Hierarchical Sliding Mode Fuzzy Control For Robots With Underactuated Joints

Underactuated system is a nonlinear system that the number of the control inputs are fewer than the number of system generalized coordinate variable (or freedom degree). The underactuated system includes actuated joints and underactuated joints (or named as passive joints/free-joints), and the desired motion is achieved that underactuated joints are drived by actuated joints through the dynamics coupling relation among them.Due to the underactuated joints, the underactuated system is an incomplete controllable system, so general smooth feedback control is invalid for such system. The motion control of an underactuated system is much more difficult than that of a conventional system. Aim at the problems of the control of underactuated system above, a method of hierarchical sliding mode fuzzy control (HSMFC) is studied in this paper through the combination of fuzzy control and sliding-mode control.In this paper, the undractuacted planar two-link manipulator is the study object and dynamics model of the system is set up using the method of Lagrange dynamics. Applied the idea of hierarchical sliding-mode control (HSMC), the whole system is divided into two subsystems which represent the actuated joint and under-actuated joint respectively. At the same time, the whole sliding-mode function is designed. For reducing the chattering of the sliding-mode control system, boundary layer is introduced. In the boundary layer, fuzzy controller based on sliding-mode theory (SMFC) replaces the sliding-mode controller. And bacause the slope of sliding surface and the influene relation of the two subsystems play an important role in governing the interactive transient responses, system parameters are adjusted by fuzzy inference system automationly to improve the system's dynamics performance.Through the study of simulation and the comparison between HSMFC and HSMC, simulation results demonstrate that HSMFC improve the dynamics performance of the system and reduce the chattering of sliding-mode control.