Robust control of underactuated bipeds using sliding modes

Abstract

SUMMARYThe purpose of this paper is to present a robust tracking control algorithm for underactuated biped robots capable of self-balancing in the presence of external disturbances. The biped is modeled as a five-link planar robot with four actuators located at hip and knee joints. A sliding mode control law has been developed for the biped to follow a human-like gait trajectory while keeping the torso nearly upright. The control forces are calculated by defining four first-order sliding surfaces as a linear combination of the torso and the four joint tracking errors. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces during each step, while the walking cycle stability is maintained through a Lyapunov function. The criteria for asymptotic stability of the surfaces are presented and a numerical search method is implemented for the selection of the corresponding surface parameters. The paper further investigates the robustness of the controller in response to disturbances. Numerical simulations demonstrate the tracking stability of the biped's multistep walk and its human-like response to an external disturbance.

A survey of underactuated mechanical systems

“…SMC has succeeded in the applications of control of underactuated satellite [131], surface vessel [85,132], helicopter [133], wheeled inverted pendulum [31], ball-and-beam system [134], underactuated fuel cell system [135], TORA [136], underactuated biped robot [137], and overhead crane [138]. Meanwhile, many researchers also devoted themselves to design universal SMC for the UMSs that have the same dynamic characteristics, e.g.…”

Rotational Stability Index (RSI) point: postural stability in planar bipeds

“…Merging the conditions for both forward (Proposition 1) and backward foot rotations in (16), the overall bipedal stability condition is rewritten as (17). It is notable for the computation of x RSI (t k ) that the constants in (8) Biped stability criteria : 0 < x RSI (t k ) < foot length, ∀k.…”

“…14,15 The ZMP criterion is not applicable to point foot bipeds. [16][17][18][19] The absolute orientation of the biped is considered as an additional passive degree of freedom (DOF) in point foot bipeds. The concepts of periodicity and orbital stability are useful while dealing with the associated stability issues.…”

Balance maintenance of the Synthetic-Wheel Biped in the presence of impulsive disturbances

“…Hobbelen and Wisse [16] investigated the effect of leg retraction on the disturbance rejection of limit cycle walkers 1 and used the Gait Sensivity Norm [17], to find the optimal swing-leg retraction. Other nonlinear control methods such as sliding mode control and passivity-based control have been proposed for a 5-DOF under-actuated biped [18] and a forcecontrollable humanoid [19] for disturbance rejection.…”