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Trajectory Planning for the Five Degree of Freedom Feeding Robot Using Septic and Nonic Functions

Priyam A. Parikh, Reena Trivedi, and Jatin Dave
Mechanical Engineering Department, Nimra University, Ahmedabad, India

Abstract— In the present research work discusses about trajectory planning of five degrees of freedom serial manipulator using higher order polynomials. This robotic arm is used to feed semi-liquid food to the physically challenged people having fixed seating arrangement. It is essential to plan a smooth trajectory for proper delivery of food, without wasting it. Trajectory planning can be done in the joint space as well as in the cartesian space. It is difficult to design trajectory in Cartesian scheme due to non-existence of the Jacobian matrix. In the present research work, trajectory planning is done using joint space scheme. The joint space scheme offers lower and higher order polynomial methods for the trajectory planning. In the present work parabolic and cubic functions are considered as lower polynomials and septic (7th order) and nonic (9th order) functions are considered as higher order polynomials. Lower order polynomial does not have any control over joint acceleration and velocity, which leads a servo actuator towards instantaneous velocity and infinite acceleration. This phenomenon can cause loss of food in the delivery root, lesser battery life, wear and tear in the joints and increases the probability of damaging the servo actuator. To address this problem, the proposed research work presents the methodology and trajectory planning of a serial manipulator using septic and nonic functions. The higher order polynomials provide zero acceleration and velocity at the beginning and at the end. It also gives the continuity in the displacement, velocity and acceleration, which is necessary for smoother delivery of the food. 

Index Terms—Feeding robot, trajectory planning, higher order polynomials, Lower order polynomials, septic function, nonic function, Physically challenged people

Cite: Priyam A. Parikh, Reena Trivedi, and Jatin Dave, "Trajectory Planning for the Five Degree of Freedom Feeding Robot Using Septic and Nonic Functions," International Journal of Mechanical Engineering and Robotics Research, Vol. 9, No. 7, pp. 1043-1050, July 2020. DOI: 10.18178/ijmerr.9.7.1043-1050

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.