Model orbit output feedback tracking of underactuated mechanical systems with actuator dynamics

Abstract

Robust periodic motion generation is developed for a class of mechanical systems with actuator dynamics. The virtual constraint (VC) approach is first refined under incomplete state measurements and it is then extended to the case where the actuator dynamics are brought into play for avoiding limitations in the system performance. The extended virtual constraint approach is subsequently coupled to the nonlinear H∞ synthesis to yield the robust output feedback periodic motion generation for mechanical systems of underactuation degree one, driven by electrical motors with their own dynamics. The effectiveness of the proposed synthesis is supported in the numerical study made for a cart-pendulum testbed.

Orbital synchronization of homogeneous mechanical systems with one degree of underactuation

“…The phase portraits of the carts and the pendulums are plotted in Figure 3A,B, respectively; the applied torques are shown in Figure 3C; and the  2 -norm of tracking error e i ⊤ , defined in (50), is presented in Figure 3D. According to the  ∞ theory, the robustness property is guaranteed in the presence of disturbances, in the sense of inequality (32). In this scenario, the systems' phase portraits do not converge to the reference orbit but they remain bounded due to inequality (32).…”

“…According to the  ∞ theory, the robustness property is guaranteed in the presence of disturbances, in the sense of inequality (32). In this scenario, the systems' phase portraits do not converge to the reference orbit but they remain bounded due to inequality (32). This is, the  2 gain of the systems is less than the attenuation level 𝛾 i .…”

“…F I G U R E 4 Top: Robustness of the cart-pendulum systems in terms of inequality (32). Bottom:  2 -norm of estimation errors…”

“…In particular, the virtual holonomic constraints (VHC) approach 13 is a powerful tool for the periodic motion generation in underactuated mechanical systems such as pendulums, helicopters, and biped robots. Its practical utility is well‐established for a particular case of underactuation degree one 31‐35 . However, it has been generalized to impulsive mechanical systems, 36 and to mechanical systems with an arbitrary number of degrees of underactuation 37 .…”

“…Its practical utility is well-established for a particular case of underactuation degree one. [31][32][33][34][35] However, it has been generalized to impulsive mechanical systems, 36 and to mechanical systems with an arbitrary number of degrees of underactuation. 37 In the latter, the approach has been confined to specific applications of underactuation degree two due to their higher complexity.…”