3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.Comment: Journal paper under revie

Fast walking with rhythmic sway of torso in a 2D passive ankle walker

There is a category of biped robots that are equipped with passive or un-actuated ankles, which we call Passive-Ankle Walkers (PAWs). Lack of actuation at ankles is a disadvantage in the fast walking of PAWs. We started this study with an intuitive hypothesis that rhythmic sway of torso may enable faster walking in PAWs. To test this hypothesis, firstly, we optimized the rhythmic sway of torso of a simulated PAW model for fast walking speed, and analyzed the robustness of the optimal trajectories. Then we implemented the optimal trajectories on a real robot. Both the simulation analysis and the experimental results indicated that optimized torso-swaying can greatly increase the walking speed by 40%. By analyzing the walking patterns of the simulated model and the real robot, we identified the reason for the faster walking with swaying-torso: The rhythmic sway of torso enables the robot to walk with a relatively large step-length while still keeninu a hizh sten-frenuencv

Humanoid Robot Soccer Locomotion and Kick Dynamics: Open Loop Walking, Kicking and Morphing into Special Motions on the Nao Robot

Striker speed and accuracy in the RoboCup (SPL) international robot soccer league is becoming increasingly important as the level of play rises. Competition around the ball is now decided in a matter of seconds. Therefore, eliminating any wasted actions or motions is crucial when attempting to kick the ball. It is common to see a discontinuity between walking and kicking where a robot will return to an initial pose in preparation for the kick action. In this thesis we explore the removal of this behaviour by developing a transition gait that morphs the walk directly into the kick back swing pose. The solution presented here is targeted towards the use of the Aldebaran walk for the Nao robot. The solution we develop involves the design of a central pattern generator to allow for controlled steps with realtime accuracy, and a phase locked loop method to synchronise with the Aldebaran walk so that precise step length control can be activated when required. An open loop trajectory mapping approach is taken to the walk that is stabilized statically through the use of a phase varying joint holding torque technique. We also examine the basic princples of open loop walking, focussing on the commonly overlooked frontal plane motion. The act of kicking itself is explored both analytically and empirically, and solutions are provided that are versatile and powerful. Included as an appendix, the broader matter of striker behaviour (process of goal scoring) is reviewed and we present a velocity control algorithm that is very accurate and efficient in terms of speed of execution

Desenvolvimento de comportamentos para robô humanoide

Mestrado em Engenharia de Computadores e TelemáticaHumanoid robotics is an area of active research. Robots with human body are better suited to execute tasks in environments designed for humans. Moreover, people feel more comfortable interacting with robots that have a human appearance. RoboCup encourages robotic research by promoting robotic competitions. One of these competitions is the Standard Platform League (SPL) in which humanoid robots play soccer. The robot used is the Nao robot, created by Aldebaran Robotics. The di erence between the teams that compete in this league is the software that controls the robots. Another league promoted by RoboCup is the 3D Soccer Simulation League (3DSSL). In this league the soccer game is played in a computer simulation. The robot model used is also the one of the Nao robot. However, there are a few di erences in the dimensions and it has one more Degree of Freedom (DoF) than the real robot. Moreover, the simulator cannot reproduce reality with precision. Both these leagues are relevant for this thesis, since they use the same robot model. The objective of this thesis is to develop behaviors for these leagues, taking advantage of the previous work developed for the 3DSSL. These behaviors include the basic movements needed to play soccer, namely: walking, kicking the ball, and getting up after a fall. This thesis presents the architecture of the agent developed for the SPL, which is similar to the architecture of the FC Portugal team agent from the 3DSSL, hence allowing to port code between both leagues easily. It was also developed an interface that allows to control a leg in a more intuitive way. It calculates the joint angles of the leg, using the following parameters: three angles between the torso and the line connecting hip and ankle; two angles between the foot and the perpendicular of the torso; and the distance between the hip and the ankle. It was also developed an algorithm to calculate the three joint angles of the hip that produce the desired vertical rotation, since the Nao robot does not have a vertical joint in the hip. This thesis presents also the behaviors developed for the SPL, some of them based on the existing behaviors from the 3DSSL. It is presented a behavior that allows to create robot movements by de ning a sequence of poses, an open-loop omnidirectional walking algorithm, and a walk optimized in the simulator adapted to the real robot. Feedback was added to this last walk to make it more robust against external disturbances. Using the behaviors presented in this thesis, the robot achieved a forward velocity of 16 cm/s, a lateral velocity of 6 cm/s, and rotated at 40 deg/s. The work developed in this thesis allows to have an agent to control the Nao robot and execute the basic low level behaviors for competing in the SPL. Moreover, the similarities between the architecture of the agent for the SPL with that of the agent from the 3DSSL allow to use the same high level behaviors in both leagues.A robótica humanoide é uma área em ativo desenvolvimento. Os robôs com forma humana estão melhor adaptados para executarem tarefas em ambientes desenhados para humanos. Além disso, as pessoas sentem-se mais confortáveis quando interagem com robôs que tenham aparência humana. O RoboCup incentiva a investigação na área da robótica através da realização de competições de robótica. Uma destas competições é a Standard Platform League (SPL) na qual robôs humanoides jogam futebol. O robô usado é o robô Nao, criado pela Aldebaran Robotics. A diferença entre as equipas que competem nesta liga está no software que controla os robôs. Outra liga presente no RoboCup é a 3D Soccer Simulation League (3DSSL). Nesta liga o jogo de futebol é jogado numa simulação por computador. O modelo de robô usado é também o do robô Nao. Contudo, existem umas pequenas diferenças nas dimensões e este tem mais um grau de liberdade do que o robô real. O simulador também não consegue reproduzir a realidade com perfeição. Ambas estas ligas são importantes para esta dissertação, pois usam o mesmo modelo de robô. O objectivo desta dissertação é desenvolver comportamentos para estas ligas, aproveitando o trabalho prévio desenvolvido para a 3DSSL. Estes comportamentos incluem os movimentos básicos necessários para jogar futebol, nomeadamente: andar, chutar a bola e levantar-se depois de uma queda. Esta dissertação apresenta a arquitetura do agente desenvolvida para a SPL, que é similar á arquitetura do agente da equipa FC Portugal da 3DSSL, para permitir uma mais fácil partilha de código entre as ligas. Foi também desenvolvida uma interface que permite controlar uma perna de maneira mais intuitiva. Ela calcula os ângulos das juntas da perna, usando os seguintes parâmetros: três ângulos entre o torso e a linha que une anca ao tornozelo; dois ângulos entre o pé e a perpendicular do torso; e a distância entre a anca e o tornozelo. Nesta dissertação foi também desenvolvido um algoritmo para calcular os três ângulos das juntas da anca que produzam a desejada rotação vertical, visto o robô Nao não ter uma junta na anca que rode verticalmente. Esta dissertação também apresenta os comportamentos desenvolvidos para a SPL, alguns dos quais foram baseados nos comportamentos já existentes na 3DSSL. É apresentado um modelo de comportamento que permite criar movimentos para o robô de nindo uma sequência de poses, um algoritmo para um andar open-loop e omnidirecional e um andar otimizado no simulador e adaptado para o robô real. A este último andar foi adicionado um sistema de feedback para o tornar mais robusto. Usando os comportamentos apresentados nesta dissertação, o robô atingiu uma velocidade de 16 cm/s para frente, 6 cm/s para o lado e rodou sobre si pr oprio a 40 graus/s. O trabalho desenvolvido nesta dissertação permite ter um agente que controle o robô Nao e execute os comportamentos básicos de baixo nível para competir na SPL. Além disso, as semelhan cas entre a arquitetura do agente para a SPL com a arquitetura do agente da 3DSSL permite usar os mesmos comportamentos de alto nível em ambas as ligas

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape