I'm working on path planning for robot. However, I would like to ask how I can minimize the cycle time for the industrial robot, the motion of the robot is between point A and point B (the problem is two points boundary value problem).
x(t0) = x0 (point a), x(tf) = x1 (point b)
However I need to minimize the cycle time by minimizing the Hamiltonian equation by applying Pontryagin’s Maximum Principle
I don't know much in Hamiltonian equations and the method you are trying to apply. But little digging, I found that it is used in dynamic modeling!? Am I right?
However in such case, this is not relevant to your problem, since it is pure planning (kinematic nature). You may use different motion profile (if you have access to low level control), for example you can use a linear with fifth order blends position motion profile. Usually robot manipulators manufacturers use trapezoidal motion profile for the velocity.
I think that you need to optimize the velocity and acceleration together Ahmad,
I mean you need to increase the velocity without increasing the acceleration at the start and end of the motion. of course this will resduce the constant speed span.
First of all, you need a dynamic model of your industrial robot (including the maximum values of the actuators torques) since the cycle time depends on the available torque on each joint.
Then, there are several methods to solve the minimum time problem. You can look for example on the early works of Dubowsky and Shiller, almost 30 years ago...
First you have to optimize the robot's traveled contour, please see in case you have a free motion between the task point (e.g. point to point path) [1] and a continues path [2], maybe you need to hadr code it, or if you are using a VBA programing language,
these methods used the traveled distance and the medium velocity to find the task's point sequence, the I'M(Inverse Kinematic Model) configuration at each point and if you want the best position and orientation of the manipulator w.r.t the task points.
Second as mentioned above you may explore dynamic model to use the max velocities,
1- K. Baizid, A. Yousnadj, A. Meddahi, R. Chellali, J. Iqbal,"Time scheduling and optimization of industrial robotized tasks based on genetic algorithms", Robotics and Computer-Integrated Manufacturing (Impact Factor: 1.84). 01/2015;(https://www.researchgate.net/publication/271225360_Time_scheduling_and_optimization_of_industrial_robotized_tasks_based_on_genetic_algorithms)
2- S. Alatartsev, V Mersheeva,M Augustine,F Ortmeier, "On Optimizing a Sequence of Robotic Tasks", EEE/RSJ International Conference on Intelligent Robots and Systems (IROS); 01/2013 (https://www.researchgate.net/publication/256445248_On_Optimizing_a_Sequence_of_Robotic_Tasks)
Article Time scheduling and optimization of industrial robotized tas...
Conference Paper On Optimizing a Sequence of Robotic Tasks
We currently got a survey paper accepted exactly on this problem. You might want to see:
Article Robotic Task Sequencing Problem: A Survey
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