scholarly journals Spring-loaded inverted pendulum goes through two contraction-extension cycles during the single-support phase of walking

Biology Open ◽  
2019 ◽  
Vol 8 (6) ◽  
pp. bio043695 ◽  
Author(s):  
Gabriel Antoniak ◽  
Tirthabir Biswas ◽  
Nelson Cortes ◽  
Siddhartha Sikdar ◽  
Chanwoo Chun ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Spring Loaded Inverted Pendulum ◽  
Single Support Phase ◽  
Support Phase

A Simple Spring-Loaded Inverted Pendulum (SLIP) Model of a Bio-Inspired Quadrupedal Robot Over Compliant Terrains

2018 ◽  
Author(s):  
Hasti Hayati ◽  
Paul Walker ◽  
Terry Brown ◽  
Paul Kennedy ◽  
David Eager
Keyword(s):  
Degrees Of Freedom ◽  
Inverted Pendulum ◽  
Viscoelastic Behavior ◽  
Slip Model ◽  
Runge Kutta Method ◽  
Synthetic Rubber ◽  
Spring Loaded Inverted Pendulum ◽  
Single Support Phase ◽  
The Impact ◽  
Three Degrees Of Freedom

To study the impact of compliant terrains on the biomechanics of rapid legged movements, a well-known spring loaded inverted pendulum (SLIP) model is deployed. The model is a three-degrees-of-freedom system (3 DOF), inspired by galloping greyhounds competing in a racing condition. A single support phase of hind-leg stance in a galloping gait is taken into consideration due to its primary function in powering the greyhounds locomotion and higher rate of musculoskeletal injuries. To obtain and solve the nonlinear second-order differential equation of motions, the Lagrangian method and MATLABb R2017b (ode45 solver), which is based on the Runge-Kutta method, has been used, respectively. To get the viscoelastic behavior of compliant terrains, a Clegg hammer test was developed and performed five times on each sample. The effective spring and damping coefficients of each sample were then determined from the hysteresis curves. The results showed that galloping on the synthetic rubber requires more muscle force compared with wet sand. However, according to the Clegg hammer test, wet sand had a higher impact force than synthetic rubber which can be a risk factor for bone fracture, particularly hock fracture, in greyhounds. The results reported in this paper are not only useful for identifying optimum terrain properties and injury thresholds of an athletic track, but also can be used to design control methods and shock impedances for legged robots performing on compliant terrains.

scholarly journals Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics

2012 ◽  
Vol 9 (4) ◽  
pp. 457-467 ◽  
Author(s):  
Liandong Zhang ◽  
Changjiu Zhou
Keyword(s):  
Kinetic Energy ◽  
Energy Saving ◽  
Humanoid Robot ◽  
Inverted Pendulum ◽  
Planning Method ◽  
Riemannian Surface ◽  
Gait Planning ◽  
Optimal Gait ◽  
Single Support Phase ◽  
Support Phase

A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP) are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.

Realization of foot rotation by breaking the kinematic contact constraint

Robotica ◽  
2014 ◽  
Vol 34 (5) ◽  
pp. 1059-1070
Author(s):  
Xuechao Chen ◽  
Qiang Huang ◽  
Zhangguo Yu ◽  
Jing Li ◽  
Gan Ma ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Walking Speed ◽  
Inverse Dynamics ◽  
Inverted Pendulum Model ◽  
Contact Constraint ◽  
Pendulum Model ◽  
Single Support Phase ◽  
Support Phase

SUMMARYPrevious research has revealed that foot rotation of the supporting foot in a single support phase could increase walking speed. This paper presents a method for force-controlled bipeds to realize foot rotation by breaking the kinematic contact constraint between the supporting foot and the ground. An inverse dynamics controller is proposed to make the biped model controllable even when the constraint is broken. In addition, a linear inverted pendulum model is extended to make its ZMP adjustable so that the ZMP can be predefined as required. When the planned ZMP is in the toe, the kinematic contact constraint will be broken and foot rotation can be achieved. A walking simulation demonstrates the effectiveness of the proposed method.

Tracking a joint path for the walk of an underactuated biped

Robotica ◽  
2004 ◽  
Vol 22 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Christine Chevallereau ◽  
Alexander Formal'sky ◽  
Dalila Djoudi
Keyword(s):  
Inverted Pendulum ◽  
Temporal Evolution ◽  
Biped Robot ◽  
Degree Of Freedom ◽  
Control Law ◽  
Reference Trajectory ◽  
Geometric Evolution ◽  
Cyclic Motion ◽  
Single Support Phase ◽  
Support Phase

This paper presents a control law for the tracking of a cyclic reference path by an under-actuated biped robot. The robot studied is a five-link planar biped. The degree of under-actuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. To achieve this objective, we consider a parametrized control. When a joint path is given, a five degree of freedom biped in single support becomes similar to a one degree of freedom inverted pendulum. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple analytical conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced. These conditions are defined on the reference trajectory path. The analytical considerations are illustrated with some simulation results.

A Simple Analytical Tool for Legged Robot Design

2012 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Analytical Solutions ◽  
Inverted Pendulum ◽  
Legged Locomotion ◽  
Robot Design ◽  
Slip Model ◽  
Legged Robot ◽  
Biologically Relevant ◽  
Analytical Approximations ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

Comparison of Hip Torque and Radial Forcing Effects on Locomotion Stability and Energetics

2013 ◽  
Author(s):  
Zhuohua Shen ◽  
Peter Larson ◽  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Legged Robots ◽  
Asymptotically Stable ◽  
Alternative Strategies ◽  
Advantages And Disadvantages ◽  
Potential Alternative ◽  
Spring Loaded Inverted Pendulum

Hip torque and radial forcing along the leg are two common actuation methods for legged robots. However, hip torque and radial forcing have not been compared as potential alternative strategies of actuation. The respective advantages and disadvantages of hip torque and radial forcing are not well known. In this paper, we compare hip torque and radial forcing actuation through the simulation of two models: a Rotary-forced Spring-Loaded Inverted Pendulum and a Radially Forced Spring-Loaded Inverted Pendulum. Both actuation methods can produce fully asymptotically stable locomotion. Interestingly, it is found that they improve locomotion stability in different ways: hip torque first destabilizes locomotion when initially introduced but greatly stabilizes locomotion when it keeps increasing; radial forcing always stabilizes locomotion, but in a moderate way.

Effect of Heel to Toe Walking on Time Optimal Walking of a Biped During Single Support Phase

2014 ◽  
Author(s):  
Tara Farizeh ◽  
Mohammad Jafar Sadigh
Keyword(s):  
Whole Body ◽  
Maximum Speed ◽  
Flat Foot ◽  
Double Support ◽  
Time Optimal ◽  
Foot Model ◽  
Two Phases ◽  
Single Support Phase ◽  
Toe Walking ◽  
Support Phase

Dynamic modeling of a biped has gained lots of attention during past few decades. While stability and energy consumption were among the first issues which were considered by researchers, nowadays achieving maximum speed and improving pattern of motion to reach that speed are the important targets in this field. Walking model of bipeds usually includes two phases, single support phase (SSP), in which only the stance foot is in contact with the ground while the opposite leg is swinging; and double support phase (DSP) in which the swing leg is in contact with the ground in addition to the rear foot. It is common in the simplified model of walking to assume the stance leg foot, flat during the entire SSP; but one may know that for human walking, there is also a sub-phase during SSP in which the heel of stance foot leaves the ground while the whole body is supported by toe link. Actually in this sub phase the stance leg foot rotates around the toe joint. This paper is trying to study the effect of toe-link and heel to toe walking model on dynamic and specially speed of walking compare to flat foot model.

scholarly journals Walking Gait of a Biped with a Wearable Walking Assist Device

2015 ◽  
Vol 12 (04) ◽  
pp. 1550018 ◽  
Author(s):  
Yannick Aoustin
Keyword(s):  
Dynamic Model ◽  
Unique Solution ◽  
Energy Cost ◽  
Assist Device ◽  
Double Support ◽  
Kinematic Chains ◽  
Walking Gait ◽  
Time Period ◽  
Single Support Phase ◽  
Support Phase

A ballistic walking gait is designed for a planar biped equipped with a wearable walking assist device. The biped is a seven-link planar biped with two legs, two feet, and a trunk. The wearable walking assist device is composed of a bodyweight support, two upper legs, two lower legs, and two shoes. The dynamic model of the biped with its walking assist device, containing two closed kinematic chains, is calculated by virtually cutting each of both loops at one of their point. In the single support phase, the biped with its assist device moves due to the existence of a momentum, produced mechanically, without applying active torques in the inter-link joints. The biped and this assist device are controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the six inter-link joints of the biped and in several inter-link joints of the wearable walking assist device. The following distributions of impulsive torques, in the knees or the ankles, hips and knees, hips and ankles, or knees and ankles and the fully assist device, are compared with the case of no assistance for the biped. Each time, an infinity of solutions exists to find the impulsive torques. An energy cost functional defined from these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, the assistance of the hips is a good compromise to help the biped.

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