Motion Planning Algorithms of Redundant Manipulators Based on Self-motion Manifolds

The current motion planning approaches for redundant manipulators mainly includes two categories： improved gradient-projection method and some other efficiency numerical methods. The former is excessively sensitive to parameters, which makes adjustment difficult; and the latter treats the motion planning as general task by ignoring the particularity, which has good universal property but reduces the solving speed for on-line real-time planning. In this paper, a novel stepwise solution based on self-motion manifold is proposed for motion planning of redundant manipulators, namely, the chief tasks and secondary tasks are implemented step by step. Firstly, the posture tracking of end-effector is achieved accurately by employing the non-redundant joint. Secondly, the end-effector is set to keep stationary. Finally, self-motion of manipulator is realized via additional work on the gradient of redundant joint displacement. To verify this solution, experiments of round obstacle avoiding are carried out via the planar 3 degree-of-~eedom manipulator. And the experimental results indicate that this motion planning algorithm can effectively achieve obstacle avoiding and posture tracking of the end-effector. Compared with traditional gradient projection method, this approach can accelerate the problem-solving process, and is more applicable to obstacle avoiding and other additional work in displacement level.

Adaptive Fuzzy Sliding Mode Controller with Nonlinear Observer for Redundant Manipulators Handling Varying External Force

An Adaptive Fuzzy Sliding Mode Controller with Nonlinear Observer （AFSMCO） for the redundant robotic manipulator is proposed in this paper. This approach could achieve a precise trajectory tracking for a robot manipulator in the presence of uncertainties and disturbances. Primarily, a suitable observer using the recursive algorithm is presented for an accurate estima- tion of external disturbances caused by the varying external force. Secondly, the adaptive fuzzy logic is designed to approximate the parameters of the sliding mode controller （AFSMC） to avoid chattering in real time. Moreover, it is shown using the Lyapunov theory that the tracking error asymptotically converges to zero. Finally, the effectiveness of the proposed control approach and theoretical discussion are demonstrated by simulation results on a 7-1ink robot and tested on a 7-DOF manipulator platform.

Motion planning for redundant prismatic-jointed manipulators in the free-floating mode

This paper investigates the motion planning of redundant free-floating manipulators with seven prismatic joints. On the earth, prismatic-jointed manipulators could only position their end-effectors in a desired way. However, in space, the end-effectors of free-floating manipulators can achieve both the desired orientation and desired position due to the dynamical coupling between manipulator and satellite movement, which is formally expressed by linear and angular momentum conservation laws. In this study, a tractable algorithm particle swarm optimization combined with differential evolution （PSODE） is provided to deal with the motion planning of redundant free-floating prismatic-jointed manipulators, which could avoid the pseudo inverse of the Jacobian matrix. The polynomial functions, as argument in sine functions are used to specify the joint paths. The co- efficients of the polynomials are optimized to achieve the desired end-effector orientation and position, and simulta- neously minimize the unit-mass-kinetic energy using the redundancy. Relevant simulations prove that this method pro- vides satisfactory smooth paths for redundant free-floating prismatic-jointed manipulators. This study could help to recognize the advantages of redundant prismatic-jointed space manipulators.

COMPLEX NUMBER MODE APPROACH FOR REDUCING VIBRATION OF STRUCTURAL FLEXIBLE REDUNDANT ROBOT MANIPULATORS

A complex number mode analysis approach is proposed for vibration reducing of structural flexible redundant manipulators by utilizing self motion. In the proposed approach, the self motion is evaluated to nullify the modal exciting force of flexural motion, and the approach can be freely used when the degree of freedom of flexural motion is much greater than the available degree of reundancy. The availability and effectiveness of the proposed approach are demonstrated through numerical simulation with a four link spatial robotic manipulator possessing an end flexible link.

Rapid Optimization of Tension Distribution for Cable-Driven Parallel Manipulators with Redundant Cables

The solution of tension distributions is infinite for cable-driven parallel manipulators（CDPMs） with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom（6-DOF） CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method. The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.

SOLVING INVERSE KINEMATICS OF REDUNDANT MANIPULATOR BASED ON NEURAL NETWORK

For the redundant manipulators, neural network is used to tackle the velocityinverse kinematics of robot manipulators. The neural networks utilized are multi-layeredperceptions with a back-propagation training algorithm. The weight table is used to save the weightssolving the inverse kinematics based on the different optimization performance criteria.Simulations verity the effectiveness of using neural network.

Self-adapting control parameters modifieddifferential evolution for trajectoryplanning of manipulators

Control parameters of original differential evolution （DE） are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optiinization problems. According to the relative position of two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the scale factor F of the difference vector is proposed. In terms of the convergence status of the target vector in the current population, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have a lower CFI while worse target vectors have a large CFI. At the same time, the mutation operator is modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark problems and applied to the trajectory planning of a three-joint redundant manipulator. Finally, the experiment results show that the proposed approaches can greatly improve robustness and convergence speed.

Obstacle Avoidance and Multitarget Tracking of a Super Redundant Modular Manipulator Based on Bezier Curve and Particle Swarm Optimization

A super redundant serpentine manipulator has slender structure and multiple degrees of freedom.It can travel through narrow spaces and move in complex spaces.This manipulator is composed of many modules that can form different lengths of robot arms for different application sites.The increase in degrees of freedom causes the inverse kinematics of redundant manipulator to be typical and immensely increases the calculation load in the joint space.This paper presents an integrated optimization method to solve the path planning for obstacle avoidance and discrete trajectory tracking of a super redundant manipulator.In this integrated optimization,path planning is established on a Bezier curve,and particle swarm optimization is adopted to adjust the control points of the Bezier curve with the kinematic constraints of manipulator.A feasible obstacle avoidance path is obtained along with a discrete trajectory tracking by using a follow-the-leader strategy.The relative distance between each two discrete path points is limited to reduce the fitting error of the connecting rigid links to the smooth curve.Simulation results show that this integrated optimization method can rapidly search for the appropriate trajectory to guide the manipulator in obtaining the target while achieving obstacle avoidance and meeting joint constraints.The proposed algorithm is suitable for 3D space obstacle avoidance and multitarget path tracking.

Research on Trajectory Tracking Method of Redundant Manipulator Based on PSO Algorithm Optimization

Aiming at the problem that the trajectory tracking performance of redundant manipulator corresponding to the target position is difficult to optimize,the trajectory tracking method of redundant manipulator based on PSO algorithm optimization is studied.The kinematic diagram of redundant manipulator is created,to derive the equation of motion trajectory of redundant manipulator end.Pseudo inverse Jacobi matrix is used to solve the problem of manipulator redundancy.Based on the tracking ellipse of redundant manipulator,the tracking shape of redundant manipulator is determined with the overall tracking index as the second index,and the optimization method of tracking index is proposed.The redundant manipulator contour is located by active contour model,on this basis,combined with particle swarm optimization algorithm,the point coordinates on the circumference with the relevant joint point as the center and joint length as the radius are selected as the algorithm particles for iteration,and the optimal tracking results of the overall redundant manipulator trajectory are obtained.The experimental results show that under the proposed method,the tracking error of the redundant manipulator is low,and the error jump range is small.It shows that this method has high tracking accuracy and reliability.

Multiple mobile-obstacle avoidance algorithm for redundant manipulator

In order to overcome the shortcomings of the previous obstacle avoidance algorithms,an obstacle avoidance algorithm applicable to multiple mobile obstacles was proposed.The minimum prediction distance between obstacles and a manipulator was obtained according to the states of obstacles and transformed to escape velocity of the corresponding link of the manipulator.The escape velocity was introduced to the gradient projection method to obtain the joint velocity of the manipulator so as to complete the obstacle avoidance trajectory planning.A7-DOF manipulator was used in the simulation,and the results verified the effectiveness of the algorithm.

Intelligent Robust Control of Redundant Smart Robotic Arm Pt I: Soft Computing KB Optimizer - Deep Machine Learning IT

Redundant robotic arm models as a control object discussed.Background of computational intelligence IT on soft computing optimizer of knowledge base in smart robotic manipulators introduced.Soft computing optimizer is the sophisticated computational intelligence toolkit of deep machine learning SW platform with optimal fuzzy neural network structure.The methods for development and design technology of control systems based on soft computing introduced in this Part 1 allow one to implement the principle of design an optimal intelligent control systems with a maximum reliability and controllability level of a complex control object under conditions of uncertainty in the source data,and in the presence of stochastic noises of various physical and statistical characters.The knowledge bases formed with the application of soft computing optimizer produce robust control laws for the schedule of time dependent coefficient gains of conventional PID controllers for a wide range of external perturbations and are maximally insensitive to random variations of the structure of control object.The robustness is achieved by application a vector fitness function for genetic algorithm,whose one component describes the physical principle of minimum production of generalized entropy both in the control object and the control system,and the other components describe conventional control objective functionals such as minimum control error,etc.The application of soft computing technologies(Part I)for the development a robust intelligent control system that solving the problem of precision positioning redundant(3DOF and 7 DOF)manipulators considered.Application of quantum soft computing in robust intelligent control of smart manipulators in Part II described.

Synchronization Control of Planar 2-DOF Robot with Redundant Actuation

Considering the special characteristics of the redundant parallel manipulator, with emphasis on the variable of structure, the relatively small workspace and the strong coupling relationship among arms, a synchronization control strategy is presented in this paper. Since in the feedforward, the inertial and the coriolis matrix are designed constant according to the relatively small workspace, position measurement of the endeffector in plane is ignored. Synchronization error and coupling error are introduced to reject the model errors of inertial and coriolis matrix as stated above. Using the method, the errors of driving arms can be reduced, and the synchronization performance among axes can be improved. The stability of the controllers was proved by Lyapunov method. Finally, experimental results show the feasibility of the method.

Development of a cable-driven redundant space manipulator with large bending angle by combining quaternion joints and segmented coupled linkages mechanism

A cable-driven redundant manipulator has significant potential in confined space applications, such as environmental exploration, equipment monitoring, or maintenance. A traditional design requires 3N driving motors/cables to supply 2N degrees of freedom(DOF) movement ability.The number of motors is 1.5 times that of the joints’ DOF, increasing the hardware cost and the complexity of the kinematics, dynamics, and control. This study develops a novel redundant space manipulator with decoupled cable-driven joints and segmented linkages. It is a 1680 mm continuum manipulator with eight DOF, consisting of four segmented linkages driven by eight motors/pairs of cables. Each segment has two equivalent DOF, which are realized by four quaternion joints synchronously driven by two linkage cables. The linkage cables of adjacent joints are symmetrically decoupled and offset at 180°. This design allows equal-angle movement of all the joints of each segment. Moreover, each decoupling driving mechanism is designed based on a pulley block composed of two fixed and movable pulleys. The two movable pulleys realize the opposite but equidistant motions of the two driving cables, i.e., pulling and loosening, assuring symmetrical movements of the two driving cables of each segment. Consequently, the equivalent 2N-DOF joints are driven only by 2N motors, significantly reducing the hardware cost and simplifying the mapping relationship between the motor angle/cable length and the joint angle. Furthermore, the bending range of each segment could reach 360°, which is three times that of a traditional design. Finally, a prototype has been developed and experimented with to verify the performance of the proposed mechanism and the corresponding algorithms.

Inverse Kinematics Analysis of a 7-DOF Space Manipulator for Trajectory Design

To solve the inverse kinematics problem for redundant degrees of freedom（DOFs）manipulators has been and still continues to be quite challenging in the field of robotics.Aiming at trajectory planning for a 7-DOF space manipulator system,joint rotation trajectories are obtained from predetermined motion trajectories and poses of the end effector in Cartesian space based on the proposed generalized inverse kinematics method.A minimum norm method is employed to choose the best trajectory among available trajectories.Numerical simulations with the7-DOF manipulator show that the proposed method can achieve the planned trajectory and pose under the circumstances of minimum angular velocities.Moreover,trajectory results from the proposed kinematics model and inverse kinematics method has the advantages of simple modelling,low computation cost,easy to solve and plan trajectory conveniently.The smooth and continuous joint rotation functions obtained from the proposed method are suitable for practical engineering applications.

PARAMETRIC IDENTIFICATION OF PARALLEL MANIPULATOR WITH REDUNDANCY DRIVEN BY PNEUMATIC MUSCLES

A new parameter estimation algorithm is proposed for parametric identification of a parallel manipulator driven by pneumatic muscles with redundancy. Due to the special physical properties of the parallel manipulator studied, the regression model for parametric identification is characterized by multieollinearity, which will result in unreliable and inaccurate parameter estimations with large eovarianee if the conventional parameter estimation algorithm based on single error minimizing criterion is used. To improve the quality of parameter estimation and achieve high precise posture trajectory tracking control of the parallel manipulator, a new parameter estimation algorithm based on composite error minimizing criterion is developed in need of theoretical contractive forces of pneumatic muscles. The experimental results indicate that the proposed algorithm integrated with adaptive robust control could provide reliable parametric identification and greatly enhance the control accuracy in the trajectory tracking control of the parallel manipulator, and that the variation of known theoretical contractive forces of pneumatic muscles has slight influence on the control performance.

A kind of biomimetic control method to anthropomorphize a redundant manipulator for complex tasks

It is an urgent problem for robots to operate complex tasks with some unknown motion mechanisms caused by the strong coupling of force and motion. However, humans can perform complex tasks well due to their natural evolution and postnatal training. A novel biomimetic control method based on a human motion mechanism with high movement adaptability is proposed in this paper. The core is to present a novel variable-parameter compliance controller based on human operation mechanisms with an action-planning method derived from optimization by human motion, and the main contribution is to change the parameters of compliance controller according to human operating intention synchronized with humanoid motion;this change could establish a humanoid map between the force and motion for a seven degree-of-freedom redundant manipulator to deal with the unknown motion mechanism in complex tasks, so the redundant manipulator can operate complex tasks with high performance. Sufficient experiments were performed, and the results validated the effectiveness of the proposed algorithm.

Precise semi-analytical inverse kinematic solution for 7-DOF offset manipulator with arm angle optimization

Seven-degree-of-freedom redundant manipulators with link offset have many advantages,including obvious geometric significance and suitability for configuration control.Their configuration is similar to that of the experimental module manipulator(EMM)in the Chinese Space Station Remote Manipulator System.However,finding the analytical solution of an EMM on the basis of arm angle parameterization is difficult.This study proposes a high-precision,semi-analytical inverse method for EMMs.Firstly,the analytical inverse kinematic solution is established based on joint angle parameterization.Secondly,the analytical inverse kinematic solution for a non-offset spherical-roll-spherical(SRS)redundant manipulator is derived based on arm angle parameterization.The approximate solution of the EMM is calculated in accordance with the relationship between the joint angles of the EMM and the SRS manipulator.Thirdly,the error is corrected using a numerical method through the analytical inverse solution based on joint angle parameterization.After selecting the stride and termination condition,the precise inverse solution is computed for the EMM based on arm angle parameterization.Lastly,case solutions confirm that this method has high precision,and the arm angle parameterization method is superior to the joint angle parameterization method in terms of parameter selection.