Spherical Foot Placement Estimator for Humanoid Balance Control and Recovery

DeHart, Brandon; Gorbet, Rob; Kulić, Dana

doi:10.1109/icra.2018.8460718

Cited by 5 publications

(9 citation statements)

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“…In the present case, in order to exploit energies and momenta, rotations along the vertical and one of the horiziontal axes have been chosen. Indicated with γ and ω the rotation velocities of the SIP, on the vertical and the horizontal axis on the frontal plane of the biped, the approach of [4,5] is based on the projection of the angular momentum on the pivot point of the pendulum on these two directions, and expressing the kinetic energy as function of these two projections. Cleverly, noting that the total energy and the momentum projected on the vertical axis remain constant during the periods before and after the collision of the swing foot with the ground, approaching the collision and the switching of the pivot foot, the problem is solved by writing the equations of the pre-impact, impact and post-impact phases.…”

Section: The Spherical Foot Placement Estimationmentioning

confidence: 99%

“…In describing the spherical inverted pendulum the same notation used in [4,5] was adopted. In addition, explicitly, θ z indicates the angle of rotation with respect to the vertical axis, and two degrees of freedom of the swing leg relative to the pendulum were introduced, with the angles α z and α, as shown in Figure 1, with the kinematics of the joints in Figure 2a.…”

Section: The Spherical Inverted Pendulum Modelmentioning

confidence: 99%

“…First, the problem was solved in two dimensions [1,2], with a first extension and test in 3-D in [3]. More recently, the approach has been transferred to 3-D adopting a specific form of a spherical inverted pendulum (SIP) and called SFPE [4,5]. However, in order to make the problem manageable several questionable simplifications were introduced, i.e.…”

Section: Introduction 1backgroundmentioning

confidence: 99%

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The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation

Menga

2021

Applied Sciences

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The gait and the Foot Placement Estimation (FPE) has recently been extended to 3-D spaces by adopting a specific form of a spherical inverted pendulum (SIP). The approach is very attractive, as it does not involve dynamics, but it is based solely on energies and momenta, however the authors (DeHart et al.) introduced several questionable approximations, in order to reach a manageable solution. The scope of the present paper is to revisit this spherical inverted pendulum applied to biped walking, offering an exact solution to the gait and the FPE by using symbolic computation. This is facilitated by exploiting the Kane’s approach to dynamical modelling, and his software environment for symbolic manipulation, called Autolev. It generates explicit formulas describing the energies and angular momenta before/after the impact, along with the mechanics of the impact. As the resulting equations, function of (measurable) angular positions and velocities, are very compact, embedded in a numerical nonlinear solver, are suitable to be implemented in real time and used in practice to control biped robots or lower limb exoskeletons. The two main contributions of the paper are: the recovery of the balance by stepping, in the presence of a push in an arbitrary direction and omnidirectional walking. In this last respect, this specific form of SIP emphasizes the expenditure of energy in the walk. For the first time, at our knowledge, the walk of the SIP, based on energy, has been compared to the simulation of a 12 degrees of freedom biped robot tracking preview signals using the Zero Moment Point (ZMP) of the Linear Inverted Pendulum (LIPM). This quantitatively shows the inefficiency, in terms of energy, of the ZMP-based walk, and the gain due to the recovery of the collision of the flying foot. Similarity in the sagittal plane and differences in the frontal plane of the center of mass trajectories of the two approaches are shown, to open the road to an integration of fully actuated and underactuated controls, for an efficient full-dimensional robot gait to be developed in a future paper.

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Section: The Spherical Foot Placement Estimationmentioning

confidence: 99%

Section: The Spherical Inverted Pendulum Modelmentioning

confidence: 99%

Section: Introduction 1backgroundmentioning

confidence: 99%

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The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation

Menga

2021

Applied Sciences

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“…Reference [13] introduces a novel approach for humanoid gait generation. The control of foot placement and human balancing problems are discussed in [14], where a predictive model is applied.…”

Section: Introductionmentioning

confidence: 99%

“…Since the mathematical description of the above-mentioned and the similar predictive models are quite challenging, these models develop slowly, and the integration of the features leads to highly intricate mathematical description. The long-term goal of our research is to reach such integrated models of hopping and running that can analyze (i) the dynamic stability issues, the neural processes such as balancing [14][15][16][17], the motion control and the motion pattern generation [18]; (ii) geometric non-linearities [10,12,19,20]; (iii) ground-foot collision intensity and impact-induced energy absorption [9,21,22]; (iv) distinct topology and actuation in the flight and ground phases [23].…”

Section: Introductionmentioning

confidence: 99%

A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

Zana

Bodor

Bencsik

et al. 2018

MCA

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Contradictory demands are present in the dynamic modeling and analysis of legged locomotion: on the one hand, the high degrees-of-freedom (DoF) descriptive models are geometrically accurate, but the analysis of self-stability and motion pattern generation is extremely challenging; on the other hand, low DoF models of locomotion are thoroughly analyzed in the literature; however, these models do not describe the geometry accurately. We contribute by narrowing the gap between the two modeling approaches. Our goal is to develop a dynamic analysis methodology for the study of self-stable controlled multibody models of legged locomotion. An efficient way of modeling multibody systems is to use geometric constraints among the rigid bodies. It is especially effective when closed kinematic loops are present, such as in the case of walking models, when both legs are in contact with the ground. The mathematical representation of such constrained systems is the differential algebraic equation (DAE). We focus on the mathematical analysis methods of piecewise-smooth dynamic systems and we present their application for constrained multibody models of self-stable locomotion represented by DAE. Our numerical approach is demonstrated on a linear model of hopping and compared with analytically obtained reference results.

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A Novel Paradigm for Controlling Navigation and Walk in Biped Robotics

Menga

2024

Preprint

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Classically the walk in biped robotics was obtained controlling balance during the whole step, i.e. guaranteeing that the pressure point under the soles always stayed in the polygon of the supporting feet. However, this assumed that the feet were able to transfer torque to the ground during the whole gait cycle. In spite of the fact that the amount of transferrable torque in the feet-ground contact is limited, it is possible only during some phases of the step, and the overall process is energetically inefficient. On the other side, starting from the passive motion of the rimless wheel falling on an inclined surface, and ending to the inverted pendulum with a compass, balance in the whole was proven in spite of dynamical instability inside each step. Along this line results of Foot Placement Estimation (FPE) in 2-D and 3-D showed how energy efficient walk was possible, emulating the human walk with a free fall on the swing foot and energy restitution at the foot collision with the ground for the next step. This model assumes pointy feet, so without torque transfer to the ground. In the realm of FPE, in previous papers the present author adopted the 3-D inverted pendulum in polar coordinates (Spherical Inverted Pendulum - SIP) to introduce omnidirectional walks with arbitrarily changing characteristics. No torque control was used during the step, i.e the pendulum was always in free fall at each step, the only control actions were at the beginning of the next step. These actions are: the change of angular velocities at the start of a new step, with respect to those given after the collision (emulating the torque action in the brief double stance period), to recover for the losses, and the preparation of the position in the frontal and sagittal planes of the swing foot for the next collision. The present paper improves this paradigm, proposing a general model to account for all characteristics of the biped and of the gait, with adding a minimum of dynamical complexity with respect to the SIP. This model allows, not only to walk omnidirectionally on a flat surface, but also to go up and down staircases.

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Spherical Foot Placement Estimator for Humanoid Balance Control and Recovery

Cited by 5 publications

References 10 publications

The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation

The Spherical Inverted Pendulum: Exact Solutions of Gait and Foot Placement Estimation Based on Symbolic Computation

A Tutorial for the Analysis of the Piecewise-Smooth Dynamics of a Constrained Multibody Model of Vertical Hopping

A Novel Paradigm for Controlling Navigation and Walk in Biped Robotics

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