A Predictive Momentum-Based Whole-Body Torque Controller: Theory and Simulations for the iCub Stepping

When balancing, a humanoid robot can be easily subjected to unexpected disturbances like external pushes. In these circumstances, reactive movements as steps become a necessary requirement in order to avoid potentially harmful falling states. In this paper we conceive a Model Predictive Controller which determines a desired set of contact wrenches by predicting the future evolution of the robot, while taking into account constraints switching in case of steps. The control inputs computed by this strategy, namely the desired contact wrenches, are directly obtained on the robot through a modification of the momentum-based whole-body torque controller currently implemented on iCub. The proposed approach is validated through simulations in a stepping scenario, revealing high robustness and reliability when executing a recovery strategy.

On-line Joint Limit Avoidance for Torque Controlled Robots by Joint Space Parametrization

This paper proposes control laws ensuring the stabilization of a time-varying desired joint trajectory, as well as joint limit avoidance, in the case of fully-actuated manipulators. The key idea is to perform a parametrization of the feasible joint space in terms of exogenous states. It follows that the control of these states allows for joint limit avoidance. One of the main outcomes of this paper is that position terms in control laws are replaced by parametrized terms, where joint limits must be avoided. Stability and convergence of time-varying reference trajectories obtained with the proposed method are demonstrated to be in the sense of Lyapunov. The introduced control laws are verified by carrying out experiments on two degrees-of-freedom of the humanoid robot iCub.

An Optimization Based Control Framework for Balancing and Walking: Implementation on the iCub Robot

A whole-body torque control framework adapted for balancing and walking tasks is presented in this paper. In the proposed approach, centroidal momentum terms are excluded in favor of a hierarchy of high-priority position and orientation tasks and a low-priority postural task. More specifically, the controller stabilizes the position of the center of mass, the orientation of the pelvis frame, as well as the position and orientation of the feet frames. The low-priority postural task provides reference positions for each joint of the robot. Joint torques and contact forces to stabilize tasks are obtained through quadratic programming optimization. Besides the exclusion of centroidal momentum terms, part of the novelty of the approach lies in the definition of control laws in SE(3) which do not require the use of Euler parameterization. Validation of the framework was achieved in a scenario where the robot kept balance while walking in place. Experiments have been conducted with the iCub robot, in simulation and in real-world experiments.

Walking of the iCub humanoid robot in different scenarios: implementation and performance analysis

The humanoid robot iCub is a research platform of the Fondazione Istituto Italiano di Tecnologia (IIT), spread among different institutes around the world. In the most recent version of iCub, the robot is equipped with stronger legs and bigger feet, allowing it to perform balancing and walking motions that were not possible with the first generations. Despite the new legs hardware, walking has been rarely performed on the iCub robot. In this work the objective is to implement walking motions on the robot, from which we want to analyze its walking capabilities. We developed software modules based on extensions of classic techniques such as the ZMP based pattern generator and position control to identify which are the characteristics as well as limitations of the robot against different walking tasks in order to give the users a reference of the performance of the robot. Most of the experiments have been performed with HeiCub, a reduced version of iCub without arms and head.

Stability Analysis and Design of Momentum-based Controllers for Humanoid Robots

Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community dealing with humanoid robotics. Momentum-based strategies have proven their effectiveness for controlling humanoids balancing, but the stability analysis of these controllers is still missing. The contribution of this paper is twofold. First, we numerically show that the application of state-of-the-art momentum-based control strategies may lead to unstable zero dynamics. Secondly, we propose simple modifications to the control architecture that avoid instabilities at the zero-dynamics level. Asymptotic stability of the closed loop system is shown by means of a Lyapunov analysis on the linearized system's joint space. The theoretical results are validated with both simulations and experiments on the iCub humanoid robot.

Momentum Control of an Underactuated Flying Humanoid Robot

The paper takes the first step towards the de- velopment of a control framework for underactuated flying humanoid robots. These robots may thus have the capacities of flight, contact locomotion, and manipulation, and benefit from technologies and methods developed for Whole-Body Control and Aerial Manipulation. As in the case of quadrotors, we as- sume that the humanoid robot is powered by four thrust forces. For convenience, these forces are placed at the robot hands and feet. The control objective is defined as the asymptotic stabilization of the robot centroidal momentum. This objective allows us to track a desired trajectory for the robot center of mass and keep small errors between a reference orientation and the robot base frame. Stability and convergence of the robot momentum are shown to be in the sense of Lyapunov. Simulations carried out on a model of the humanoid robot iCub verify the soundness of the proposed approach.

A Receding Horizon Push Recovery Strategy for Balancing the iCub Humanoid Robot

Balancing and reacting to strong and unexpected pushes is a critical requirement for humanoid robots. We recently designed a capture point based approach which interfaces with a momentum-based torque controller and we implemented and validated it on the iCub humanoid robot. In this work we implement a Receding Horizon control, also known as Model Predictive Control, to add the possibility to predict the future evolution of the robot, especially the constraints switching given by the hybrid nature of the system. We prove that the proposed MPC extension makes the step-recovery controller more robust and reliable when executing the recovery strategy. Experiments in simulation show the results of the proposed approach.

Torque-Controlled Stepping-Strategy Push Recovery: Design and Implementation on the iCub Humanoid Robot

One of the challenges for the robotics community is to deploy robots which can reliably operate in real world scenarios together with humans. A crucial requirement for legged robots is the capability to properly balance on their feet, rejecting external disturbances. iCub is a state-of-the-art humanoid robot which has only recently started to balance on its feet. While the current balancing controller has proved successful in various scenarios, it still misses the capability to properly react to strong pushes by taking steps. This paper goes in this direction. It proposes and implements a control strategy based on the Capture Point concept [1]. Instead of relying on position control, like most of Capture Point related approaches, the proposed strategy generates references for the momentum-based torque controller already implemented on the iCub, thus extending its capabilities to react to external disturbances, while retaining the advantages of torque control when interacting with the environment. Experiments in the Gazebo simulator and on the iCub humanoid robot validate the proposed strategy.

The Static Center of Pressure Sensitivity: a further Criterion to assess Contact Stability and Balancing Controllers

Legged locomotion has received increasing attention from the robotics community. In this respect, contact stability plays a critical role in ensuring that robots maintain balance, and it is a key element for balancing and walking controllers. The Center of Pressure is a contact stability criterion that defines a point that must be kept strictly inside the support polygon in order to ensure postural stability. In this paper, we introduce the concept of the sensitivity of the static center of pressure: roughly speaking, the rate of change of the center of pressure with respect to the system equilibrium configurations. This new concept can be used as an additional criterion to assess the robustness of the contact stability. We show how the sensitivity of the center of pressure can also be used as a metric to assess balancing controllers by considering two state-of-the-art control strategies. The analytical analysis is performed on a simplified model, and validated during balancing tasks on the iCub humanoid robot.

Inverse, forward and other dynamic computations computationally optimized with sparse matrix factorizations

We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational complexity of the underlying solution. This optimisation step consists in formulating the dynamic computations as a system of linear equations. The computational complexity of computing the associated solution is reduced by performing a permuted LU-factorisation with off-line optimised permutations. We apply our algorithm to solve classical dynamic problems: inverse and forward dynamics. The computational complexity of the proposed solution is compared to `gold standard' algorithms: recursive Newton-Euler and articulated body algorithm. It is shown that our algorithm reduces the number of floating point operations with respect to previous approaches. We also evaluate the numerical complexity of our algorithm by performing tests on dynamic computations for which no gold standard is available.