Hierarchical sliding-mode control of spatial inverted pendulum with heterogeneous comprehensive learning particle swarm optimization

As the extension of the present inverted pendulums (IPs), a novel spatial inverted pendulum (SIP) is proposed for the first time, which can move in three-dimensional space. The proposed SIP is viewed as the most general IP and is different from the existing IPs. Firstly, the model equations of the SIP are deduced from Lagrangian equations. The dynamic model equations of the SIP have five degrees of freedom and three control forces. To simplify the model equations of the SIP, a state transformation method is devised and presented step by step, assuming that all SIP parameters are exactly known. Through the proposed transformation, a concise block model of the SIP is obtained. Based on the concise block model of the SIP, hierarchical sliding-mode control (HSMC) is deployed in the trajectory tracking controller design for the SIR. To guarantee the convergence of the auxiliary sliding surfaces of the HSMC, heterogeneous comprehensive learning particle swarm optimization (HCLPSO) algorithm is used to optimize the control parameters for the HSMC. The proposed control method is capable to realize the spatial trajectory tracking of the SIP with high control performance. Simulation results verify the plausibility and effectiveness of the proposed control and optimization strategy for the SIR. (C) 2019 Elsevier Inc. All rights reserved.