Here are presentations I gave with a summary of the discussions that followed. See also the publications section for conference presentations.


  • Divergent components of motion
    Talk given at the CNRS-AIST Joint Robotics Laboratory (JRL) on 29 October 2019. (pdf)

    Some nonlinear control systems admit an exponential dichotomy (Coppel, 1966), that is to say, their dynamics can be decomposed into (exponentially) stable and unstable components. Walking robots fall into this category, and we call their unstable components divergent components of motion (DCM). The concept of DCM has been fruitfully applied to the linear inverted pendulum (LIP) for both walking pattern generation and balance feedback control. But DCMs can be found for other models as well! In this talk, we will discuss DCMs for the variable-height inverted pendulum (VHIP), an extension of the LIP where the controller can add height variations. Ideally, we would like our robot to behave as a LIP (nominal height) unless some perturbation occurs and the robot resorts to the height-variation strategy, if it has to. Deciding when to use or not this strategy may seem "smart" or predictive, but we will see that it can be implemented straightforwardly as linear feedback over a 4D DCM.

  • Walking and stair climbing controller for locomotion in an aircraft factory
    Talk given at the NASA-Caltech Jet Propulsion Laboratory on 5 June 2019. (pdf)

    The task was initially phrased for humans: go upstairs, walk into the aircraft, pick up the object and place it on the fuselage. Yet, repetition and the disposition of target locations turned out to cause chronic back pain, and the question of automation was raised: can a robot do that? In this talk, we will see how the HRP-4 humanoid can do that, and discuss the components we developed for the final demonstrator of the COMANOID project that ran at the Airbus Saint-Nazaire factory on 21 February 2019: self localization, locomotion, object localization and manipulation. We will focus on walking and stair climbing control. The audience is encouraged to bring plastic bottles.

  • How do biped robots walk?
    Talk given at the WILLOW team seminar, Computer Science Department of the École Normale Supérieure de Paris (DI ENS), on 26 March 2019. (pdf)

    In this introductory talk, we will see the general methods used nowadays to make humanoid robots walk or climb stairs. Predictive and feedback controls will be presented from a high-level perspective, with more videos than equations. At its end, our bird-eye trip will leave us with open questions, for instance: what is missing in our robots' brains today? The audience is encouraged to bring lightweight plastic bottles.

  • Walking and stair climbing stabilization for position-controlled biped robots
    Talk given at Wandercraft on 19 March 2019. (pdf)

    In this talk, we will see the walking and stair climbing stabilizer implemented on the HRP-4 humanoid robot as part of the final demonstrator for an Airbus manufacturing use case. Our solution is based on DCM feedback control, quadratic-programming wrench distribution and a whole-body admittance controller that combines three kinds of tasks: single-effector CoP control at each foot, multi-effector foot pressure control during double-support phases, and CoM admittance control.


  • Stair Climbing Stabilization of the HRP-4 Humanoid Robot
    Talk given at the CNRS-AIST Joint Robotics Laboratory (JRL) on 11 December 2018 and at the University of Tokyo on 14 December 2018. (pdf)

    In this talk, we will discuss stair climbing experiments carried out with the HRP-4 humanoid as part of an Airbus manufacturing use case. Our solution is based on linear inverted pendulum tracking, quadratic-programming wrench distribution and a whole-body admittance controller that relies on both end-effector and CoM strategies. After presenting these components, we will open up the discussion on the interplay between end-effector and CoM strategies, as well as their potential applications in multi-contact.

  • 3D Bipedal Walking including COM height variations
    Talk given at Nanyang Technological University on 14 May 2018 and at Queensland University of Technology on 29 May 2018. (pdf)

    Real robots that walk in the field today rely on the Linear Inverted Pendulum Mode (LIPM) for walking control. Rigorously, the LIPM requires the robot's center-of-mass to lie in a plane, which is valid for walking on flat surfaces but becomes inexact over more general terrains. In this talk, we will see how to extend the LIPM to 3D walking, opening up old but refreshed questions on the analysis and control of bipeds. Technically, we will encounter a nonlinear control problem that we address by model predictive control of a quasi-convex optimization problem. We will see how the resulting controller works on the HRP-4 humanoid robot.


  • Pendular models for walking over rough terrains
    Talk given at the University of Rome "La Sapienza" on 19 October 2017, and at the Journées Nationales de la Robotique Humanoïde on 20 June 2017. (pdf)

    The Newton-Euler equations that govern multi-body systems are not integrable in general. However, they become so in the pendular mode, a specific way of moving where conservation of the angular momentum is enforced. This property was successfully showcased for locomotion over horizontal floors (2D locomotion) by walking-pattern generators based on the LIPM and CART-table models. In this talk, we will see how to generalize these two models to 3D locomotion while taking into account both friction and tilted contacts, resulting into the FIP (3D version of LIPM) and COM-accel (3D version of CART-table) models. We will demonstrate both approaches in live simulations with the HRP-4 humanoid model.

  • Une histoire de la locomotion humanoïde : du sol plat au tout-terrain
    Talk given at SoftBank Robotics Europe (SBRE) on 8 March 2017. (pdf)

    Cette présentation retrace les étapes importantes du développement des contrôleurs de marche pour les robots humanoïdes, depuis la démonstration publique du Honda P2 en 1997 jusqu'aux récents développements en marche tout-terrain. Elle n'aborde que des résultats partagés dans le monde ouvert, chaque slide étant associé à un article de recherche. La première partie revisite les concepts majeurs qui ont permis de résoudre la locomotion sur sol plat. La seconde décrit plusieurs développements récents en marche tout-terrain.


  • Time-Optimal Parameterization: a tool for Humanoid Motion Planning and Predictive Control
    Talk given at Humanoids 2016, Cancún, Mexico, in workshop W3 on The use of dynamics in the field of humanoid robotics: identification, planning, perception and control.

    Numerical optimization and dynamic models have given roboticists the tools to implement instantaneous whole-body control (e.g. finding joint torques at time t to track at best a reference trajectory). However, it provided no turnkey solution as to whole-body planning, where successful planners were historically grounded on stochastic sampling and state-space discretization rather than active sets and gradient descents. Yet, this does not mean that the two fields are hermetically separated. In this talk, we will go through the recent history of Time-Optimal Path Parameterization (TOPP), an optimization routine that has been successfully applied to both motion planning and predictive control. A key feature of TOPP is its ability to return not only optimal solutions for a given dynamic model, but also higher-level information such as intervals of reachable velocities. We will discuss these practicalities and show both simulation and real-hardware applications.

  • Support Areas and Volumes for Humanoid Locomotion under Frictional Contacts
    Talk given at the Max Planck Institute for Intelligent Systems on 19 September 2016.

    Humanoid locomotion on horizontal floors was solved by closing the feedback loop on the Zero-tiling Moment Point (ZMP), a measurable dynamic point that needs to stay inside the foot contact area to prevent the robot from falling (contact stability criterion). However, this criterion does not apply to general multi-contact settings, the "new frontier" in humanoid locomotion.

  • ZMP support areas for multi-contact locomotion
    Talk given at the Journées Nationales de la Robotique Humanoïde on 23 June 2016.

    The Zero-tilting Moment Point (ZMP) and its support area are the two notions thanks to which roboticitsts solved the problem of walking on horizontal floor. Its historic definition presents two major limitations: all contacts between the robot and the environment need to be coplanar, and frictional effects (such as sliding or yaw rotations) are not taken into account. We present here a generalization of the ZMP "support area" that overcomes these two limitations. We show how to apply it with a linear-pendulum control law to generate stable multi-contact locomoting motions for humanoids in general environments.

  • Perspectives on Motion Planning and Control for Humanoid Robots in Multi-contact Scenarios
    Talk given at Nanyang Technological University on 7 March 2016.

    When today's robots move around, the motion that you observe is the result of two software stages: planning and control. Planning is the part that computes a trajectory from the initial state of the system to some goal state. Control is the part that deals with perturbations or modelling errors, and stabilizes the system at best while it performs the trajectory output by the planner.


  • Modèles simplifiés pour la locomotion des robots humanoïdes en terrain accidenté
    Présentation donnée à la Journée Francophone de la Recherche au Japon, Maison Franco-Japonaise de Tokyo, novembre 2015.

    La robotique humanoïde distingue deux domaines : planification et locomotion. Tous deux servent le même objectif, qui est de permettre au robot de se déplacer d'un endroit à un autre. La locomotion repose sur des mouvements répétés (comme les pas d'une démarche) ou générés par des modèles simplifiés du robot (comme le pendule inversé, que nous allons voir). Elle nécessite généralement un sol plat ou peu accidenté. La planification fait moins d'hypothèses, ce qui la rend adaptée aux déplacements dans les environnements encombrés. Toutefois, elle nécessite d'avantage de calculs et a tendance à produire des mouvements peu naturels. Marcher en forêt relève par exemple de la locomotion, tandis qu'escalader une montagne relève de la planification.

© Stéphane Caron — All content on this website is licensed under the CC BY 4.0 license.