Humanoid gait generation for walk-to locomotion using single-stage MPC

We consider the problem of gait generation for a humanoid robot that must walk to an assigned Cartesian goal. As a first solution, we consider a rather straightforward adaptation of our previous work: An external block produces high-level velocities, which are then tracked by a double-stage intrinsically stable MPC scheme where the orientation of the footsteps is chosen before determining their location and the CoM trajectory. The second solution, which represents the main contribution of the paper, is conceptually different: no high-level velocity is generated, and footstep orientations are chosen at the same time of the other decision variables in a singlestage MPC. This is made possible by carefully redesigning the motion constraints so as to preserve linearity. Preliminary results on a simulated NAO confirm that the single-stage method outperforms the conventional double-stage scheme

MPC-based humanoid pursuit-evasion in the presence of obstacles

We consider a pursuit-evasion problem between humanoids in the presence of obstacles. In our scenario, the pursuer enters the safety area of the evader headed for collision, while the latter executes a fast evasive motion. Control schemes are designed for both the pursuer and the evader. They are structurally identical, although the objectives are different: the pursuer tries to align its direction of motion with the line- of-sight to the evader, whereas the evader tries to move in a direction orthogonal to the line-of-sight to the pursuer. At the core of the control architecture is a Model Predictive Control scheme for generating a stable gait. This allows for the inclusion of workspace obstacles, which we take into account at two levels: during the determination of the footsteps orientation and as an explicit MPC constraint. We illustrate the results with simulations on NAO humanoids

Efficient Humanoid Contact Planning using Learned Centroidal Dynamics Prediction

Humanoid robots dynamically navigate an environment by interacting with it via contact wrenches exerted at intermittent contact poses. Therefore, it is important to consider dynamics when planning a contact sequence. Traditional contact planning approaches assume a quasi-static balance criterion to reduce the computational challenges of selecting a contact sequence over a rough terrain. This however limits the applicability of the approach when dynamic motions are required, such as when walking down a steep slope or crossing a wide gap. Recent methods overcome this limitation with the help of efficient mixed integer convex programming solvers capable of synthesizing dynamic contact sequences. Nevertheless, its exponential-time complexity limits its applicability to short time horizon contact sequences within small environments. In this paper, we go beyond current approaches by learning a prediction of the dynamic evolution of the robot centroidal momenta, which can then be used for quickly generating dynamically robust contact sequences for robots with arms and legs using a search-based contact planner. We demonstrate the efficiency and quality of the results of the proposed approach in a set of dynamically challenging scenarios

Walking Stabilization Using Step Timing and Location Adjustment on the Humanoid Robot, Atlas

While humans are highly capable of recovering from external disturbances and uncertainties that result in large tracking errors, humanoid robots have yet to reliably mimic this level of robustness. Essential to this is the ability to combine traditional "ankle strategy" balancing with step timing and location adjustment techniques. In doing so, the robot is able to step quickly to the necessary location to continue walking. In this work, we present both a new swing speed up algorithm to adjust the step timing, allowing the robot to set the foot down more quickly to recover from errors in the direction of the current capture point dynamics, and a new algorithm to adjust the desired footstep, expanding the base of support to utilize the center of pressure (CoP)-based ankle strategy for balance. We then utilize the desired centroidal moment pivot (CMP) to calculate the momentum rate of change for our inverse-dynamics based whole-body controller. We present simulation and experimental results using this work, and discuss performance limitations and potential improvements

Gait generation via intrinsically stable MPC for a multi-mass humanoid model

We consider the problem of generating a gait with no a priori assigned footsteps while taking into account the contribution of the swinging leg to the total Zero Moment Point (ZMP). This is achieved by considering a multi-mass model of the humanoid and distinguishing between secondary masses with known pre-defined motion and the remaining, primary, masses. In the case of a single primary mass with constant height, it is possible to transform the original gait generation problem for the multi-mass system into a single LIP-like problem. We can then take full advantage of an intrinsically stable MPC framework to generate a gait that takes into account the swinging leg motion

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

A framework for safe human-humanoid coexistence

This work is focused on the development of a safety framework for Human-Humanoid coexistence, with emphasis on humanoid locomotion. After a brief introduction to the fundamental concepts of humanoid locomotion, the two most common approaches for gait generation are presented, and are extended with the inclusion of a stability condition to guarantee the boundedness of the generated trajectories. Then the safety framework is presented, with the introduction of different safety behaviors. These behaviors are meant to enhance the overall level of safety during any robot operation. Proactive behaviors will enhance or adapt the current robot operations to reduce the risk of danger, while override behaviors will stop the current robot activity in order to take action against a particularly dangerous situation. A state machine is defined to control the transitions between the behaviors. The behaviors that are strictly related to locomotion are subsequently detailed, and an implementation is proposed and validated. A possible implementation of the remaining behaviors is proposed through the review of related works that can be found in literature

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