Trajectory Planning Of Manipulators Research Articles

Multi-Objective Trajectory Planning of FFSM Carrying a Heavy Payload

Aiming at carrying a heavy payload to a desired pose (including position and orientation), a multi-objective optimization-based approach for maximum-payload trajectory planning of free-floating space manipulators (FFSM) is proposed in this paper. The presented approach corresponds to two typical applications: (i) the manipulator joints attain the desired states; (ii) the inertial pose of the end-effector (pose with respect to the inertial frame) attains the desired values, for which a novel two-stage method is presented. Firstly, for the purpose of reducing computational complexity, dynamics equations are derived using a spatial operator algebra (SOA) method. Secondly, objective functions are defined according to the improvement of load-carrying capacity and pose requirements of the end-effector. Then, the joint trajectories are specified using sinusoidal polynomial functions. Finally, a multi-objective particle optimization (MOPSO) algorithm is employed to obtain a non-dominated solution set, during which process particles that do not satisfy the constraints are eliminated. Simulations are performed for a 7-DOF FFSM, considering three and five objectives for optimization in the two applications, respectively. The results demonstrate that the proposed approach can provide satisfactory joint trajectories and improve load-carrying capacity effectively.

A trajectory planning of redundant manipulators based on bilevel optimization

In this paper, a novel trajectory planning approach is proposed for redundant manipulators in the case of several obstacles. The trajectory is discretized and at each step, we search for a new position of the end effector in the Cartesian space to reach the final position. Because of the redundancy, this position can be achieved by an infinity of configurations in the joint space. Thus, we use this property to find the best configuration that allows to avoid obstacles and singularities of the robot. The proposed method is based on a bilevel optimization formulation of the problem and bi-genetic algorithm to solve it. In order to avoid obstacles, we also proposed to manage constraints of the problem dynamically. This technique adapts the number of constraints in the formulation of the problem with the position of the obstacles. Simulation results showed the effectiveness of the proposed method.

Tractable Algorithm for Robust Time-Optimal Trajectory Planning of Robotic Manipulators under Confined Torque

In this paper, the problem of time optimal trajectory planning under confined torque and uncertain dynamics and torque parameters along a predefined geometric path is considered. It is shown that the robust optimal solution to such a problem can be obtained by solving a linear program. Thus a tractable algorithm is given for robust time-optimal path-tracking control under confined torque.

Application of RBF Neural Network in the Manipulator Trajectory Planning

In view of the high order, nonlinear characteristics of target trajectory, control strategy is proposed for a kind of RBF neural network and polynomial interpolation combining. According to the specific requirements of trajectory planning, the manipulator in joint space variables are expressed as one or two order derivative function by polynomial interpolation algorithm, then the RBF neural network is used for tracking the target trajectory. Finally, through MATLAB simulation, the accuracy of this method is verified.

Simulation on Trajectory Planning of 6R Manipulator Based on the Shortest Distance Criterion

This paper concerns the trajectory planning and simulation for 6R Manipulator. First, algebraic method was used to deduce the forward and inverse kinematics of 6R manipulator. All inverse solutions were expressed in atan2 to eliminate redundant roots to get the corresponding inverse formula. For the trajectory planning of manipulator in Cartesian space, using the cubic spline interpolation to get the drive function of joint, getting a unique solution from eight group inverses by the shortest distance criterion, and then obtained the actual end-effector trajectory. Using Matlab to verify the proposed trajectory planning method, validated results show that the proposed algorithm is feasible and effective.

The Precollision Trajectory Planning of Redundant Space Manipulator for Capture Task

Aiming at on-orbit capture task, a scheme for precollision trajectory planning of redundant space manipulator is proposed in this paper. The minimized collision impulsive force and the correct capture pose of the end-effector can be achieved at the same time by the scheme. At the contact point, the configuration of the manipulator is optimized in a new way to minimize the impulsive force without affecting the correct capture pose. After obtaining the optimal configuration, particle swarm optimization (PSO) algorithm is employed to solve the trajectory planning from the initial point to the desired point (desired configuration and correct capture pose are both contained). Firstly, the joint trajectory is parameterized using sinusoidal functions with the arguments of high-order polynomials. Then the objective function is defined according to the end-effector pose requirements. Finally, the PSO method is used to search for the unknown parameters to obtain the appropriate precollision joint trajectory. The proposed method can satisfy the whole capture process of redundant space manipulator before collision, and simulation results of a 7-dof space manipulator verify the effectiveness.

Optimal Trajectory Planning for Parallel Robots Considering Time-Jerk

A method for optimization in trajectory planning of 3RUU robot manipulators is presented in this paper. At first, to get the optimal trajectory, position analyses has been done on the 3RUU robot, then an objective function which have two terms is minimized: first term relevant to the total execution time and another one relevant to the integral of the squared jerk (defined as the derivative of the acceleration toward time) along the trajectory and this Guarantees that the obtained trajectory is smooth. This technique let to calculate the kinematic constraints on the motion of the robot, defined as upper limits on the absolute values of velocity, acceleration and jerk. , the total execution time does not require to be set priori. The algorithm has been tested in simulation and in comparison with other important trajectory planning techniques it has been given good results.

Research on Flexible Joint Stiffness Test and Trajectory Planning of Space Manipulator

Both Natural Coordinate Formulation describing rigid bodies and Absolute Nodal Coordinate Formulation describing flexible bodies are used to model a flexible manipulator with flexible joint and flexible link. The torsional stiffness of flexible joint is tested using a specialized stiffness test equipment, and then the nonlinear torsional stiffness is determined by fitting the experimental data. A new trajectory planning function called the cosine-based function is proposed to design the joint trajectory, which is smoother than the fifth-polynomial and cycloidal motion functions. Finally, a one-link manipulator with flexible joint and flexible link is used to compare the performance of the three trajectory planning functions. Results show that residual vibration can be remarkably reduced by the proposed cosine-based function, which exhibits a significantly better performance than the fifth-polynomial and cycloidal motion functions.

Application of Artificial Bee Colony Algorithm in Time-optimal Trajectory Planning of Manipulators

Application of Artificial Bee Colony Algorithm in Time-optimal Trajectory Planning of Manipulators

Trajectory planning of mobile manipulators using dynamic programming approach

SUMMARYThis paper presents a solution for optimal trajectory planning problem of robotic manipulators with complicated dynamic equations. The main goal is to find the optimal path with maximum dynamic load carrying capacity (DLCC). Proposed method can be implemented to problems of both motion along a specified path and point-to-point motion. Dynamic Programming (DP) approach is applied to solve optimization problem and find the positions and velocities that minimize a pre-defined performance index. Unlike previous attempts, proposed method increases the speed of convergence by using the sequential quadratic programming (SQP) formulation. This formulation is used for solving problems with nonlinear constraints. Also, this paper proposes a new algorithm to design optimal trajectory with maximum DLCC for both fixed and mobile base mechanical manipulators. Algorithms for DLCC calculations in previous works were based on indirect optimization method or linear programming approach. The proposed trajectory planning method is applied to a linear tracked Puma and the mobile manipulator named Scout. Application of this algorithm is confirmed and simulation results are compared with experimental results for Scout robot. In experimental test, results are obtained using a new stereo vision system to determine the position of the robot end-effector.

A Mathematical Modeling and Optimization Approach for Trajectory Planning of Robot Manipulators

This paper presents a method for the problem of optimal trajectory planning of redundant robot manipulators in the presence of fixed obstacles. Quadrinomial and quintic polynomials are used to describe the segment of the trajectory. Cultural based PSO algorithm (CBPSO) is proposed to design a collision-free trajectory for planar redundant manipulators. CBPSO optimizes the trajectory and ensures that obstacle avoidance can be achieved. Simulations are carried out for different obstacles to prove the validity of the proposed algorithm. Different test data generated by GA, QPSO and CBPSO are provided with a tabular comparison. Simulation studies show CBPSO has potential online usage in engineering and distinct fast computation speed compared with the other two algorithms. Results demonstrate the effectiveness and capability of the proposed method in generating optimized collision-free trajectories.

Working Space Analysis of 6-DOF Manipulator Based on MONTE-CARIO Method

The working space of manipulator is an important dynamic index. Based on Monte-Carlo method, working space of the 6-DOF (degrees of freedom) underwater manipulator is analyzed in this paper. The virtual prototype of the manipulator is established. Simulation graph is obtained with the aid of arithmetic procedure and computer graphical. Simulation result shows that the manipulator’s working space is bigger and has obtained better effect, which can meet the 6-DOF underwater manipulator operational requirements. The results provide an important reference for the 6-DOF underwater manipulator body design and trajectory planning.

Energy-optimal trajectory planning for robot manipulators with holonomic constraints

In this paper, we study two different trajectory planning problems for robot manipulators. In the first case, the end-effector of the robot is constrained to move along a prescribed path in the workspace, whereas in the second case, the trajectory of the end-effector has to be determined in the presence of obstacles. Constraints of this type are called holonomic constraints. Both problems have been solved as optimal control problems. Given the dynamic model of the robot manipulator, the initial state of the system, some specifications about the final state and a set of holonomic constraints, one has to find the trajectory and the actuator torques that minimize the energy consumption during the motion. The presence of holonomic constraints makes the optimal control problem particularly difficult to solve. Our method involves a numerical resolution of a reformulation of the constrained optimal control problem into an unconstrained calculus of variations problem in which the state space constraints and the dynamic equations, also regarded as constraints, are treated by means of special derivative multipliers. We solve the resulting calculus of variations problem using a numerical approach based on the Euler–Lagrange necessary condition in the integral form in which time is discretized and admissible variations for each variable are approximated using a linear combination of piecewise continuous basis functions of time. The use of the Euler–Lagrange necessary condition in integral form avoids the need for numerical corner conditions and the necessity of patching together solutions between corners. In this way, a general method for the solution of constrained optimal control problems is obtained in which holonomic constraints can be easily treated. Numerical results of the application of this method to trajectory planning of planar horizontal robot manipulators with two revolute joints are reported.

Kinematic Modelling and Simulation of a 2-R Robot Using SolidWorks and Verification by MATLAB/Simulink

The simulation of robot systems is becoming very popular, especially with the lowering of the cost of computers, and it can be used for layout evaluation, feasibility studies, presentations with animation and off-line programming. The trajectory planning of redundant manipulators is a very active area since many tasks require special characteristics to be satisfied. The importance of redundant manipulators has increased over the last two decades because of the possibility of avoiding singularities as well as obstacles within the course of motion. The angle that the last link of a 2 DOF manipulator makes with the x-axis is required in order to find the solution for the inverse kinematics problem. This angle could be optimized with respect to a given specified key factor (time, velocity, torques) while the end-effector performs a chosen trajectory (i.e., avoiding an obstacle) in the task space. Modeling and simulation of robots could be achieved using either of the following models: the geometrical model (positions, postures), the kinematic model and the dynamic model. To do so, the modelization of a 2-R robot type is implemented. Our main tasks are comparing two robot postures with the same trajectory (path) and for the same length of time, and establishing a computing code to obtain the kinematic and dynamic parameters. SolidWorks and MATLAB/Simulink softwares are used to check the theory and the robot motion simulation. This could be easily generalized to a 3-R robot and possibly therefore to any serial robot (Scara, Puma, etc.). The verification of the obtained results by both softwares allows us to qualitatively evaluate and underline the validityof the chosen model and obtain the right conclusions. The results of the simulations are discussed and an agreement between the two softwares is certainly obtained.

Inverse Kinematics and Trajectory Planning of 6R Serial Manipulators

An inverse kinematic solution is introduced with the trajectory planning method for a kind of 6R serial manipulators,which has a close relationship with the initial pose configurations.On the basis of the unit axis vector and position vector of the joints of the 6R serial manipulator in the folded status,the screw theory and exponential production approach are used for the manipulator's kinematic solutions in the initial configurations,and a complete set of the 16 inverse kinematic solutions are deduced by the analytical method.The trajectories of the manipulator's joints are planned by the inverse kinematic solutions,which are guided by the end-effector's trajectories in the global coordinate system.The simulation results show that it is correct for the inverse kinematic solutions and the trajectory planning method for the 6R serial manipulator.The method for the inverse kinematic solution of the 6R serial manipulators is proved to have the advantages of simple to be modeled,easy to be solved and convenient to be planed for the trajectories.

Manipulator Trajectory Planning Based on the Algebraic-Trigonometric Hermite Blended Interpolation Spline

The algebraic-trigonometric Hermite polynomials curves possess the properties similar to those of normal cubic Hermite curves, while preserving the Ck – continuity without solving linear equation systems. In this paper, we design the manipulator trajectory using algebraic-trigonometric Hermite polynomials curves, and we can interpolate data points for manipulator via given curves. Therefore, in manipulator joint space, the continuous displacement, angular velocity and angular acceleration can be achieved, which lead to smooth and continuous manipulator movements. This new method approved to be practicable by the experimental results, meets the requirements of the manipulator.

Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints

This paper is concerned with mathematical modeling and optimal motion designing of flexible mobile manipulators. The system is composed of a multiple flexible links and flexible revolute joints manipulator mounted on a mobile platform. First, analyzing on kinematics and dynamics of the model is carried out then; open-loop optimal control approach is presented for optimal motion designing of the system. The problem is known to be complex since combined motion of the base and manipulator, non-holonomic constraint of the base and highly non-linear and complicated dynamic equations as a result of the flexible nature of both links and joints are taken into account. In the proposed method, the generalized coordinates and additional kinematic constraints are selected in such a way that the base motion coordination along the predefined path is guaranteed while the optimal motion trajectory of the end-effector is generated. This method by using Pontryagin’s minimum principle and deriving the optimality conditions converts the optimal control problem into a two point boundary value problem. A comparative assessment of the dynamic model is validated through computer simulations, and then additional simulations are done for trajectory planning of a two-link flexible mobile manipulator to demonstrate effectiveness and capability of the proposed approach.

Optimal trajectory planning of wheeled mobile manipulators in cluttered environments using potential functions

This paper presents an advanced methodology for collision-free trajectory planning of wheeled mobile manipulators in obstructed environments by means of potential functions. In the presented method, all mobile manipulator parts and environmental obstacles are modeled as ellipsoids. Due to collision avoidance, the ellipsoid equations are expressed in a reference coordinate system and the corresponding dimensionless potential functions are defined. Then, the trajectory planning of a spatial mobile robot in cluttered environment is performed, employing optimal control theory. Beyond simplicity and novelty of the proposed method, depletion of prior methods is rectified, which lead to excessive computation and singularity during process. Also, a number of simulations and experiments for Scout mobile manipulator are carried out, which illustrate the power and efficiency of the proposed method.

Time-optimal trajectory planning of robot manipulators in point-to-point motion using an indirect method

In this study, an iterative method for computing the time-optimal point-to-point control of robot manipulators is studied, subject to limits on the actuator torques and actuator jerks. This method uses the indirect solution of an open-loop optimal control problem so that the optimal control problem is translated to a non-linear two-point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and solving the TPBVP, a simple iterative method is proposed. This method is based on solving the minimum-energy problem without the necessity of finding the switching point. So, the resultant TPBVP can be solved using the usual algorithms. In addition, since the solution of the TPBVPs is sensitive to the initial guess, a simple procedure for making proper initial guesses is introduced. Furthermore, since the inverse kinematic of redundant manipulators is an ill-posed problem, the general form for boundary conditions corresponding to the final time is considered. In addition, it is shown that the proposed method has no sensitivity for specifying the time-optimal trajectory of manipulators that may contain singular arcs.

Research on the Trajectory Planning of the 4-DOF Manipulator

Based on kinematics analysis, trajectory planning of a 4-DOF manipulator is researched on in this paper. Quintic polynomials is adopted to plan trajectory. The trajectory simulation of the manipulator is realized through using SimMechanics toolbox in MATLAB . The simulation experiments show the correctness and feasibility of the kinematics equations and algorithm of the manipulator trajectory planning.