Kernkonzepte
A novel hybrid formulation of the linear inverted pendulum model is proposed to stabilize bipedal locomotion, using a Lyapunov-based feedback controller and a reference spreading mechanism to handle the non-synchronized contact times between the reference and the actual robot motion.
Zusammenfassung
The paper presents a novel hybrid formulation of the linear inverted pendulum model (LIPM) for bipedal locomotion, where the foot switches are triggered based on the center of mass position, removing the need for pre-defined footstep timings.
The key highlights are:
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A hybrid modification of the reference dynamics, similar to the "reference spreading" concept, is adopted to handle the non-synchronized contact times between the reference and the actual robot motion.
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A saturated linear feedback controller is designed by solving a convex optimization problem to stabilize the hybrid error dynamics. The gains are selected to ensure local asymptotic stability of the tracking error, with a certified estimate of the basin of attraction.
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The stability proof is based on an optimized selection of a quadratic Lyapunov function, where the decrease along flows is ensured by the linear feedback, and the increase across jumps is bounded using an extended class K∞ function of the position error.
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The proposed framework is shown to have advantages over a standard model predictive control formulation, as it can better describe the natural interplay between stepping frequency and walking speed.
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The theoretical results are validated through simulations on a full-body model of a real humanoid robot, demonstrating the practical applicability of the proposed approach.
Statistiken
The paper provides the following key figures and metrics:
The linear inverted pendulum model (LIPM) dynamics are described by the equations:
¨xc = ω^2(xc - u)
where xc is the center of mass position, u is the center of pressure, and ω = sqrt(g/zc) with g the gravity acceleration and zc the constant CoM height.
The half-step size is denoted as r̄, corresponding to half the longitudinal length of a step.
The periodic reference motion has a period T that depends on the half-step size r̄ and the peak forward speed v̄ according to the relations:
v̄ = (cosh(ωT) + 1) / (ω sinh(ωT)) * r̄
T = 1/ω * ln((v̄/ω + r̄) / (v̄/ω - r̄))
The control gains K and L are obtained by solving the convex optimization problem (24), where the parameter α > ω is selected to ensure feasibility.
Zitate
"Contrary to the classical approach, where the contact timings are fixed a priori, we assume that contacts occur when the CoM reaches a given position, using hybrid jumps to shift the reference frame at each step, so that it corresponds to the center of the foot on the ground."
"Our solution presents two main advantages with respect to the classical fixed-contact approach. First, it well describes the natural interplay between the stepping frequency and the walking speed. As the robot walks faster, its stepping frequency automatically increases. As empirically shown in our results in Section 6, this can allow the robot to keep walking in cases where a classic approach would lead to a fall."
"Secondly, in view of a well-posed formulation, it allows proving rigorous robust stability guarantees (see [16, Chapter 7]). In particular, our stability proof is based on an optimized selection of a quadratic Lyapunov function for which we can ensure asymptotic stability of the error dynamics despite a mismatch in the impact times of the reference and actual motion."