Straight-Leg Walking Through Underconstrained Whole-Body Control

We present an approach for achieving a natural, efficient gait on bipedal robots using straightened legs and toe-off. Our algorithm avoids complex height planning by allowing a whole-body controller to determine the straightest possible leg configuration at run-time. The controller solutions are biased towards a straight leg configuration by projecting leg joint angle objectives into the null-space of the other quadratic program motion objectives. To allow the legs to remain straight throughout the gait, toe-off was utilized to increase the kinematic reachability of the legs. The toe-off motion is achieved through underconstraining the foot position, allowing it to emerge naturally. We applied this approach of under-specifying the motion objectives to the Atlas humanoid, allowing it to walk over a variety of terrain. We present both experimental and simulation results and discuss performance limitations and potential improvements.Comment: Submitted to 2018 IEEE International Conference on Robotics and Automatio

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

Sample Efficient Optimization for Learning Controllers for Bipedal Locomotion

Learning policies for bipedal locomotion can be difficult, as experiments are expensive and simulation does not usually transfer well to hardware. To counter this, we need al- gorithms that are sample efficient and inherently safe. Bayesian Optimization is a powerful sample-efficient tool for optimizing non-convex black-box functions. However, its performance can degrade in higher dimensions. We develop a distance metric for bipedal locomotion that enhances the sample-efficiency of Bayesian Optimization and use it to train a 16 dimensional neuromuscular model for planar walking. This distance metric reflects some basic gait features of healthy walking and helps us quickly eliminate a majority of unstable controllers. With our approach we can learn policies for walking in less than 100 trials for a range of challenging settings. In simulation, we show results on two different costs and on various terrains including rough ground and ramps, sloping upwards and downwards. We also perturb our models with unknown inertial disturbances analogous with differences between simulation and hardware. These results are promising, as they indicate that this method can potentially be used to learn control policies on hardware.Comment: To appear in International Conference on Humanoid Robots (Humanoids '2016), IEEE-RAS. (Rika Antonova and Akshara Rai contributed equally

3LP: a linear 3D-walking model including torso and swing dynamics

In this paper, we present a new model of biped locomotion which is composed of three linear pendulums (one per leg and one for the whole upper body) to describe stance, swing and torso dynamics. In addition to double support, this model has different actuation possibilities in the swing hip and stance ankle which could be widely used to produce different walking gaits. Without the need for numerical time-integration, closed-form solutions help finding periodic gaits which could be simply scaled in certain dimensions to modulate the motion online. Thanks to linearity properties, the proposed model can provide a computationally fast platform for model predictive controllers to predict the future and consider meaningful inequality constraints to ensure feasibility of the motion. Such property is coming from describing dynamics with joint torques directly and therefore, reflecting hardware limitations more precisely, even in the very abstract high level template space. The proposed model produces human-like torque and ground reaction force profiles and thus, compared to point-mass models, it is more promising for precise control of humanoid robots. Despite being linear and lacking many other features of human walking like CoM excursion, knee flexion and ground clearance, we show that the proposed model can predict one of the main optimality trends in human walking, i.e. nonlinear speed-frequency relationship. In this paper, we mainly focus on describing the model and its capabilities, comparing it with human data and calculating optimal human gait variables. Setting up control problems and advanced biomechanical analysis still remain for future works.Comment: Journal paper under revie

Feedback Control of an Exoskeleton for Paraplegics: Toward Robustly Stable Hands-free Dynamic Walking

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.Comment: Submitted to IEEE Control System Magazine. This version addresses reviewers' concerns about the robustness of the algorithm and the motivation for using such exoskeleton

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