  Many methods have been developed in trajectory planning in order to achieve
smooth and accurate motion with considering the constraints of kinematics
constraints such as angular position, velocity, acceleration, and jerk. The
problem of using the combination of n-order polynomials is that there is no
ideally match between the segments of trajectory path at the via point in terms
of the number of kinematic constraints. It leads to generate undesirable
trajectory path at the via point that connects between two segments of the
trajectory path. In this paper, we aim to investigate the effect of increasing
to higher order polynomial blends on the accuracy of the via points with
considering different kinematics constraints. Based on that, the methodology
that was used in this paper is based on the polynomial segment with the higher
polynomial blend (PSPB). Three techniques implemented which are 4-3-4 PSPB,
5-4-5 PSPB, and 6-5-6 PSPB. Each technique implemented based on applying
different kinematic constraints. The three techniques validated using a
modeling design in SemiMechanics. According to the methodology, the result
analyzed and discussed in terms of angular position, angular velocity, angular
acceleration, and angular jerk based on Root Mean Square Error (RMSE) and
Average Difference Error (ADE). The result shows that RMSE of angular position
for 4-3-4 PSPB-1, 4-3-4 PSPB-2, 5-4-5 PSPB-1, 5-4-5 PSPB-2, 6-5-6 PSPB-1, and
6-5-6 PSPB-2 are 0.4574, 0.0172, 10.9089, 0.1242, 0.6153, and 0.3128 degrees
respectively. At the same time, the ADE are 0.0455, 0.0017, 1.0855, 0.0124,
0.0612, and 0.0311 degrees respectively. Thus, the error is increased obviously
when there is no ideal match at the via point in terms of a number of kinematic
constraints.
