Creating Through Points in Linear Function with Parabolic Blends Path by Optimization Method


The linear segment with parabolic blend (LSPB) trajectory deviates from the specified waypoints. It is restricted to that the acceleration must be sufficiently high. In this work, it is proposed to engage modified LSPB trajectory with particle swarm optimization (PSO) so as to create through points on the trajectory. The assumption of normal LSPB method that parabolic part is centered in time around waypoints is replaced by proposed coefficients for calculating the time duration of the linear part. These coefficients are functions of velocities between through points. The velocities are obtained by PSO so as to force the LSPB trajectory passing exactly through the specified path points. Also, relations for velocity correction and exact velocity solution are derived. Simulation results show that the engagement of modified LSPB trajectory with PSO to work well on the tested cases. This proposed method is very simple which can be used for on-line path planning, and not necessarily to use high acceleration magnitude.