Comparative study between quintic and cubic polynomial equations based walking trajectory of exoskeleton system

Trajectory planning is the most crucial part in robot design especially for exoskeleton robot. The suitable trajectory will directly affect safety, health, and comfort of the wearer. In trajectory generation profile of lower limb exoskeleton robot, the cubic polynomial is commonly used to generate smooth trajectory generation profile. Whereas, the quintic polynomial is not widely used due to complexity. This paper aims to make comparative studies between cubic and quintic polynomials. Whereas, the accuracy of generated profile will be investigated and analyzed to understand the gap of knowledge. Based on that, the gait cycle motion is divided into seven sub-phases. Each sub-phase is presented by one polynomial equation either cubic or quintic. Accuracy analysis was involved in order to show either cubic or quintic polynomial is accurately matched to human walking motion profile. The result shows that quintic generates an accurate profile motion of ankle, knee, and hip joints with 0.4852⁰,0.4283⁰, 0.3917⁰ RMS error respectively. Meanwhile, cubic polynomial generates the trajectory motion profile of ankle, knee, hip joints with 0.8417⁰, 0.9728⁰, 0.2639⁰ RMS error respectively. Thus, the quintic polynomial is more accurate than cubic polynomial to generate trajectory profile with the smooth transition.