Computer Algorithm of Optimal Planning for Single-hand Suspension Motion

The primary purpose of this study was to design a set of algorithm, which can compute the optimal trajectory (OT) for 3D human single-hand suspension motion. To achieve this goal, the study first established a 15-segment human body model (HBM). Then based on Lagrange-Euler equations (LEE) of motion and seven types of homogeneous transformation matrices (CH-7T) proposed by Chiu [1] , the study defined primary human segments as a dynamic system with 38 degrees of freedom (DoF). Finally, the Open-loop Linear Quadratic Controller (OLLQC) was applied to transform the dynamic system (DS) into a linear state of space. With established boundary conditions (BC) for positions and velocities, the set of algorithm, which complied with the principle of minimum energy expenditure (MEE), was adopted to compute the OT for those primary segments involved in single-hand suspension motion. To solidify the practicability of the algorithm, the subject’s segment lengths were measured, and a computer was used to simulate the motion of suspending his right hand. The simulation results showed that the algorithm in the designed DS is capable of computing the OT, velocity, and moment. The significance of this study lies in its wide application: (1) the DS designed for single-hand suspension can be used to simulate the dynamics for the gymnastics motion on flying rings and horizontal bar, rock climbing, and the movement of an astronaut in a spacecraft ; (2) this DS can be transformed into a control system (CS), which corresponds to the principle of MEE and can compute the OT for body segments.