A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint

Asano, Fumihiko; Yamakita, Masaki; Kamamichi, Norihiro; Zhang, Luo

doi:10.1109/tra.2004.824685

Cited by 146 publications

(42 citation statements)

References 14 publications

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“…In addition to increasing energy consumption, it is harmful for the robot in long term and less human like, though providing full controllability. arXiv:1605.03036v1 [cs.RO] 10 May 2016 [6] [7] [8] [9] [8] [10]…”

Section: B Inverted Pendulumsmentioning

confidence: 99%

3LP: A linear 3D-walking model including torso and swing dynamics

Faraji

Ijspeert

2017

The International Journal of Robotics Research

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Abstract-In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speedfrequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.

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Section: B Inverted Pendulumsmentioning

confidence: 99%

3LP: A linear 3D-walking model including torso and swing dynamics

Faraji

Ijspeert

2017

The International Journal of Robotics Research

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“…Due to (10) and (11), the initial values of S 3 f (λ, x 0 , t) and the terminal values of S 3b (λ, x t f , t) are as follows respectively:…”

Section: Double Generating Functions Methodsmentioning

confidence: 99%

“…By solving the first equation in (10) and (11) for x(t) and λ(t), the following theorem is proposed, which gives a parametrization of the optimal state and input trajectories for different boundary conditions and different time intervals for a finite time linear quadratic optimal control problem. Theorem 1.…”

Section: Double Generating Functions Methodsmentioning

confidence: 99%

Optimal Gait Generation for a Compass Biped Robot via the Double Generating Functions Method

Hao

Fujimoto

Hayakawa

2014

SICE Journal of Control, Measurement, and System Integration

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To control a compass biped robot walking in a complex environment, it is necessary to adjust its step length and walking speed for every step. Therefore, the computation time to calculate the suitable gait for each step, which is called on-demand computation time in this paper, should be short enough to walk continuously. Recently, the double generating functions method for finite time linear quadratic optimal control problems was proposed, whose advantage is that it can generate a parametrization of optimal trajectories for different boundary conditions and different time periods. It is very useful to the on-demand computation of optimal gait for the real biped robots walking in a complex environment. This paper applies the double generating functions method to a compass biped robot walking on the level ground. Considering the energy consumption, we generate a family of reference optimal gaits and inputs for different boundary conditions (the step length and the walking speed) for the linearized model by employing the double generating functions method. The simulation result shows that the modeling error caused by the linear approximation is small enough when the compass biped robot walks with a suitable step length and walking speed. This implies that the optimal gaits and inputs for the linearized system can be used as the optimal gaits and inputs for the original nonlinear system.

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“…Due to a relatively weak coupling of swing and CoM dynamics in slow walking conditions, adjusting the next footstep location becomes effective only in the next phase where this position becomes the new stance position which is tightly coupled to other system variables Raibert (1986); Koolen et al (2012). Modulating the CoP through ankle torques can provide immediate stabilization, but is only useful in small disturbance conditions Asano et al (2004); Moro et al (2011).…”

Section: Control Approachmentioning

confidence: 99%

Bipedal walking and push recovery with a stepping strategy based on time-projection control

Faraji

Razavi

Ijspeert

2019

The International Journal of Robotics Research

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In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.

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A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint

Cited by 146 publications

References 14 publications

3LP: A linear 3D-walking model including torso and swing dynamics

3LP: A linear 3D-walking model including torso and swing dynamics

Optimal Gait Generation for a Compass Biped Robot via the Double Generating Functions Method

Bipedal walking and push recovery with a stepping strategy based on time-projection control

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