Pareto design of fuzzy tracking control based on particle swarm optimization algorithm for a walking robot in the lateral plane on slope

Many researchers have controlled and analyzed biped robots that walk in the sagittal plane. These robots require the capability of walking merely laterally when they are faced with the obstacles such as a wall. In this field of study, both nonlinearity of the dynamic equations and also having a tracking system cause an effective control has to be utilized to address these problems. Therefore, this paper presents a nonlinear fuzzy tracking control for the walking robots that step in the lateral plane on a slopes. When fuzzy control is utilized to track the desired trajectories of the joints, there has to be a tradeoff between tracking errors and control efforts. Consequently, a particle swarm optimization algorithm is used to obtain the Pareto front of these non-commensurable objective functions to determine the fuzzy control parameters. In this paper, normalized summation of angle errors and normalized summation of control efforts are considered as the objective functions. These objective functions have to be minimized simultaneously. A vector which contains the control parameters is considered as the vector of selective parameters with positive constant values. The obtained Pareto front by the proposed multi-objective algorithm is compared with three prominent algorithms, modified NSGAII, Sigma method and MATLAB Toolbox MOGA. The result dramatizes the superiority of innovative particle swarm optimization over the algorithms.