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Underactuated robot systems, due to their unique flexibility and economy, are widely used in modern industry and intelligent manufacturing. However, their underactuated nature and complex nonlinearity make the control problem challenging. In addition, most existing control methods for underactuated systems take the measurable actuated and unactuated states as an implicit premise and do not consider the unknown measurement sensitivity of sensors. Unfortunately, due to space/costs or manufacturing technology limitations in practical underactuated robot systems, it is difficult to measure unactuated states and achieve the ideal working mode of sensors. To this end, an adaptive fuzzy control scheme is proposed for a class of uncertain underactuated robot systems without unactuated state sensors, which stabilizes the system even with actuated state measurement errors. Specifically, the dynamics of underactuated systems are reconstructed into a nontriangular normal form, and the backstepping design is completed by using the boundedness of fuzzy basis functions. At the same time, the explosion of complexity is avoided by using dynamic surface control technology. Moreover, the proposed update law availably compensates parameter/structure uncertainties for underactuated robot systems. The asymptotic stability of the closed-loop system is proved by incorporating Lyapunov candidates with sensitivity information. Finally, the proposed control scheme is applied to a tower crane system, whose effectiveness is verified by hardware experiments. Note to Practitioners —This paper is motivated by the common sensor problems in uncertain underactuated robot systems control. Some states in underactuated systems are called unactuated states because they have no direct corresponding control inputs. Such states bring significant challenges to controllers design of underactuated systems. Furthermore, most existing control methods require all states to be measurable and ignore the measurement uncertainty of sensors. However, in many practical situations, it is difficult to install unactuated state sensors, and there are inevitable measurement errors in actuated state sensors. These factors make the feedback controllers developed for underactuated systems difficult to practically apply. To address these issues, this paper presents a control scheme that does not require unactuated state measurements and model information, which can still stabilize underactuated systems to the origin even in the presence of actuated state measurement errors. The stability is rigorously proven theoretically and the experimental results obtained on a self-built tower crane platform demonstrate the feasibility and effectiveness of the proposed control scheme. In future efforts, we intend to apply the proposed control scheme to practical industrial underactuated robot systems.
Zhai et al. (Mon,) studied this question.