Pareto design of fuzzy tracking control based on the 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. Nevertheless, walking robots require the capability to walk merely laterally, when they are faced with the obstacles such as a wall. In walking robot field, 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 purely in the lateral plane on slope. When fuzzy control is utilized to track the desired trajectories of the joints, there has to be a trade-off 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 determinate the fuzzy control parameters. In this paper, normalized summation of angles 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 contrasted 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.