Inverse kinematic model of multi-section continuum robots using particle swarm optimization and comparison to four meta-heuristic approaches

Abstract

Multi-section continuum robots’ (CRs) behavior is still an outstanding problem because of the highly non-linearity of its equation of motions. To this end, in this paper, particle swarm optimization (PSO) is adopted to solve the inverse kinematic model (IKM) of CRs. First, the CR’s structure is properly described. Then, the aforementioned algorithm is elaborately discussed and implemented in figuring out the IKM of CR and verified through forward kinematic model by choosing the PSO parameters, namely, cognitive factors $(C_1=C_2=1.2)$ and inertia weight $(\omega =0.79)$ for 200 positions on an arc-like trajectory. The optimal angle values ( $\theta =0.0346$ and $\phi =0.00013$ ) which ensure the lowest distance between the attainably desired position and the robot’s end effector are $1.04497\times {10}^{-9}\mathrm{mm}$ which is perfectly accurate. After that, simulation through MATLAB is carried out, namely, in the first simulation, a three-section CR follows a linear trajectory with a precision approximately equal to $0.75\times {10}^{-9}\mathrm{mm}$ . Furthermore, PSO takes 7 ms as a mean consumption time to make the robot’s end effector attain to each position. Then, a circular trajectory is followed using PSO. Comparatively speaking, PSO is compared with four meta-heuristic approaches; it is remarked that PSO is a good compromise between accuracy and time consumption. Based on the obtained results, PSO can be considered as a trade-off between accuracy and time consumption for solving the IKM of CRs with complex structure.