Multi-contact bipedal robotic locomotion

Robotica ◽  
2015 ◽  
Vol 35 (5) ◽  
pp. 1072-1106 ◽  
Author(s):  
Huihua Zhao ◽  
Ayonga Hereid ◽  
Wen-loong Ma ◽  
Aaron D. Ames
Keyword(s):  
Optimization Problem ◽  
Human Locomotion ◽  
System Model ◽  
Human Model ◽  
Slip Model ◽  
Robotic Locomotion ◽  
Walking Gait ◽  
Trajectory Reconstruction ◽  
Formal Framework ◽  
Reconstruction Strategy

SUMMARYThis paper presents a formal framework for achieving multi-contact bipedal robotic walking, and realizes this methodology experimentally on two robotic platforms: AMBER2 and Assume The Robot Is A Sphere (ATRIAS). Inspired by the key feature encoded in human walking—multi-contact behavior—this approach begins with the analysis of human locomotion and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. Human-inspired outputs are extracted from reference locomotion data to characterize the human model or the spring-loaded invert pendulum (SLIP) model, and then employed to develop the human-inspired control and an optimization problem that yields stable multi-domain walking. Through a trajectory reconstruction strategy motivated by the process that generates the walking gait, the mathematical constructions are successfully translated to the two physical robots experimentally.

Analytical Method for the Analysis and Simulation of Human Locomotion

1990 ◽  
Vol 112 (4) ◽  
pp. 379-386 ◽  
Author(s):  
F. M. L. Amirouche ◽  
S. K. Ider ◽  
J. Trimble
Keyword(s):  
Equations Of Motion ◽  
Human Locomotion ◽  
Human Model ◽  
Dynamical Equations ◽  
Friction Forces ◽  
Closed Loops ◽  
Walking Gait ◽  
Nonlinear Springs ◽  
External Forces ◽  
Selection Of

An all purpose computer algorithm used in the analysis and simulation of human locomotion is presented. The utility of the program “DYAMUS” stems from its simplicity in defining the initial configuration of the human model through a configuration graph called the “tree-array,” and the handling of individual cases of human locomotion through separate sets of constraints conditions. Both the forward and inverse dynamical problems are presented together with the accommodation of kinematical experimental data. Closed-loops, linear and nonlinear springs and dampers at the joints, friction forces, and other external forces are easily incorporated. The selection of mathematical constraint equations to predict the human behavior during normal walking (gait) is presented. The intention of this paper is to emphasize how the constraints equations play a major role in the simulation of human locomotion once the dynamical equations of motion for a particular model are developed.

Fuzzy Labeled Transition Refinement Tree

2014 ◽  
Vol 6 (3) ◽  
pp. 1-31 ◽  
Author(s):  
Sofia Kouah ◽  
Djamel-Eddine Saidouni
Keyword(s):  
Dynamic Systems ◽  
Transition System ◽  
System Model ◽  
Design Parameters ◽  
Concurrent Design ◽  
Incremental Development ◽  
Action Refinement ◽  
Formal Framework ◽  
Labeled Transition System ◽  
Multi Agents

This paper aims to provide a formal framework that supports an incremental development of dynamic systems such as multi agents systems (MAS). We propose a fuzzy labeled transition system model (FLTS for short). FLTS allows a concise action refinement representation and deals with incomplete information through its fuzziness representation. Afterward, based on FLTS model, we propose a refinement model called fuzzy labeled transition refinement tree (FLTRT for short). The FLTRT structure serves as a tree of potential concurrent design trajectories of the system. Also, we introduce bisimulation relations for both models in order to identify equivalent design trajectories, which could be assessed with respect to relevant design parameters.

Towards Robustly Stable Musculo-Skeletal Simulation of Human Gait: Merging Lumped and Component-Based Modeling Approaches

2012 ◽  
Author(s):  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Dynamic Models ◽  
Sagittal Plane ◽  
Center Of Mass ◽  
Human Model ◽  
Whole Body ◽  
Human Gait ◽  
Slip Model ◽  
Spring Loaded Inverted Pendulum ◽  
Low Dimensional

The objective of work presented in this paper is to increase the center-of-mass stability of human walking and running in musculo-skeletal simulation. The approach taken is to approximate the whole-body dynamics of the low-dimensional Spring-Loaded Inverted Pendulum (SLIP) model of locomotion in the OpenSim environment using existing OpenSim tools. To more directly relate low-dimensional dynamic models to human simulation, an existing OpenSim human model is first modified to more closely represent bilateral above-knee amputee locomotion with passive prostheses. To increase stability further beyond the energy-conserving SLIP model, an OpenSim model based upon the Clock-Torqued Spring-Loaded-Inverted-Pendulum (CT-SLIP) model of locomotion is also created. The result of this work is that a multi-body musculo-skeletal simulation in Open-Sim can approximate the whole-body sagittal-plane dynamics of the passive SLIP model. By adding a plugin controller to the OpenSim environment, the Clock-Torqued-SLIP dynamics can be approximated in OpenSim. To change between walking and running, only one parameter representing the preferred period of a stride is changed. The result is a robustly stable simulation of the center-of-mass locomotion for both walking and running that could serve as a first step toward increasingly anatomically accurate and robustly stable musculo-skeletal simulations.

9. Models for Generalized Location Systems

2007 ◽  
Vol 37 (1) ◽  
pp. 283-348 ◽  
Author(s):  
Carter T. Butts
Keyword(s):  
Exponential Family ◽  
Social Systems ◽  
System Model ◽  
Social Phenomena ◽  
Location System ◽  
Formal Framework ◽  
Model Complex ◽  
Exponential Family Of Distributions ◽  
Residential Settlement ◽  
Family Of Distributions

A formal framework is introduced for a general class of assignment systems that can be used to characterize a range of social phenomena. An exponential family of distributions is developed for modeling such systems, allowing for the incorporation of both attributional and relational covariates. Methods are shown for simulation and inference using the location system model. Two illustrative applications (occupational stratification and residential settlement patterns) are presented, and simulation is employed to show the behavior of the location system model in each case; a third application, involving occupancy of positions within an organization, is used to demonstrate inference for the location system. By leveraging established results in the fields of social network analysis, spatial statistics, and statistical mechanics, it is argued that sociologists can model complex social systems without sacrificing inferential tractability.

Optimization-Based Digital Human Dynamics: Santos™ Walking Backwards

2007 ◽  
Author(s):  
Hyun Jung Kwon ◽  
Yujiang Xiang ◽  
Salam Rahmatalla ◽  
R. Timothy Marler ◽  
Karim Abdel-Malek ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Joint Angle ◽  
Spline Interpolation ◽  
Performance Measure ◽  
Degree Of Freedom ◽  
Human Model ◽  
Entire Body ◽  
Joint Torques ◽  
Digital Human

An objective of this study is to simulate the backward walking motion of a full-body digital human model. The model consists of 55 degree of freedom – 6 degrees of freedom for global translation and rotation and 49 degrees of freedom representing the kinematics of the entire body. The resultant action of all the muscles at a joint is represented by the torque for each degree of freedom. The torques and angles at a joint are treated as unknowns in the optimization problem. The B-spline interpolation is used to represent the time histories of the joint angles and the well-established robotics formulation of the Denavit-Hartenberg method is used for kinematics analysis of the mechanical system. The recursive Lagrangian formulation is used to develop the equations of motion, and was chosen because of its known computational efficiency. The backwards walking problem is formulated as a nonlinear optimization problem. The control points of the B-splines for the joint angle profiles are treated as the design variables. For the performance measure, total dynamic effort that is represented as the integral of the sum of the squares of all the joint torques is minimized using a sequential quadratic programming algorithm. The solution is simulated in the Santos™ environment. Results of the optimization problem are the torque and joint angle profiles. The torques at the key joints and the ground reaction forces are compared to those for the forward walk in order to study the differences between the two walking patterns. Simulation results are approximately validated with the experimental data which is motion captured in the VSR Lab at the University of Iowa.

Optimization-Based Prediction of Aiming and Kneeling Military Tasks Performed by a Soldier

2012 ◽  
Author(s):  
Mahdiar Hariri ◽  
Jasbir Arora ◽  
Karim Abdel-Malek
Keyword(s):  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Human Model ◽  
Ground Reaction Forces ◽  
Optimization Approach ◽  
Ground Contact ◽  
Digital Human Model ◽  
Reaction Forces ◽  
Digital Human ◽  
The Given

The objective of this study is to predict the “Aiming While Standing” and “Aiming While Kneeling” motion tasks for a soldier (human) using a full-body, three dimensional digital human model. The digital human is modeled as a 55 degree of freedom branched mechanism. Six degrees of freedom specify the global position and orientation of the coordinate frame attached to the pelvis of the digital human and 49 degrees of freedom represent the revolute joints which model the human joints and determine the kinematics of the entire digital human. Motion is generated by a multi-objective optimization approach minimizing the mechanical energy and joint discomfort simultaneously. A sequential quadratic programming (SQP) algorithm in SNOPT is used to solve the nonlinear optimization problem. The optimization problem is subject to constraints which represent the limitations of the environment, the digital human model and the motion task. Design variables are the joint angle profiles. All the forces, inertial, gravitational as well as external, are known, except the ground reaction forces. The feasibility of the generation of that arbitrary motion by using the given ground contact areas is ensured by using the well known Zero Moment Point (ZMP) constraint. During the kneeling motion, different parts of the body come in contact and lose contact with the ground which is modeled using a general approach. The ground reaction force on each transient ground contact area is determined using the equations of motion. It is assumed that enough friction exists that allow the human to generate reaction forces as determined by the ZMP constraint. Using these ground reaction forces, the required torques at all joints are calculated by the recursive Lagrangian formulation. Using the given method, we can predict realistic motions for the “Aiming While Standing” and “Aiming While Kneeling” tasks. The optimization approach is able to very well predict the “Natural Point of Aim” which is a well known concept for soldiers. In other words, the approach is able to predict the most comfortable final orientation of the feet on the ground for engaging a specific target. We also predict cases where the orientation of the soldier’s feet are enforced. Many virtual experiments have been conducted by changing the target location in the 3D space, changing the anthropometry of the soldier, adding armor to different joints, changing the variable parameters of the rifle, adding backpack and using different weapons.

scholarly journals A Model-Based Approach to Optimizing Partition Scheduling of Integrated Modular Avionics Systems

Electronics ◽  
2020 ◽  
Vol 9 (8) ◽  
pp. 1281
Author(s):  
Pujie Han ◽  
Zhengjun Zhai ◽  
Lei Zhang
Keyword(s):  
Analytical Methods ◽  
Optimization Problem ◽  
Timed Automata ◽  
System Model ◽  
Parallel Genetic Algorithm ◽  
Statistical Model Checking ◽  
Convex Optimization Problem ◽  
Temporal Partitioning ◽  
Model Based ◽  
Integrated Modular Avionics

The architecture of Integrated Modular Avionics (IMA) provides airborne software with a robust temporal partitioning mechanism, which achieves the reliable fault containment between avionics applications. However, the partition scheduling of an IMA system is a complex nonlinear non-convex optimization problem, making it difficult to solve the optimal temporal allocation for partitions using traditional analytical methods. This paper presents a model-based approach to optimizing the partition scheduling of IMA systems, whose temporal behavior is modeled as a network of timed automata. Given a system model, the optimizer employs a parallel genetic algorithm to search for the optimal partition resource parameters with respect to minimum processor occupancy. For each promising parameter combination, the schedulability constraints and processor occupancy of the system are precisely evaluated by Classical and Statistical Model Checking (i.e., CMC and SMC), respectively. We also apply SMC hypothesis testing to the fast falsification of non-schedulable solutions, thereby speeding up the schedulability verification based on CMC. Two case studies demonstrate that our proposed approach outperforms classical analytical methods on the processor occupancy of typical IMA systems.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

2011 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Human Locomotion ◽  
Whole Body ◽  
Slip Model ◽  
Mass Model ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum ◽  
Passive Model

The concept of passive dynamic walking and running [5] has demonstrated that a simple passive model can represent the dynamics of whole-body human locomotion. Since then, many passive models were developed and studied: [3,1,2,11]. The later developed Spring-Loaded Inverted Pendulum (SLIP) [1, 4, 11, 2] exhibits stable center of mass (CoM) motions just by resetting the landing angle at each touch down. Also, compared to SLIP, a SLIP-like model with simple flight leg control is better at resisting perturbations of the angle of velocity but not the magnitude [11, 2, 7]. Energy conserving models explain much about whole-body locomotion. Recently, there has been investigations of modified spring-mass models capable of greater stability, like that of animals and robots [9, 10, 8, 12]. Inspired by RHex [6], the Clock-Torqued Spring-Loaded Inverted Pendulum (CT-SLIP) model [9] was developed, and has been used to explain the robust stability of animal locomotion [12]. Here we present a model (mechanism) simpler than CT-SLIP called Forced-Damped SLIP (FD-SLIP) that can attain full asymptotically stability of the CoM during locomotion, and is capable of both walking and running motions. The FD-SLIP model, having fewer parameters, is more accessible and easier to analyze for the exploration and discovery of principles of legged locomotion.

scholarly journals Multi-task offloading scheme for UAV-Enabled Fog Computing networks

2020 ◽  
Author(s):  
Xujie LI ◽  
Lingjie Zhou ◽  
Ying Sun
Keyword(s):  
Optimization Problem ◽  
Scheduling Algorithm ◽  
Fog Computing ◽  
System Model ◽  
Total Delay ◽  
Single Node ◽  
Fireworks Algorithm ◽  
Multiple Tasks ◽  
Random Algorithm ◽  
Task Offloading

Abstract In UAV-enabled fog Computing networks, how to efficiently offload multiple tasks to the computing nodes is a challenge combinatorial optimization problem. In this paper, in order to optimize the total delay for the UVA-Enabled Fog Computing networks, a simple scheduling algorithm and a multi-task offloading scheme based on fireworks algorithm (FWA) are proposed. First, the system model of multiple tasks offloading in UVA-Enabled fog computing networks is described in detail. Then, a simple scheduling algorithm is proposed to optimize the delay of the tasks allocated to a single node. Based on the scheduling algorithm, a multi-task offloading scheme for all tasks and all computing nodes is presented. Finally, simulation results show that the performance of proposed scheduling algorithm and offloading strategy outperform than that of genetic algorithm and random algorithm. This result can provide an effective optimization for multi-task offloading in UVA-Enabled Fog Computing networks.

Sign in / Sign up

Export Citation Format

Share Document