysis to determine the performance and the ability of the prosthetic human finger design to work normally and smoothly when it's drive by two sets of links that embedded in its structure and pulled by a servomotor, so the Denvit-Hartenberg method was used to analyse the forward kinematics for the prosthetic finger joints to deduction the trajectory of the fingertip and the velocity of the joints was computed by using the Jacobian matrix. The prosthetic finger was modelled by the Solidwork - 2018 program and the results of kinematics were verified using MATLAB. The analyses that were conducted on the design showed that the designed prosthetic finger has the ability to perform movements and meets the functional requirements for which it is designed.

Overcoming Kinematic Singularities for Motion Control in a Caster Wheeled Omnidirectional Robot

Omnidirectional planar robots are common these days due to their high mobility, for example in human–robot interactions. The motion of such mechanisms is based on specially designed wheels, which may vary when different terrains are considered. The usage of actuated caster wheels (ACW) may enable the usage of regular wheels. Yet, it is known that an ACW robot with three actuated wheels needs to overcome kinematic singularities. This paper introduces the kinematic model for an ACW omni robot. We present a novel method to overcome the kinematic singularities of the mechanism’s Jacobian matrix by performing the time propagation in the mechanism’s configuration space. We show how the implementation of this method enables the estimation of caster wheels’ swivel angles by tracking the plate’s velocity. We present the mechanism’s kinematics and trajectory tracking in real-world experimentation using a novel robot design.

A new limited memory method for unconstrained nonlinear least squares

This paper suggests a new limited memory trust region algorithm for large unconstrained black box least squares problems, called LMLS. Main features of LMLS are a new non-monotone technique, a new adaptive radius strategy, a new Broyden-like algorithm based on the previous good points, and a heuristic estimation for the Jacobian matrix in a subspace with random basis indices. Our numerical results show that LMLS is robust and efficient, especially in comparison with solvers using traditional limited memory and standard quasi-Newton approximations.

Collision-Free Motion Planning of a Six-Link Manipulator Used in a Citrus Picking Robot

This paper presents the results of a motion planning algorithm that has been used in an intelligent citrus-picking robot consisting of a six-link manipulator. The real-time performance of a motion planning algorithm is urgently required by the picking robot. Within the artificial potential field (APF) method, the motion planning of the picking manipulator was basically solved. However, the real-time requirement of the picking robot had not been totally satisfied by APF because of some native defects, such as the large number of calculations used to map forces into torques by the Jacobian matrix, local minimum trap, and target not reachable problem, which greatly reduce motion planning efficiency and real-time performance of citrus-picking robots. To circumvent those problems, this paper proposed some novel methods that improved the mathematical models of APF and directly calculates the attractive torques in the joint space. By using the latter approach, the calculation time and the total joint error were separately reduced by 54.89% and 45.41% compared with APF. Finally, the novel algorithm is presented and demonstrated with some illustrative examples of the citrus picking robot, both offline during the design phase as well as online during a realistic picking test.

The Estimation of Image Jacobian Matrix with Time-Delay Compensation

Time delay exists in image-based visual servo system, which will have a certain impact on the system control. To solve the impact of time delay, the time delay compensation of the object feature point image and the image Jacobian matrix is discussed in this paper. Some work is done in this paper: The estimation of the object feature point image under time delay is based on a proposed robust decorrelation Kalman filtering model, for the measurement vectors which cannot be obtained during time delay in the robust Kalman filtering model, a polynomial fitting method is proposed in which the selection of the polynomial includes the position, velocity and acceleration of the object feature point which impact the feature point trajectory, then the more accurate object feature point image can be obtained. From the estimated object feature point image under time delay, the more accurate image Jacobian matrix under time delay can be obtained. Simulation and experimental results verify the feasibility and superiority of this paper method.