Optimal Trajectory Generation for a Robotic Worm via Parameterization by B-Spline Curves

Subject Areas : journal of Artificial Intelligence in Electrical Engineering

Mohammad Reza Sayyed Noorani ¹ , Pouya Nourfar ²

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Received: 2016-02-17 Accepted : 2016-02-17 Published : 2015-06-01

Keywords: Genetic Algorithm, Optimization, Worm-like Robot, B-spline Curves,

Abstract :

In this paper we intend to generate some set of optimal trajectories according to the number of control points has been applied for parameterizing those using B-spline curves. The trajectories are used to generate an optimal locomotion gait in a crawling worm-like robot. Due to gait design considerations it is desired to minimize the required torques in a cycle of gait. Similar to caterpillars, progress in our crawling robot is achieved by propagating a trapezoidal wave from tail to head in the vertical plane. According to this model, the optimization problem has been solved via parameterization of joint trajectories, and consequently cost function, using cubic B-spline curves versus variant numbers of control points (CPs) needed in building those. Indeed, it is tried to find the best number of the CPs, of which the cost function obtains a minimum dynamical effort. To this end, the Genetic Algorithm is employed to find the minimal cost value once a nominated number of CPs is considered. Furthermore, since a complete period of this locomotion gait is composed of separated stages called sub-motions, thus the optimal trajectories for each sub-motion is examined independently. The results show choosing the number of CPs between 8 to 12 points constructs the optimized trajectories that reduce the dynamical effort of crawl in comparison with ones are reported by previous researches.

References:

[1] G. Li, W. Li, J. Zhang, H. Zhang,(2015). “Analysis and Design of Asymmetric Oscillation for Caterpillar-Like Locomotion,” Journal of Bionic Engineering, vol. 12(2), pp. 190-203.
[2] R.H. Plaut, (2015). “Mathematical Model of Inchworm Locomotion,” International Journal of Non-Linear Mechanics, in press.
[3] J. Lim, H. Park, J. An, Y-S. Hong, B. Kim, B-J. Yi, (2007). “One pneumatic line based inchworm-like micro robot for half-inch pipe inspection,” Mechatronics, vol. 18(7), pp. 315-322.
[4] A. Goldenberg, M. Gryniewski, T. Campbell, (2010). “AARM: A robot arm for internal operations in nuclear reactors,” IEEE Proc. of 1st Int. Conf. on Applied Robotics for the Power Industry, pp. 375-402, Montréal, Canada.
[5] P.R. Vundavilli, D.K. Pratihar, (2011). “Near-optimal gait generations of a two-legged robot on rough terrains using soft computing,” Robotics and Computer-Integrated Manufacturing, vol. 27(3), pp. 521-530.
[6] J. Blair, T. Iwasaki, (2010). “Optimal Gaits for Mechanical Rectifier Systems,” IEEE Trans. on Automatic Control, vol. 56(1), pp. 59-71.
[7] L. Biagiotti, C. Melchiorri, (2013). “Online Trajectory Planning and Filtering for Robotic Applications via B-spline Smoothing Filters,” Proc. of the IEEE Int. Conf. on Intelligent Robots and Systems (IROS) , pp. 5668-5673, Tokyo, Japan..
[8] M. Kong, Ch. Ji, Zh.Chen, R. Li, (2013). “Smooth and Near Time-optimal Trajectory Planning of Robotic Manipulator with Smooth Constraint based on Cubic B-spline,” Proc. of the IEEE Int. Conf. on Robotics and Biomimetics, pp. 2328-2333, Shenzhen, China.
[9] J.C. Restrepo, J. Villegas, A. Arias, S. Serna, C. Madrigal, (2012). “Trajectory Generation for a Robotic in a Robocup Test Scenery using Kalman Filter and B-Spline Curves,” XVII Simposio de Tratamiento de Señales, Imágenes Y Visión Artificial, pp. 110-115, Antioquia.
[10] H. Kang, B. An, F.C. Park, (2010). “A Switching Formula for Optimal Gait Transitions,” Proc. of

the IEEE Int. Conf. on Robotics and Biomimetics, pp. 30-35, Tianjin, China.
[11] J.D. Caigny, B. Demeulenaere, J. Swevers, J. D. Schutter, (2007). “Optimal Design of Spline-Based Feedforward for Trajectory Tracking,” IEEE Proc. of the American Control Conference, pp. 4524-4529, New York, USA.
[12] K. Yang, (2013). “An Efficient Spline-based RRT Path Planner for Non-Holonomic Robots in Cluttered Environments,” Proc. of the IEEE Int. Conf. on Unmanned Aircraft Systems , pp. 288-297, Atlanta, GA.
[13] W. Zhang, T. Inanc, S. Ober-Blobaum, J.E. Marsden, (2008). “Optimal Trajectory Generation for a Glider in Time-Varying 2D Ocean Flows B-spline Model,” Proc. of the IEEE Int. Conf. on Robotics and Automation, pp. 1083-1088, California, USA.
[14] S.MR.S. Noorani, A. Ghanbari, (2009). “Using PSO for finding the optimal trajectory in minimizing the consumed energy of a crawling robot,” Proc. of 17th ISME Annual Int. Conf. on Mechanical Engineering, Tehran, Iran.
[15] A. Ghanbari, SMRS. Noorani, (2011). “Trajectory Planning in Design of a Crawling Gait for a Modular Robot Using Genetic Algorithm,” Int. J. Advanced Robotic Systems, vol. 8(1), pp. 29-36.
[16] A. Ghanbari, A. Rostami, SMRS. Noorani, MMS. Fakhrabadi, (2008). “Modeling &
Simulation of Inchworm Mode Locomotion,” Lecture Notes in Computer Science, Springer, Berlin, vol. 5314, pp. 617-624.
[17] SMRS. Noorani, A. Ghanbari, (2011). “Explicit Dynamic Formulation for n-R Planar Manipulators with Frictional Interaction between End-effecter and Environment,” Int. J. Advanced Robotic Systems, vol. 8(2), pp. 91-100.