Dynamics Synchronization of the Running of Planar Biped Robots With SLIP Model in Stance Phase

2014 ◽  
Author(s):  
Behnam Dadashzadeh ◽  
Mohammad Mahjoob Jahromi
Keyword(s):  
Stance Phase ◽  
Lagrange Equation ◽  
Center Of Mass ◽  
Biped Robot ◽  
Control Law ◽  
Slip Model ◽  
Initial State ◽  
Biped Robots ◽  
Model Dynamics ◽  
Vast Literature

In this work a control law is derived to synchronize dynamics of multibody biped robots and the spring loaded inverted pendulum (SLIP) model in stance phase of running. The goal is to use the vast literature on the SLIP model dynamics for the control of real multibody robots. Three kneed biped robot models are considered in this work: with springs parallel to motors, with springs series to motors, and without springs. Dynamic equations of the multibody biped models are derived using Lagrange equation and then the applicability of the derived control law to these models are investigated using simulation. The initial state of the multibody robot is found such that its center of mass (CoM) has the same initial condition as SLIP model. Then the trajectory of its CoM is compared to SLIP model. Also motor torque profiles are compared for the models with and without springs and also for the motors with and without rotor inertias. The results show that the effect of rotor inertia is a big challenge in implementing fast biped running on real robots.

scholarly journals Control of a Biped Robot by Total Rate of Angular Momentum Using the Task Function Approach

2005 ◽  
Vol 2 (2) ◽  
pp. 111-116
Author(s):  
J. A. Rojas-Estrada ◽  
J. Marot ◽  
P. Sardain ◽  
G. Bessonnet
Keyword(s):  
Angular Momentum ◽  
Control Problem ◽  
Degrees Of Freedom ◽  
Biped Robot ◽  
Function Approach ◽  
Control Law ◽  
Total Rate ◽  
Biped Robots ◽  
Formal Problem

In this work we address the control problem of biped robots by using the task function approach. A problem arrives when one of the feet is in contact with the ground, which presents imperfections. There is then the possibility that the biped robot undergoes a fall. It is difficult to track any trajectory due to the presence of unevenness on the ground. What we propose is to use the task function approach combined with the application of the total rate of angular momentum to obtain a control law for the ankle. By this technique, the tracking becomes more smooth and the balance is assured. The control law proposed allows the upper part of the robot to be controlled independently since only the ankle actuators are concerned. We enounce the formal problem and present some simulations with real parameters of a 21 degrees of freedom biped robot.

Robust backstepping control of an underactuated one-legged hopping robot in stance phase

Robotica ◽  
2009 ◽  
Vol 28 (4) ◽  
pp. 583-596 ◽  
Author(s):  
Guangping He ◽  
Zhiyong Geng
Keyword(s):  
Stance Phase ◽  
Control Method ◽  
Center Of Mass ◽  
Backstepping Control ◽  
Model Systems ◽  
Slip Model ◽  
Nonholonomic Mechanical Systems ◽  
Model Based ◽  
Hopping Robot ◽  
Dynamics And Control

SUMMARYExponentially stabilizing a non-Spring Loaded Inverted Pendulum (SLIP) model-based one-legged hopping robot in stance phase is studied. Differing from the SLIP model systems, the hopping robot with non-SLIP model considered in this paper does not restrict the center of mass of the robot coinciding to the hip joint. A specific underactuated one-legged hopping robot with two actuated arms are selected to investigate the dynamics and control problem. It is shown that the system holds the essential nonlinear prosperities of general systems and belongs to a class of second-order nonholonomic mechanical systems, which cannot be stabilized by any smooth time-invariant state feedback. By using a coordinates transform based on the so-called normalized momentum, a robust backstepping control method is presented for the specific hopping robot system. Both theoretical analysis and numerical simulations show that the robust backstepping controller can stabilize the underactuated one-legged hopping robot to its balance configuration as well as a periodic motion trajectory near to the balance configuration. These results are significative for designing a new non-SLIP model based hopping robot systems with more biological characteristics.

Sliding Mode Control of Underactuated Biped Robots

2005 ◽  
Author(s):  
Mehdi Nikkhah ◽  
Hashem Ashrafiuon ◽  
Farbod Fahimi
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Biped Robot ◽  
Control Law ◽  
Robust Tracking Control ◽  
Biped Robots ◽  
Control Approach ◽  
Double Support ◽  
Mode Control ◽  
The Impact

This paper presents a robust tracking control algorithm for underactuated biped robots. The biped considered in this work is modeled as a five-link planar robot with four actuators located at hip and knee joints to control the joint angles. The control law is defined based on the sliding mode control approach. The objective of the controller is to generate stable walking based on predefined desired trajectories. The planning of the trajectory in swing phase is discussed while the double support phase is considered to be instantaneous and the impact of the swing leg with the ground is modeled as rigid body contact. In order to formulate the sliding control law, we define four first-order sliding surfaces, based on the number of actuators, as a linear combination of tracking joint positions and velocities. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces. The surface parameters are then selected to ensure the stability of the surfaces leading to an asymptotically stable control law. Numerical simulation is presented for tracking a multi-step walk of a biped robot.

scholarly journals Trajectory Planning of Flexible Walking for Biped Robots Using Linear Inverted Pendulum Model and Linear Pendulum Model

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1082
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Trajectory Planning ◽  
Inverted Pendulum ◽  
Negative Impact ◽  
Center Of Mass ◽  
Biped Robot ◽  
Biped Robots ◽  
Double Support ◽  
Inverted Pendulum Model ◽  
Pendulum Model ◽  
Support Phase

Linear inverted pendulum model (LIPM) is an effective and widely used simplified model for biped robots. However, LIPM includes only the single support phase (SSP) and ignores the double support phase (DSP). In this situation, the acceleration of the center of mass (CoM) is discontinuous at the moment of leg exchange, leading to a negative impact on walking stability. If the DSP is added to the walking cycle, the acceleration of the CoM will be smoother and the walking stability of the biped will be improved. In this paper, a linear pendulum model (LPM) for the DSP is proposed, which is similar to LIPM for the SSP. LPM has similar characteristics to LIPM. The dynamic equation of LPM is also linear, and its analytical solution can be obtained. This study also proposes different trajectory-planning methods for different situations, such as periodic walking, adjusting walking speed, disturbed state recovery, and walking terrain-blind. These methods have less computation and can plan trajectory in real time. Simulation results verify the effectiveness of proposed methods and that the biped robot can walk stably and flexibly when combining LIPM and LPM.

scholarly journals Vertical Jumping for Legged Robot Based on Quadratic Programming

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3679
Author(s):  
Dingkui Tian ◽  
Junyao Gao ◽  
Xuanyang Shi ◽  
Yizhou Lu ◽  
Chuzhao Liu
Keyword(s):  
Quadratic Programming ◽  
Stance Phase ◽  
Center Of Mass ◽  
Maximum Error ◽  
Legged Robot ◽  
Flight Phase ◽  
Programming Framework ◽  
Vertical Jumping ◽  
Control Schemes ◽  
And Control

The highly dynamic legged jumping motion is a challenging research topic because of the lack of established control schemes that handle over-constrained control objectives well in the stance phase, which are coupled and affect each other, and control robot’s posture in the flight phase, in which the robot is underactuated owing to the foot leaving the ground. This paper introduces an approach of realizing the cyclic vertical jumping motion of a planar simplified legged robot that formulates the jump problem within a quadratic-programming (QP)-based framework. Unlike prior works, which have added different weights in front of control tasks to express the relative hierarchy of tasks, in our framework, the hierarchical quadratic programming (HQP) control strategy is used to guarantee the strict prioritization of the center of mass (CoM) in the stance phase while split dynamic equations are incorporated into the unified quadratic-programming framework to restrict the robot’s posture to be near a desired constant value in the flight phase. The controller is tested in two simulation environments with and without the flight phase controller, the results validate the flight phase controller, with the HQP controller having a maximum error of the CoM in the x direction and y direction of 0.47 and 0.82 cm and thus enabling the strict prioritization of the CoM.

scholarly journals Effects of Torso Pitch Motion on Energy Efficiency of Biped Robot Walking

2021 ◽  
Vol 11 (5) ◽  
pp. 2342
Author(s):  
Long Li ◽  
Zhongqu Xie ◽  
Xiang Luo ◽  
Juanjuan Li
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Biped Robot ◽  
Gait Pattern ◽  
Pattern Generation ◽  
Biped Robots ◽  
Pitch Motion ◽  
Double Support ◽  
Gait Parameters ◽  
Support Phase

Gait pattern generation has an important influence on the walking quality of biped robots. In most gait pattern generation methods, it is usually assumed that the torso keeps vertical during walking. It is very intuitive and simple. However, it may not be the most efficient. In this paper, we propose a gait pattern with torso pitch motion (TPM) during walking. We also present a gait pattern with torso keeping vertical (TKV) to study the effects of TPM on energy efficiency of biped robots. We define the cyclic gait of a five-link biped robot with several gait parameters. The gait parameters are determined by optimization. The optimization criterion is chosen to minimize the energy consumption per unit distance of the biped robot. Under this criterion, the optimal gait performances of TPM and TKV are compared over different step lengths and different gait periods. It is observed that (1) TPM saves more than 12% energy on average compared with TKV, and the main factor of energy-saving in TPM is the reduction of energy consumption of the swing knee in the double support phase and (2) the overall trend of torso motion is leaning forward in double support phase and leaning backward in single support phase, and the amplitude of the torso pitch motion increases as gait period or step length increases.

scholarly journals Optimal Control Based on the Polynomial Least Squares Method

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Constantin Bota ◽  
Bogdan Cǎruntu ◽  
Mǎdǎlina Sofia Pașca ◽  
Marioara Lǎpǎdat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variational Problem ◽  
Least Squares ◽  
Least Squares Method ◽  
Lagrange Equation ◽  
Control Law

In this paper an approach for computing an optimal control law based on the Polynomial Least Squares Method (PLSM) is presented. The initial optimal control problem is reformulated as a variational problem whose corresponding Euler-Lagrange equation is solved by using PLSM. A couple of examples emphasize the accuracy of the method.

Simple Leg Placement Strategy for a One Legged Running Model

2012 ◽  
Author(s):  
Timothy Sullivan ◽  
Justin Seipel
Keyword(s):  
Stance Phase ◽  
Energy State ◽  
Center Of Mass ◽  
Mass Movement ◽  
Legged Locomotion ◽  
Energy Conserving ◽  
Lower Torque ◽  
The Stability ◽  
Time Required ◽  
Torque Values

The Spring Loaded Inverted Pendulum (SLIP) model was developed to describe center of mass movement patterns observed in animals, using only a springy leg and a point mass. However, SLIP is energy conserving and does not accurately represent any biological or robotic system. Still, this model is often used as a foundation for the investigation of improved legged locomotion models. One such model called Torque Damped SLIP (TD-SLIP) utilizes two additional parameters, a time dependent torque and dampening to drastically increase the stability. Forced Damped SLIP (FD-SLIP), a predecessor of TD-SLIP, has shown that this model can be further simplified by using a constant torque, instead of a time varying torque, while still maintaining stability. Using FD-SLIP as a base, this paper explores a leg placement strategy using a simple PI controller. The controller takes advantage of the fact that the energy state of FD-SLIP is symmetric entering and leaving the stance phase during steady state conditions. During the flight phase, the touch down leg angle is adjusted so that the energy dissipation due to dampening, during the stance phase, compensates for any imbalance of energy. This controller approximately doubles the region of stability when subjected to velocity perturbations at touchdown, enables the model to operate at considerably lower torque values, and drastically reduces the time required to recover from a perturbation, while using less energy. Finally, the leg placement strategy used effectively imitates the natural human response to velocity perturbations while running.

scholarly journals Comparative stable walking gait optimization for small-sized biped robot using meta-heuristic optimization algorithms

2018 ◽  
Vol 40 (4) ◽  
pp. 407-424
Author(s):  
Tran Thien Huan ◽  
Ho Pham Huy Anh
Keyword(s):  
Humanoid Robot ◽  
Differential Evolution Algorithm ◽  
Biped Robot ◽  
The Novel ◽  
Biped Robots ◽  
Walking Gait ◽  
Gait Parameters ◽  
Lift Height ◽  
Evolution Algorithm ◽  
Gait Optimization

This paper proposes a new way to optimize the biped walking gait design for biped robots that permits stable and robust stepping with pre-set foot lifting magnitude. The new meta-heuristic CFO-Central Force Optimization algorithm is initiatively applied to optimize the biped gait parameters as to ensure to keep biped robot walking robustly and steadily. The efficiency of the proposed method is compared with the GA-Genetic Algorithm, PSO-Particle Swarm Optimization and Modified Differential Evolution algorithm (MDE). The simulated and experimental results carried on the prototype small-sized humanoid robot demonstrate that the novel meta-heuristic CFO algorithm offers an efficient and stable walking gait for biped robots with respect to a pre-set of foot-lift height value.

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