Abstract
This article presents the modeling process of the lower part of a humanoid biped robot in terms of kinematic/dynamic states and the creation of a full dynamic simulation environment for a walking robot using MATLAB/Simulink. This article presents two different approaches for offline walking pattern generation: one relying on a closed-form solution of the linear inverted pendulum model (LIPM) mathematical model and another that considers numerical optimization as means of desired output trajectory following for a cart table state-space model. This article then investigates the possibility of introducing solution-dependent modifications to both approaches that could increase the reliability of basic walking pattern generation models in terms of smooth single support–double support phase transitioning and power consumption optimization. The algorithms were coded into offline walking pattern generators for NAO humanoid robot as a valid example and the two approaches were compared against each other in terms of stability, power consumption, and computational effort as well as against their basic unmodified counterparts.
Highlights
A humanoid robot is a robot that resembles human body form and is bipedal in nature
Ten years following that discovery, Waseda University has produced a handful of humanoid robots like the musician robot WABOT-2 made in 1984, Hadaly-2, which cooperates with a human partner to do specific jobs,[1] and the biped robot, WABIAN, which could perform impressive walking maneuvers in 1997.2 Based on the promising fruits of research in that field, Waseda University
The simulations show that the upgraded numerical approach is superior to the upgraded closed-form approach in terms of zero moment point (ZMP) trajectory following since it has lower root mean square error (RMSE) in both axes
Summary
A humanoid robot is a robot that resembles human body form and is bipedal in nature. The first human-resembling robot was developed by Ichiro Kato et al from Waseda University in 1973. Equation (39) shows that the desired final displacement of the center of mass trajectory along local x-axis is equal to half the magnitude of the step plus the x-coordinate of the foot placement point It shows a similar expression for the desired final displacement of COM trajectory along local y-axis with the exception of the sign, which flips at each instant of time to reflect support exchange. The cart responds by an equivalent force in the opposite direction, creating a moment about the table ZMP as follows treaction 1⁄4 ÀF push  zc 1⁄4 Àm€x  zc (51) Another way of interpreting the biped robot dynamics is by representing it in terms of a simpler model known as the cart table model.
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