A fuzzy decentralized sliding-mode robust adaptive under-actuated control for autonomous dynamic balance of an electrical bicycle

Abstract

Based on the previous studies, the dynamic balance of an electrical bicycle includes two control inputs: steering and pendulum torques, and three system outputs: steering, lean and pendulum angles. Two novel reference signals are first designed so that the uncontrolled mode is simultaneously included into these two control modes. Two scaling factors for each subsystem are first employed to normalize the sliding surface and its derivative. The so-called fuzzy decentralized sliding-mode under-actuated control (FDSMUC) is first designed. Because the uncertainties of a bicycle system, caused by different ground conditions, gusts of wind, and interactions among subsystems, are often huge, an extra compensation of learning uncertainty is plunged into FDSMUC to enhance system performance. We call it as "fuzzy decentralized sliding-mode adaptive under-actuated control" (FDSMAUC). To avoid the unnecessary transient response and then destroy the balance of the bicycle, the combination of FDSMUC and FDSMAUC with a transition (i.e., fuzzy decentralized sliding-mode robust adaptive under-actuated control, FDSMRAUC) is designed. Finally, the compared simulations for an electrical bicycle among the FDSMUC, FDSMAUC and FDSMRAUC validate the efficiency of the proposed method.

A survey on the application of fuzzy systems for underactuated systems

“…In Hwang et al, 79 Hwang proved that the traditional PID method could not stabilize or control an underactuated electrical bicycle because the characteristics of this system are highly nonlinear, coupled, nonholonomic, and unstable. Hwang et al 80 applied the method of Li and Shieh 76 to control an underactuated electrical bicycle.…”

Underactuated robotics: A review

“…Neural fuzzy control [193][194][195][196][197][198][199] Fuzzy neural network control 200,202,[294][295][296] Optimization methods for fuzzy control 203,297-304 PFL Collocated PFL 8,210,[305][306][307][308][309] Non-collocated PFL 211,[310][311][312][313] Energy-based methods 19,215,216,226, SMC SMC with a model-free fuzzy system [243][244][245][246][247][248]252,257,[259][260][261][262]265,267,268,270,271,303,337 Adaptive SMC with a direct or indirect fuzzy system 205,…”

Steering and balance controls of an electrical bicycle using integral sliding mode control

“…It is seen that an e-bicycle is an underactuated system subject to nonholonomic contact constrains associated with the rolling constrains on the front and rear wheels. The fuzzy sliding mode underactuated control in [5] is proposed to deal with huge uncertainties caused by different ground conditions and gusts of wind for a bicycle system. In [6], [7], a hybrid controller with lateral velocity control and steering function control is proposed to stabilize the bicycle posture and achieve trajectory tracking control to follow a straight-line.…”