Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations

International audienceA humanoid walking robot is a highly nonlinear dynamical system that relies strongly on contact forces between its feet and the ground in order to realize stable motions, but these contact forces are unfortunately severely limited. Model Predictive Control, also known as Receding Horizon Control, is a general control scheme specifically designed to deal with such contrained dynamical systems, with the potential ability to react efficiently to a wide range of situations. Apart from the question of computation time which needs to be taken care of carefully (these schemes can be highly computation intensive, the initial question of which optimal control problems should be considered to be solved online in order to lead to the desired walking movements is still unanswered. A key idea for answering to this problem can be found in the ZMP Preview Control scheme. After presenting here this scheme with a point of view slightly different from the original one, we focus on the problem of compensating strong perturbations of the dynamics of the robot and propose a new Linear Model Predictive Control scheme which is an improvement of the original ZMP Preview Control scheme

Some comments on the structure of the dynamics of articulated motion

International audienceWalking, running or jumping are special cases of articulated motions which rely heavily on contact forces for their accomplishment. This central role of the contact forces is widely recognized now, but it is rarely connected to the structure of the dynamics of articulated motion. Indeed, this dynamics is generally considered as a complex nonlinear black-box without any specific structure, or its structure is only partly uncovered. We propose here to precise this structure and show in details how it shapes the movements that an articulated system might realize. Some propositions are made then to improve the design of control laws for walking, running, jumping or free-floating motions

Development of a Locomotion and Balancing Strategy for Humanoid Robots

The locomotion ability and high mobility are the most distinguished features of humanoid robots. Due to the non-linear dynamics of walking, developing and controlling the locomotion of humanoid robots is a challenging task. In this thesis, we study and develop a walking engine for the humanoid robot, NAO, which is the official robotic platform used in the RoboCup Spl. Aldebaran Robotics, the manufacturing company of NAO provides a walking module that has disadvantages, such as being a black box that does not provide control of the gait as well as the robot walk with a bent knee. The latter disadvantage, makes the gait unnatural, energy inefficient and exert large amounts of torque to the knee joint. Thus creating a walking engine that produces a quality and natural gait is essential for humanoid robots in general and is a factor for succeeding in RoboCup competition. Humanoids robots are required to walk fast to be practical for various life tasks. However, its complex structure makes it prone to falling during fast locomotion. On the same hand, the robots are expected to work in constantly changing environments alongside humans and robots, which increase the chance of collisions. Several human-inspired recovery strategies have been studied and adopted to humanoid robots in order to face unexpected and avoidable perturbations. These strategies include hip, ankle, and stepping, however, the use of the arms as a recovery strategy did not enjoy as much attention. The arms can be employed in different motions for fall prevention. The arm rotation strategy can be employed to control the angular momentum of the body and help to regain balance. In this master\u27s thesis, I developed a detailed study of different ways in which the arms can be used to enhance the balance recovery of the NAO humanoid robot while stationary and during locomotion. I model the robot as a linear inverted pendulum plus a flywheel to account for the angular momentum change at the CoM. I considered the role of the arms in changing the body\u27s moment of inertia which help to prevent the robot from falling or to decrease the falling impact. I propose a control algorithm that integrates the arm rotation strategy with the on-board sensors of the NAO. Additionally, I present a simple method to control the amount of recovery from rotating the arms. I also discuss the limitation of the strategy and how it can have a negative impact if it was misused. I present simulations to evaluate the approach in keeping the robot stable against various disturbance sources. The results show the success of the approach in keeping the NAO stable against various perturbations. Finally,I adopt the arm rotation to stabilize the ball kick, which is a common reason for falling in the soccer humanoid RoboCup competitions

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

ZMP based reference generation for a bipedal humanoid robot

Recent fifteen years witnessed fast improvements in the field of humanoid robotics. The human-like robot structure is more suitable to human environment with its supreme obstacle avoidance properties when compared with wheeled service robots. However, the walking control for bipedal robots is a challenging task due to their complex dynamics. Stable reference generation plays a very important role in control. Linear Inverted Pendulum Model (LIPM) and the Zero Moment Point (ZMP) criterion are applied in a number of studies for stable walking reference generation of biped walking robots. This thesis takes this main approach too. This thesis proposes a natural and continuous ZMP reference trajectory for a stable and human-like walk. Natural, human-like walking is obtained by ZMP trajectories which move forward under the sole of the support foot when the robot body is supported by a single leg. Robot center of mass trajectory is obtained from predefined ZMP reference trajectories by a Fourier series approximation method. The Gibbs phenomenon problem common with Fourier approximations of discontinuous functions is avoided by employing continuous ZMP references. Also, these ZMP reference trajectories, unlike many examples in the literature, possess pre-assigned single and double support phases, which are very useful in experimental tuning work. In this thesis, a method for generating a stepping sequence of finite number of steps is proposed too. The ZMP based reference generation strategy is applied on the full body humanoid robot SURALP designed at Sabanci University. Experimental results indicate that the proposed reference trajectory generation technique is successful

Humanoid robot omnidirectional walking trajectory generation and control

Walking humanoid machines, once only seen or read in science fiction, became reality with the intensive research of the last four decades. However, there is a long way to go in the direction of technical achievements before humanoid robots can be used widely as human assistants. The design of a controller which can achieve a steady and stable walk is central in humanoid robotics. This control cannot be achieved if the reference trajectories are not generated suitably. The Zero Moment Point (ZMP) is the most widely used stability criterion for trajectory generation. The Center of Mass (CoM) reference can be obtained from the ZMP reference in a number of ways. A natural ZMP reference trajectory and a Fourier series approximation based method for computing the CoM reference from it, was previously proposed and published for the Sabanci University Robotics ReseArch Laboratory Platform (SURALP), for a straight walk. This thesis improves these techniques by modifying the straight walk reference trajectory into an omnidirectional one. The second contribution of this thesis is controller designs in order to cope with the changing slopes of the walking surface. The proposed controllers employ the trunk link rotational motion to adapt to the ground surface. A virtual pelvis link is introduced for the robots which do not posses roll and pitch axis in pelvis link. The proposed reference generation and control algorithms are tested on the humanoid robot SURALP. The experiments indicate that these methods are successful under various floor conditions

Bipedal humanoid robot walking reference tuning by the use of evolutionary algorithms

Various aspects of humanoid robotics attracted the attention of researchers in the past four decades. One of the most challenging tasks in this area is the control of bipedal locomotion. The dynamics involved are highly nonlinear and hard to stabilize. A typical fullbody humanoid robot has more than twenty joints and the coupling effects between the links are significant. Reference generation plays a vital role for the success of the walking controller. Stability criteria including the Zero Moment Point (ZMP) criterion are extensively applied for this purpose. However, the stability criteria are usually applied on simplified models like the Linear Inverted Pendulum Model (LIPM) which only partially describes the equations of the motion of the robot. There are also trial and error based techniques and other ad-hoc reference generation techniques as well. This background of complicated dynamics and difficulties in reference generation makes automatic gait (step patterns of legged robots) tuning an interesting area of research. A natural command for a legged robot is the velocity of its locomotion. A number of walk parameters including temporal and spatial variables like stepping period and step size need to be set properly in order to obtain the desired speed. These problems, when considered from kinematics point of view, do not have a unique set of walking parameters as a solution. However, some of the solutions can be more suitable for a stable walk, whereas others may lead to instability and cause robot to fall. This thesis proposes a gait tuning method based on evolutionary methods. A velocity command is given as the input to the system. A ZMP based reference generation method is employed. Walking simulations are performed to assess the fitness of artificial populations. The fitness is measured by the amount of support the simulated bipedal robot received from torsional virtual springs and dampers opposing the changes in body orientation. Cross-over and mutation mechanisms generate new populations. A number of different walking parameters and fitness functions are tested to improve this tuning process. The walking parameters obtained in simulations are applied to the experimental humanoid platform SURALP (Sabanci University ReseArch Labaratory Platform). Experiments verify the merits of the proposed reference tuning method