3D Linear Inverted Pendulum Model Research Articles

Oscillation Preventing Closed-Loop Controllers via Genetic Algorithm for Biped Walking on Flat and Inclined Surfaces

In this study, a closed-loop controller is designed to overcome the dynamical insufficiency of the 3D Linear Inverted Pendulum Model (LIPM) via the Genetic Algorithm (GA). The main idea is to still use the 3D LIPM with a closed-loop controller because of its ease at modeling. While suppressing the dynamical flaws only the legs are used, in other words a robot is used which does not have any upper body elements to have a more modular robot. For this purpose, a biped is modeled with the 3D LIPM which is one of the most famous modeling methods of humanoid robots for the ease of modeling and fast calculations during the trajectory planning. After obtaining the simple model, Model Predictive Control (MPC) is applied to the 3D LIPM to find the reference trajectories for the biped while satisfying the Zero Moment Point (ZMP) criteria. The found reference trajectories applied to the full dynamical model on Matlab Simulink and the real biped in the laboratory at Istanbul Technical University. From the simulation results on the flat and inclined surfaces and real-time experiments on a flat surface some dynamical flaws are observed due to the simple modeling. To overcome these flaws a Proportional-Integral (PI) controller is designed, and the optimal value of the controller gains are found by the GA. The results assert that the designed controller can overcome the observed flaws and makes biped move more stable, smoother, and move without steady-state error.

Підхід до створення системи моделювання гнучкого виробництва

This paper dealing with the problem of generation motion of biped robot, to solve this problem, was introduces a new method of implementation a biped robot walking pattern generation byusing a Model Predictive control (MPC) First, the basic of biped robots’ motion was reviewed and was discussed the elements of motion controller. The dynamics of a biped robot is modeled as a runningcart on a table which gives a convenient representation for generation ZMP trajectory. After reviewing approach of 3D Linear Inverted Pendulum Model, a pattern generator was designed, lastly in MATLAB/Simulink and using Model Predictive Control Toolbox (MPCT) which provides functions, an app, and Simulink blocks was used for designing and simulating a motion generator based on model predictive controllers (MPC).The results of simulation are shown that we can realize such controller for generating trajectory of Center of Mass and Zero Moment point by using the MPC. The smooth trajectory of CoM is generated and the resulted ZMP follows the reference with good accuracy.Ref. 13, pic. 6

Planning Trajectory of Anthropomorphic Walking Robot (Biped Robot)

Humanoid robots have been a topic of great interest for a long time. Among the various motions of a humanoid robot, the most basic and important motion is bipedal walking. Bipedal walking is probably the most appropriate way for robots to move around in a real environment. However Building trajectories for biped robot walking is a complex task considering all degrees of freedom (DOFs) commonly bound within the mechanical structure. To study the stable motion of any bipedal robot we should study the Kinematics, Dynamics, design a control system and of most important the trajectories. This work deals with planning trajectory of humanoid robots (AK Biped robot), especially for planning trajectory of center of mass (CoM), zero moment point (ZMP)a and planning trajectory of swing foot. diffident method used in planning trajectory like 3D linear inverted pendulum (LIMP), polynomial interpolation. The object of study is the process of automatic control walking of an anthropomorphic walking robot (AK biped robot), for that this paper proposes an approach of joint trajectory generation for the biped robot using the three Three-dimensional linear inverted pendulum for planning trajectory of CoM which keep the ZMP to be inside the support polygon which and guarantee stable dynamic walking of AK biped robot, then trajectory of swing foot derived using the polynomial interpolation function for smooth motion. The aim of this paper is to present a full 3D walking strategy using dynamic model of 3D inverted pendulum for generation references joint trajectories with simulation also design a control system that granites a stable walking of Biped Robot. This is done by first reviewing the literature about different walking strategies. During this literature review the 3D-Linear Inverted Pendulum Model appeared to be the most interesting strategy for further research. The idea of the strategy is simple. It models the human as a linear inverted pendulum with massless rods, which represent the legs, and a point mass at the end of the rods representing the total mass of the body. During walking, there is always at least one foot on the ground which can be seen as stance leg. This stance leg is then modeled as an inverted pendulum. The general closed form solution of the dynamics of the linear inverted pendulum are used to design a trajectory for the center of mass (CoM ) for stance leg. In the trajectory generator, the general solution of the 3D-LIPM is used to prescribe a trajectory. for the CoM of the biped robot AK. The trajectory of the swing leg is designed by a cosine velocity profile interpolation function. The joint trajectories are used as the input for a dynamic model of biped robot in SimMechanics. The proposed control system in simulation are carried out to tune the trajectory such that the dynamic model is able to walk balanced and the robustness of the gait was verified by adding of disturbances. For example, the position of the CoM was increased or decreased and the steps were simulated with different ground levels. These simulations showed that the trajectory is relatively robust. Ref. 10, fig. 4.

An essential model for generating walking motions for humanoid robots

The modeling of humanoid robots with many degrees-of-freedom (DoF) can be done via the complete dynamic model. However, the complexity of the model can hide the essential factor of the walking, i.e. the equilibrium of the robot. One alternative is to simplify the model by neglecting some dynamical effects like in the 3D Linear Inverted Pendulum (LIP) model. Nonetheless, the assumption that the ZMP will be at the base of the pendulum is not ensured and the resulting walking gaits can make the Zero Moment Point (ZMP) evolve outside of the convex hull of support when they are replicated on the complete model of any humanoid robot. The objective of this paper is to propose a new model for walking that has the same dimension as the 3D LIP model but considers the complete dynamics of the humanoid. The proposed model is called essential model and it can be written based on the internal states of the robot and possible external information, thereby generating models for different purposes. The main advantage of the essential model is that it allows to generate walking gaits that ensure that the Zero Moment Point (ZMP) is kept in a desired position or it follows a desired path while the gait is performed. Furthermore, impacts of the swing foot with the ground can be considered to compute periodic walking gaits. In order to show the advantages of the proposed model, numerical studies are performed to design periodic walking gaits for the humanoid robot ROMEO.

Biped Robot Gait Planning Based on 3D Linear Inverted Pendulum Model

In order to optimize the biped robot’s gait, the biped robot’s walking motion is simplify to the 3D linear inverted pendulum motion mode. The Center of Mass (CoM) locus is determined from the relationship between CoM and the Zero Moment Point (ZMP) locus. The ZMP locus is planned in advance. Then, the forward gait and lateral gait are simplified as connecting rod structure. Swing leg trajectory using B-spline interpolation. And the stability of the walking process is discussed in conjunction with the ZMP equation. Finally the system simulation is carried out under the given conditions to verify the validity of the proposed planning method.

Humanoid robot gait planning based on 3D linear inverted pendulum model

In order to real-time adjust the humanoid robot gait,a humanoid robot gait generation method was proposed.The robot motion was simplified to the inverted pendulum motion of the three-dimensional linear model,and passed the pre-planned Zero Moment Point(ZMP) trajectory.According to the Center of Mass(CoM) and ZMP relations,the CoM trajectory was obtained.The front side gait and lateral gait were simplified into seven-link and five-link structures,the triangle theorem was used to calculate the angle of each joint,and the ZMP equation was introduced to discuss the stability of the walking process.The system simulation was done according to given conditions and combined with the actual system and its operation conditions were analyzed to verify the validity of the proposed planning method.

Retraction Notice: Novel Control Algorithm for the Foot Placement of a Walking Bipedal Robot

A novel control algorithm for the foot placement of walking bipedal robots is proposed which can output the optimal step time and step location to obtain a desired walking gait from every feasible robot state. The step time and step location are determined by approximating the robot dynamics with the 3D linear inverted pendulum model and analytically solving the constraint equations. Intensive simulation studies are conducted to check the validity of the theoretical results. The results of this study show that the proposed control algorithm can get the system to a desired gait cycle from every feasible state within a finite number of steps.

Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

This two-part paper discusses the analysis and control of legged locomotion in terms of N-step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. In this part (Part 1), we introduce a theoretical framework for assessing N-step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N-step capturability, for any N > 0. Part 2 will show that these results can be used to control a humanoid robot.