An Optimized Trajectory Planning for Industrial Robots using Mathematical and Heuristic Methods

Abstract

In recent times, robots are being extensively employed in various industries to achieve higher productivity through automation. The robots in industries are mostly engaged for various operations such as assembly,machining,machine loading/unloading,welding,material handling,etc.During such applications the robotic manipulators inversekinematics (IK)
trajectory planning is an important and challenging task due to mathematical complexity and inexact non-closed equations. The conventional mathematical methods used to solve the nonclosed IK equations results in unwanted inaccurate multiple solutions. The existing basic
heuristic methods that has been used for this purpose provides non-optimal inaccurate solutions. In order to counter the aforementioned difficulties, this research work aims to develop some mathematical and heuristic methods for the optimal, smooth and accurate trajectory for industrial robotic manipulators.

The IK trajectories of the manipulators are computed using the conventional homogeneous transformation (HT) and dual quaternion (DQ) methods. The present research proposes a new approach to manipulator trajectory planning by implementing geodesic scheme. The geometrical features of the geodesic have been used to find the optimal
path/trajectory of the manipulator end-effector between two points in robot workspace. As the manipulator joints are successively connected via manipulator links, a combined
Riemannian metric for position and orientation space has been defined to evaluate the geodesic equations for the stated Riemannian workspace of robot. The Christoffel symbols are calculated for the defined Riemannian metric which are then put in the geodesic formulation equations to establish geodesic equations. The geodesic equalities are solved for the boundary conditions by using a developed code of Runge-kutta fourth step method in C++ and the IK trajectories results are stored. In order to demonstrate the entire trajectory planning process by implementing various methods, this research work adopted two
industrial robots viz. 4-DOF SCARA and 6-DOF Kawasaki robot. The effectiveness of the proposed geodesic method in accomplishing optimal, precise and smooth trajectory has been verified by comparing the IK trajectories results of computer simulation results geodesic with that of the HT and DQ methods. The validation of developed geodesic method is performed by conducting real-time pick and place operations with the two considered manipulators. The
comparison of computed geodesic trajectories results and real-time experiment results confirms that the method can be efficiently implemented in real-time robotic trajectory
planning.

In the heuristic approach to manipulator trajectory part, this research adopted seven the existing basic optimization algorithms such as artificial bee colony (ABC), bat algorithm (BA), cuckoo search (CS), firefly algorithm (FA), invasive weed optimization (IWO), particle swarm optimization (PSO), teaching learning based optimization (TLBO) algorithm.This present work proposes three new heuristic techniques i.e. modified bat algorithm (MBA), hybrid cuckoo-bat (HCB) and crab algorithm (CA) that has been developed for desired the trajectory optimization problem. The modification introduced in the MBA is such
that the loudness and pulse emission rate of the bat is updated in the every iteration of the algorithm. This enhances the solutions optimality and accuracy by having wider search space. In the HCB algorithm, CS is used to perform the local search part and BA for global search
which improves the search ability of the method to produce better solution accuracy. The CAuses the concept of swarm behaviour, crossing and shell selection criterion of crabs in nature for function optimizations. For the desired optimal, smooth and accurate trajectory of robotic
manipulators, a combined objective fitness function for position and orientation has been defined for the task. The algorithms are executed in MATLAB 2015a software in a 64-bit
system having 4GB RAM and 3.4 GHz processor. In order to evaluate algorithms significance and effectiveness, they are analysed in terms of performance parameters such as
best cost, variation in joint angles, and error in positions. The trajectories results of the adopted manipulators attained with the proposed algorithms are compared against the results of existing adopted methods. The post optimization analysis of algorithms includes the
comparison of computational time. And the statistical significance of the algorithms have also been performed by conducting student t-test(Freidman ANOVA in OriginPro2016) for the trajectory results of 10 runs of algorithms. Also, Friedman rank test is done to verify the statistical significance and effectiveness of the three proposed algorithms over the seven existing algorithms adopted. The comparison of statistical data of the algorithms shows that
the developed methods can be meritoriously employed for optimal, smooth and precise trajectory planning of industrial robot manipulators.