Kinematics and dynamics motion planning by polar piecewise interpolation and geometric considerations

The importance of numerical methods in science and engineering [Chapra, S.C., and R.P. Canale, “Numerical Methods for Engineers,” McGraw-Hill, 6th Ed., 2010] was long recognised and considered a fundamental factor in improving productivity and reducing production costs. The ability to model flexible systems and describe their trajectories [Gasparetto A., Boscariol P., Lanzutti A., Vidoni R., Trajectory planning in Robotics, Mathematics in Computer Science 6 (2012), pp. 269–279] involves usually the study of nonlinear coupled partial differential equations. Since their exact solutions are not normally feasible in practice, computational methods [V. Kumar, M. Zefran, J.P. Ostrowski, Motion Planning and Control of Robots, Handbook of Industrial Robotics, 2nd Edition, J. Wiley and Sons (2007), pp. 295–315] can be considered