The Effectiveness of Kinematic Constraints on The Accuracy of Trajectory Profile of Human Walking Using PSPB Technique

TL;DR

This study investigates how increasing polynomial order in trajectory planning improves the accuracy of human walking trajectory profiles considering kinematic constraints, using PSPB techniques validated through modeling and error analysis.

Contribution

It introduces higher-order polynomial blends (PSPB) for trajectory planning and evaluates their effectiveness in improving via point accuracy under various kinematic constraints.

Findings

Higher polynomial blends reduce RMSE and ADE in trajectory accuracy.

Matching the number of polynomial segments to kinematic constraints improves trajectory smoothness.

Errors increase when there is a mismatch between polynomial segments and kinematic constraints.

Abstract

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.