A Convex Optimization Approach to Time-Optimal Path Tracking Problem for Cooperative Manipulators

Abstract Previous works solve the time-optimal path tracking problems considering piece-wise constant parametrization for the control input, which may lead to the discontinuous control trajectory. In this paper, a practical smooth minimum time trajectory planning approach for robot manipulators is proposed, which considers complete kinematic constraints including velocity, acceleration and jerk limits. The main contribution of this paper is that the control input is represented as the square root of a polynomial function, which reformulates the velocity and acceleration constraints into linear form and transforms the jerk constraints into the difference of convex form so that the time-optimal problem can be solved through sequential convex programming (SCP). The numerical results of a real 7-DoF manipulator show that the proposed approach can obtain very smooth velocity, acceleration and jerk trajectories with high computation efficiency.

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An optimal trajectory planning method for path tracking of industrial robots

Robotica ◽

10.1017/s0263574718001145 ◽

2018 ◽

Vol 37 (3) ◽

pp. 502-520 ◽

Cited By ~ 3

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.

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Near Time-Optimal Path Tracking Method for Waiter Motion Problem

IFAC-PapersOnLine ◽

10.1016/j.ifacol.2017.08.749 ◽

2017 ◽

Vol 50 (1) ◽

pp. 4929-4934 ◽

Cited By ~ 6

Author(s):

Gábor Csorvási ◽

Ákos Nagy ◽

István Vajk

Keyword(s):

Optimal Path ◽

Path Tracking ◽

Tracking Method ◽

Time Optimal ◽

Motion Problem ◽

Path Tracking Method

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Sequential Time-Optimal Algorithm for Extended Path Tracking Problem

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4046614 ◽

2020 ◽

Vol 142 (8) ◽

Author(s):

Gábor Csorvási ◽

István Vajk

Keyword(s):

Degrees Of Freedom ◽

Optimal Algorithm ◽

Real Life ◽

Path Tracking ◽

Robotic Arm ◽

Tracking Problem ◽

Six Degrees Of Freedom ◽

Time Optimal ◽

Path Tracking Algorithm ◽

Extended Path

Abstract This paper presents a fast and easily implementable path tracking algorithm for robots. Usually, for a path tracking problem, the goal is to move the robot on a predefined path, while the joint velocities and accelerations are kept within their limits. This paper deals with the extended case, constraining the forces applied to the objects at the manipulator. First, a problem with a special set of constraints is presented, and a sequential solver method is formulated. The presented sequential solver algorithm has significant computational benefits compared to the direct transcription approach. Then, a practical example is introduced where the proposed algorithm can be applied. At last, the algorithm is validated by real-life experimental results with a six degrees-of-freedom robotic arm.

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Closed-loop trajectory generation for robust time-optimal path tracking

Proceedings of IEEE International Conference on Robotics and Automation ◽

10.1109/robot.1996.506926 ◽

2002 ◽

Cited By ~ 4

Author(s):

J.C. Kieffer ◽

A.J. Cahill ◽

M.R. James

Keyword(s):

Closed Loop ◽

Optimal Path ◽

Trajectory Generation ◽

Path Tracking ◽

Time Optimal

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Time-optimal path tracking for robots under dynamics constraints based on convex optimization

Robotica ◽

10.1017/s0263574715000247 ◽

2015 ◽

Vol 34 (9) ◽

pp. 2116-2139 ◽

Cited By ~ 12

Author(s):

Qiang Zhang ◽

Shurong Li ◽

Jian-Xin Guo ◽

Xiao-Shan Gao

Keyword(s):

Convex Optimization ◽

High Speed ◽

Optimal Path ◽

Robotic Manipulators ◽

Path Tracking ◽

Minimum Time ◽

Linear Functions ◽

Change Rate ◽

Time Path ◽

Motion Time

SUMMARYTo fully utilize the dynamic performance of robotic manipulators and enforce minimum motion time in path tracking, the problem of minimum time path tracking for robotic manipulators under confined torque, change rate of the torque, and voltage of the DC motor is considered. The main contribution is the introduction of the concepts of virtual change rate of the torque and the virtual voltage, which are linear functions in the state and control variables and are shown to be very tight approximation to the real ones. As a result, the computationally challenging non-convex minimum time path tracking problem is reduced to a convex optimization problem which can be solved efficiently. It is also shown that introducing dynamics constraints can significantly improve the motion precision without costing much in motion time, especially in the case of high speed motion. Extensive simulations are presented to demonstrate the effectiveness of the proposed approach.

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