Optimal Trajectory Planning for Redundant Manipulators Based on Minimum Jerk

2008 ◽  
Author(s):  
Jingzhou Yang ◽  
Joo Kim ◽  
Esteban Pena Pitarch ◽  
Karim Abdel-Malek
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Initial Point ◽  
Planning Problem ◽  
Optimization Approach ◽  
Control Points ◽  
Unknown Parameters ◽  
Spline Curve ◽  
Minimum Jerk ◽  
Optimal Trajectory Planning

This paper presents an optimization-based method to solve the smooth trajectory planning problem where the user knows only the start and end points of the end-effector or the via point plus the start and end target points. For the start and end target points, we use an optimization approach to determine the manipulator configurations. Having obtained the desired minimum jerk path in the Cartesian space using the minimum jerk theory and having represented each joint motion by the third-degree B-spline curve with unknown parameters (i.e., control points), an optimization approach, rather than the pseudoinverse technique for inverse kinematics, is used to calculate the control points of each joint spline curve. The objective function includes several parts: (a) dynamic effort; (b) the inconsistency function, which is the joint rate change (first derivative) and predicted overall trend from the initial point to the end point; and (c) the nonsmoothness function of the trajectory, which is the second derivative of the joint trajectory. This method can be used for robotic manipulators with any number of degrees of freedom. Minimum jerk trajectories are desirable for their similarity to human joint movements, for their amenability to limit robot vibrations, and for their control (i.e., enhancement of control performance). Illustrative examples are presented to demonstrate the method.

An optimal trajectory planning method for path tracking of industrial robots

Robotica ◽  
2018 ◽  
Vol 37 (3) ◽  
pp. 502-520 ◽  
Author(s):  
Xianxi Luo ◽  
Shuhui Li ◽  
Shubo Liu ◽  
Guoquan Liu
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Optimal Path ◽  
Path Tracking ◽  
Industrial Robots ◽  
Planning Method ◽  
Coordinate Frame ◽  
Optimization Approach ◽  
Cartesian Coordinate ◽  
Optimal Trajectory Planning

SUMMARYThis paper presents an optimal trajectory planning method for industrial robots. The paper specially focuses on the applications of path tracking. The problem is to plan the trajectory with a specified geometric path, while allowing the position and orientation of the path to be arbitrarily selected within the specific ranges. The special contributions of the paper include (1) an optimal path tracking formulation focusing on the least time and energy consumption without violating the kinematic constraints, (2) a special mechanism to discretize a prescribed path integration for segment interpolation to fulfill the optimization requirements of a task with its constraints, (3) a novel genetic algorithm (GA) optimization approach that transforms a target path to be tracked as a curve with optimal translation and orientation with respect to the world Cartesian coordinate frame, (4) an integration of the interval analysis, piecewise planning and GA algorithm to overcome the challenges for solving the special trajectory planning and path tracking optimization problem. Simulation study shows that it is an insufficient condition to define a trajectory just based on the consideration that each point on the trajectory should be reachable. Simulation results also demonstrate that the optimal trajectory for a path tracking problem can be obtained effectively and efficiently using the proposed method. The proposed method has the properties of broad adaptability, high feasibility and capability to achieve global optimization.

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

Time-Jerk Synthetic Optimal Trajectory Planning of Robot Using Strength Pareto Evolutionary Algorithm

2010 ◽  
Vol 108-111 ◽  
pp. 1141-1146
Author(s):  
Jie Yan ◽  
Dao Xiong Gong
Keyword(s):  
Evolutionary Algorithm ◽  
Trajectory Planning ◽  
Optimal Trajectory ◽  
High Speed ◽  
Mathematic Model ◽  
Stair Climbing ◽  
Planning Problem ◽  
Hexapod Robot ◽  
Strength Pareto Evolutionary Algorithm ◽  
Optimal Trajectory Planning

The Strength Pareto Evolutionary Algorithm (SPEA) is adopted to find time-jerk synthetic optimal trajectory of a hexapod robot in the joint space. In order to get the optimal trajectory, cubic splines are employed and derived under the constraint condition of via points to assure overall continuity of velocity and acceleration. Taken both the execution time and minimax approach of jerk as objectives, and expressed the kinematics constraints as upper bounds on the absolute values of velocity and acceleration, the mathematic model of time-jerk synthetic optimal trajectory planning is built. Finally, SPEA is adopted to optimize the stair-climbing trajectory of a hexapod robot, the simulation results show that this method can solve the trajectory planning problem effectively, and the stair-climbing trajectory can meet the contradictory objective functions of high speed and low robot vibration well.

scholarly journals Minimum-jerk trajectory planning pertaining to a translational 3-degree-of-freedom parallel manipulator through piecewise quintic polynomials interpolation

2020 ◽  
Vol 12 (3) ◽  
pp. 168781402091366 ◽  
Author(s):  
Song Lu ◽  
Bingxiao Ding ◽  
Yangmin Li
Keyword(s):  
Trajectory Planning ◽  
Virtual Work ◽  
Angular Position ◽  
Programming Algorithm ◽  
Planning Problem ◽  
Typical Application ◽  
Parallel Kinematic Manipulator ◽  
Minimum Jerk ◽  
Planning Approach ◽  
Parallel Kinematic

This article aims to present a minimum-jerk trajectory planning approach to address the smooth trajectory generation problem of 3-prismatic-universal-universal translational parallel kinematic manipulator. First, comprehensive kinematics and dynamics characteristics of this 3-prismatic-universal-universal parallel kinematic manipulator are analyzed by virtue of the accepted link Jacobian matrices and proverbial virtual work principle. To satisfy indispensable continuity and smoothness requirements, the discretized piecewise quintic polynomials are employed to interpolate the sequence of joints’ angular position knots which are transformed from these predefined via-points in Cartesian space. Furthermore, the trajectory planning problem is directly converted into a constrained nonlinear multi-variables optimization problem of which objective function is to minimize the maximum of the joints’ angular jerk throughout the whole trajectory. Finally, two typical application simulations using the reliable sequential quadratic programming algorithm demonstrate that this proposed minimum-jerk trajectory planning approach is of explicit feasibility and appreciable effectiveness.

Minimum jerk for trajectory planning and control

Robotica ◽  
1994 ◽  
Vol 12 (2) ◽  
pp. 109-113 ◽  
Author(s):  
K.J. Kyriakopoulos ◽  
G.N. Saridis
Keyword(s):  
Trajectory Planning ◽  
Tracking Control ◽  
Optimization Problem ◽  
Control Algorithms ◽  
Planning Problem ◽  
Cartesian Space ◽  
Planning And Control ◽  
Minimum Jerk ◽  
And Control ◽  
Trajectory Planning And Control

SUMMARYIt has been experimentally verified that the jerk of the desired trajectory adversely affects the performance of the tracking control algorithms for robotic manipulators. In this paper, we investigate the reasons behind this effect, and state the trajectory planning problem as an optimization problem that minimizes a norm of joint jerk over a prespecified Cartesian space trajectory. The necessary conditions are derived and a numerical algorithm is presented.

L2-Norm Optimal Trajectory Planning for Mobile Ground Vehicles in a Dynamically Changing Environment with both “Hard” and “Soft” Obstacles

2011 ◽  
Vol 130-134 ◽  
pp. 339-342
Author(s):  
Jian Yang ◽  
Mi Dong
Keyword(s):  
Boundary Conditions ◽  
Trajectory Planning ◽  
Design Parameter ◽  
Optimal Trajectory ◽  
Kinematic Model ◽  
Optimal Solution ◽  
Planning Problem ◽  
Ground Vehicles ◽  
Operational Environment ◽  
Optimal Trajectory Planning

In this paper, the real-time trajectory planning problem is considered for a differential vehicles in a dynamically changing operational environment. Some obstacles in the environment are not known apriori, they are either static or moving, and classified to two types: “hard” obstacles that must be avoided, and “soft” obstacles that can be run over/through. The proposed method presents trajectories, satisfying boundary conditions and vehicle’s kinematic model, in terms of polynomials with one design parameter. With a cost function ofL2norm, an optimal feasible trajectory is analytically solved for “hard” obstacles. By relaxing the optimal solution, “soft” obstacles are prioritized to be bypassed or overcome. The proposed method offers an automatic and systematic way of handling obstacles.The simulation is used to illustrate the proposed algorithm.

Combined Trajectory Planning and Parameter Identification of a Two-Link Rigid Manipulator

1998 ◽  
Author(s):  
Reza Fotouhi-C. ◽  
Peter N. Nikiforuk ◽  
Walerian Szyszkowski
Keyword(s):  
Path Planning ◽  
Trajectory Planning ◽  
Equations Of Motion ◽  
Adaptive Controller ◽  
Time Variable ◽  
Physical Parameters ◽  
Planning Problem ◽  
Unknown Parameters ◽  
On Line ◽  
Line Path

Abstract A combined trajectory planning problem and adaptive control problem for a two-link rigid manipulator is presented in this paper. The problem is divided into two parts: path planning for off-line processing, followed by on-line path tracking using an adaptive controller. The path planning is done at the joint level. The motion of the robot is specified by a sequence of knots (positions of the robot’s tip) in space Cartesian coordinates. These knots are then transformed into two sets of joint displacements, and piecewise cubic polynomials are used to fit these two sequences of joint displacements. The cubic spline function is used to construct a trajectory with the velocity and the acceleration as constraints. Linear scaling of the time variable is used to accommodate the velocity and acceleration constraints. A nonlinear scaling of the time variable is performed to fit the velocity to a pre-specified velocity profile. The adaptive scheme used takes full advantage of the known parameters of the manipulator while estimating the unknown parameters. In deriving the dynamic equations of motion, all of the physical parameters of the manipulator, including the distributed masses of the links, are taken into account. Some simulation results for the manipulator with unknown payload masses following a planned trajectory are presented.

scholarly journals Navigation of Autonomous Light Vehicles Using an Optimal Trajectory Planning Algorithm

2021 ◽  
Vol 13 (3) ◽  
pp. 1233
Author(s):  
Ángel Valera ◽  
Francisco Valero ◽  
Marina Vallés ◽  
Antonio Besa ◽  
Vicente Mata ◽  
...  
Keyword(s):  
Energy Consumption ◽  
Trajectory Planning ◽  
Autonomous Navigation ◽  
Optimal Trajectory ◽  
Computational Cost ◽  
Initial Point ◽  
Target Point ◽  
Software Components ◽  
Planning Algorithm ◽  
Optimal Trajectory Planning

Autonomous navigation is a complex problem that involves different tasks, such as location of the mobile robot in the scenario, robotic mapping, generating the trajectory, navigating from the initial point to the target point, detecting objects it may encounter in its path, etc. This paper presents a new optimal trajectory planning algorithm that allows the assessment of the energy efficiency of autonomous light vehicles. To the best of our knowledge, this is the first time in the literature that this is carried out by minimizing the travel time while considering the vehicle’s dynamic behavior, its limitations, and with the capability of avoiding obstacles and constraining energy consumption. This enables the automotive industry to design environmentally sustainable strategies towards compliance with governmental greenhouse gas (GHG) emission regulations and for climate change mitigation and adaptation policies. The reduction in energy consumption also allows companies to stay competitive in the marketplace. The vehicle navigation control is efficiently implemented through a middleware of component-based software development (CBSD) based on a Robot Operating System (ROS) package. It boosts the reuse of software components and the development of systems from other existing systems. Therefore, it allows the avoidance of complex control software architectures to integrate the different hardware and software components. The global maps are created by scanning the environment with FARO 3D and 2D SICK laser sensors. The proposed algorithm presents a low computational cost and has been implemented as a new module of distributed architecture. It has been integrated into the ROS package to achieve real time autonomous navigation of the vehicle. The methodology has been successfully validated in real indoor experiments using a light vehicle under different scenarios entailing several obstacle locations and dynamic parameters.

Singularity-free trajectory planning of platform-type parallel manipulators for minimum actuating effort and reactions

Robotica ◽  
2008 ◽  
Vol 26 (3) ◽  
pp. 371-384 ◽  
Author(s):  
Chun-Ta Chen ◽  
Hua-Wei Chi
Keyword(s):  
Trajectory Planning ◽  
Particle Swarm Optimization Algorithm ◽  
Numerical Technique ◽  
Parallel Manipulators ◽  
Singular Points ◽  
Planning Problem ◽  
Control Points ◽  
Swarm Optimization ◽  
Trajectory Representation

SUMMARYDue to the existence of singular configurations within the workspace for a platform- type parallel manipulator (PPM), the actuating force demands increase drastically as the PPM approaches or crosses singular points. Therefore, in this report, a numerical technique is presented to plan a singularity-free trajectory of the PPM for minimum actuating effort and reactions. By using the parametric trajectory representation, the singularity-free trajectory planning problem can be cast to the determination of undetermined control points, after which a particle swarm optimization algorithm is employed to find the optimal control points. This algorithm ensures that the obtained trajectories can avoid singular points within the workspace and that the PPM has the minimum actuating effort and reactions. Simulations and discussions are presented to demonstrate the effectiveness of the algorithm.

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

2012 ◽  
Vol 157-158 ◽  
pp. 1388-1392
Author(s):  
Jin Chao Guo ◽  
Zheng Liu ◽  
Guang Zhao Cui
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Robot Manipulators ◽  
Pso Algorithm ◽  
Optimization Approach ◽  
Redundant Manipulators ◽  
Simulation Studies ◽  
Fast Computation ◽  
Optimal Trajectory Planning ◽  
Computation Speed

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.

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