Contact estimation is a key ability for limbed robots, where making and breaking contacts has a direct impact on state estimation and balance control. Existing approaches typically rely on gait-cycle priors or designated contact sensors. We design a contact estimator that is suitable for the emerging wheeled-biped robot types that do not have these features. To this end, we propose a Bayes filter in which update steps are learned from real-robot torque measurements while prediction steps rely on inertial measurements. We evaluate this approach in extensive real-robot and simulation experiments. Our method achieves better performance while being considerably more sample efficient than a comparable deep-learning baseline.

A novel control scheme for biped robots to manipulate the ZMP three-dimensionally apart from the actual ground profile is presented. It is shown that the linear inverted-pendulum-like dynamics with this scheme can represent a wider class of movements including variation of the body height. Moreover, this can also represent the motion in aerial phase. Based on this, the foot-guided controller proposed by the authors is enhanced to enable the robots to locomote on highly uneven terrains and also to seamlessly transition between walking and running without pre-planning the overall motion reference. The controller guarantees the capturability at landing and defines the motion by a time-variant state feedback, which is analytically derived from a model predictive optimization. It is verified through some computer simulations.

The variable-height inverted pendulum (VHIP) model enables a new balancing strategy by height variations of the center of mass, in addition to the well-known ankle strategy. We propose a biped stabilizer based on linear feedback of the VHIP that is simple to implement, coincides with the state-of-the-art for small perturbations and is able to recover from larger perturbations thanks to this new strategy. This solution is based on "best-effort" pole placement of a 4D divergent component of motion for the VHIP under input feasibility and state viability constraints. We complement it with a suitable whole-body admittance control law and test the resulting stabilizer on the HRP-4 humanoid robot.

This study deals with the balance of humanoid or multi-legged robots in a multi-contact setting where a chosen subset of contacts is undergoing desired sliding-task motions. One method to keep balance is to hold the center-of-mass (CoM) within an admissible convex area. This area is calculated based on the contact positions and forces. We introduce a methodology to compute this CoM support area (CSA) for multiple fixed and intentionally sliding contacts. To select the most appropriate CoM position within CSA, we account for (i) constraints of multiple fixed and sliding contacts, (ii) desired wrench distribution for contacts, and (iii) desired CoM position (eventually dictated by other tasks). These are formulated as a quadratic programming (QP) optimization problems. We illustrate our approach with pushing against a wall and wiping, and conducted experiments using the HRP-4 humanoid robot.

Capturability analysis of the linear inverted pendulum (LIP) model enabled walking with constrained height based on the capture point. In this paper, we generalize this analysis to the variable-height inverted pendulum (VHIP) and show how it enables 3-D walking over uneven terrains based on capture inputs. Thanks to a tailored optimization scheme, we can compute these inputs fast enough for real-time model predictive control. We implement this approach as open-source software and demonstrate it in dynamic simulations.

In legged locomotion, the projection of the robot's Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot be realized because the joint-torques required to sustain them would be above their limits (actuation limits). In this article, we rule out such configurations and define the feasible region, a revisited support region that guarantees both global static stability in the sense of tip-over and slippage avoidance and of existence of a set of joint-torques that are able to sustain the robot's body weight. We show that the feasible region can be employed for the online selection of feasible footholds and CoM trajectories to achieve statically stable locomotion on rough terrains, also in presence of load-intensive tasks. Key results of our approach include the efficiency in the computation of the feasible region using an Iterative Projection (IP) algorithm and the successful execution of hardware experiments on the HyQ robot, that was able to negotiate obstacles of moderate dimensions while carrying an extra 10-kg payload.

We consider dynamic stair climbing with the HRP-4 humanoid robot as part of an Airbus manufacturing use-case demonstrator. We share experimental knowledge gathered so as to achieve this task, which HRP-4 had never been challenged to before. In particular, we extend walking stabilization based on linear inverted pendulum tracking [1] by quadratic programming-based wrench distribution and a whole-body admittance controller that applies both end-effector and CoM strategies. While existing stabilizers tend to use either one or the other, our experience suggests that the combination of these two approaches improves tracking performance. We demonstrate this solution in an on-site experiment where HRP4 climbs an industrial staircase with 18.5 cm high steps, and release our walking controller as open source software.

Animated virtual humans may rely on full-body tracking system to reproduce user motions. In this paper, we reduce tracking to the upper-body and reconstruct the lower body to follow autonomously its upper counterpart. Doing so reduces the number of sensors required, making the application of virtual humans simpler and cheaper. It also enable deployment in cluttered scenes where the lower body is often hidden. The contribution here is the inversion of the well-known capture problem for bipedal walking. It determines footsteps rather than center-of-mass motions and yet can be solved with an off-the-shelf capture problem solver. The quality of our method is assessed in real-time tracking experiments on a wide variety of movements.

Developments for 3D control of the center of mass (CoM) of biped robots are currently located in two local minima: on the one hand, methods that allow CoM height variations but only work in the 2D sagittal plane; on the other hand, nonconvex direct transcriptions of centroidal dynamics that are delicate to handle. This paper presents an alternative that controls the CoM in 3D via an indirect transcription that is both low-dimensional and solvable fast enough for real-time control. The key to this development is the notion of boundedness condition, which quantifies the capturability of 3D CoM trajectories.

We present a novel technique that unobtrusively estimates forces exerted by human participants in multicontact interaction with rigid environments. Our method uses motion capture only, thus circumventing the need to set up cumbersome force transducers at all potential contacts between the human body and the environment. This problem is particularly challenging, as the knowledge of a given motion only characterizes the resultant force, which can generally be caused by an infinity of force distributions over individual contacts. We collect and release a large-scale dataset on how humans instinctively regulate interaction forces on diverse multicontact tasks and motions. The force estimation framework we propose leverages physics-based optimization and neural networks to reconstruct force distributions that are physically realistic and compatible with real interaction force patterns. We show the effectiveness of our approach on various locomotion and multicontact scenarios.

We present a real-time pattern generator for dynamic walking over rough terrains. Our method automatically finds step durations, a critical issue over rough terrains where they depend on terrain topology. To achieve this level of generality, we consider a Floating-base Inverted Pendulum (FIP) model where the center of mass can translate freely and the zero-tilting moment point is allowed to leave the contact surface. This model is equivalent to a linear inverted pendulum with variable center-of-mass height, but its equations of motion remain linear. Our solution then follows three steps: (i) we characterize the FIP contact-stability condition; (ii) we compute feedforward controls by solving a nonlinear optimization over receding-horizon FIP trajectories. Despite running at 30 Hz in a model-predictive fashion, simulations show that the latter is too slow to stabilize dynamic motions. To remedy this, we (iii) linearize FIP feedback control into a constrained linear-quadratic regulator that runs at 300 Hz. We finally demonstrate our solution in simulations with a model of the HRP-4 humanoid robot, including noise and delays over state estimation and foot force control.

We propose a method for checking and enforcing multicontact stability based on the zero-tilting moment point (ZMP). The key to our development is the generalization of ZMP support areas to take into account: 1) frictional constraints and 2) multiple noncoplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots by using the linear pendulum mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call the pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multicontact motions where an HRP-4 humanoid locomotes in challenging multicontact scenarios.

Humanoids locomote by making and breaking contacts with their environment. Thus, a crucial question for them is to anticipate whether a contact will hold or break under effort. For rigid surface contacts, existing methods usually consider several point-contact forces, which has some drawbacks due to the underlying redundancy. We derive a criterion, the Contact Wrench Cone (CWC), which is equivalent to any number of applied forces on the contact surface, and for which we provide a closed-form formula. It turns out that the CWC can be decomposed into three conditions: (i) Coulomb friction on the resultant force, (ii) CoP inside the support area, and (iii) upper and lower bounds on the yaw torque. While the first two are well-known, the third one is novel. It can, for instance, be used to prevent the undesired foot yaws observed in biped locomotion. We show that our formula yields simpler and faster computations than existing approaches for humanoid motions in single support, and assess its validity in the OpenHRP simulator.

The panorama of probabilistic completeness results for kinodynamic planners is still confusing. Most existing completeness proofs require strong assumptions that are difficult, if not impossible, to verify in practice. To make completeness results more useful, it is thus sensible to establish a classification of the various types of constraints and planning methods, and then attack each class with specific proofs and hypotheses that can be verified in practice. We propose such a classification, and provide a proof of probabilistic completeness for an important class of planners, namely those whose steering method is based on the interpolation of system trajectories in the state space. We also provide design guidelines for the interpolation function and discuss two criteria arising from our analysis: local boundedness and acceleration compliance.