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Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential to address for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for humanoid walking on periodically swaying rigid surface. The first key contribution is an analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds whose motion period may be different than the robot’s gait period. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller’s stabilizing effect. Finally, experiments conducted on a Digit humanoid robot, both in simulations and on hardware, demonstrate the framework’s effectiveness in addressing bipedal locomotion on swaying ground, even under uncertain surface motions and unknown external pushes. 

This article presents an invariant extended Kalman filter (InEKF) approach for estimating the relative pose and linear velocity of ground robots—either legged or wheeled—using an inertial measurement unit (IMU) attached to the robot, encoders, and an external IMU placed on the moving ground. The approach explicitly accounts for ground motion in noninertial environments, such as ships or airplanes, where the ground rotates or accelerates in the inertial frame. Unlike previous methods, it does not rely on known ground pose. This consideration introduces complexity due to the nonlinear dynamics and kinematics of the reference frame. Despite this complexity, the proposed filter, based on the InEKF methodology, includes a process model that partially satisfies the group affine condition. The leg odometry-based measurement model meets the right-invariant observation form for deterministic scenarios, though the wheel odometry model does not. Observability analysis demonstrates that all state variables are observable during a broad range of ground motions, overcoming the partial observability limitations of previous filters. Experiments on a Digit humanoid robot and a Jackal wheeled robot verify the filter’s effectiveness across various ground motions. 

We consider estimation of motion on spheres as a variational problem. The concept of variational estimation for mechanical systems is based on application of variational principles from mechanics, to state estimation of mechanical systems evolving on configuration manifolds. If the configuration manifold is a symmetric space, then the overlying connected Lie group of which it is a quotient space, can be used to design nonlinearly stable observers for estimation of configuration and velocity states from measurements. If the configuration manifold is a sphere, then it can be globally represented by an unit vector. We illustrate the design of variational observers for mechanical systems evolving on spheres, through its application to estimation of pointing directions (reduced attitude) on the regular sphere S^2. 

This work investigates the robot state estimation problem within a non-inertial environment. The proposed state estimation approach relaxes the common assumption of static ground in the system modeling. The process and measurement models explicitly treat the movement of the non-inertial environments without requiring knowledge of its motion in the inertial frame or relying on GPS or sensing environmental landmarks. Further, the proposed state estimator is formulated as an invariant extended Kalman filter (InEKF) [1] with the deterministic part of its process model obeying the groupaffine property, leading to log-linear error dynamics. The observability analysis confirms the robot’s pose (i.e., position and orientation) and velocity relative to the non-inertial environment are observable under the proposed InEKF. 

Differentiable Neural Architecture Search (DNAS) has demonstrated great success in designing state-of-the-art, efficient neural networks. However, DARTS-based DNAS's search space is small when compared to other search methods', since all candidate network layers must be explicitly instantiated in memory. To address this bottleneck, we propose a memory and computationally efficient DNAS variant: DMaskingNAS. This algorithm expands the search space by up to 10^14x over conventional DNAS, supporting searches over spatial and channel dimensions that are otherwise prohibitively expensive: input resolution and number of filters. We propose a masking mechanism for feature map reuse, so that memory and computational costs stay nearly constant as the search space expands. Furthermore, we employ effective shape propagation to maximize per-FLOP or per-parameter accuracy. The searched FBNetV2s yield state-of-the-art performance when compared with all previous architectures. With up to 421x less search cost, DMaskingNAS finds models with 0.9% higher accuracy, 15% fewer FLOPs than MobileNetV3-Small; and with similar accuracy but 20% fewer FLOPs than Efficient-B0. Furthermore, our FBNetV2 outperforms MobileNetV3 by 2.6% in accuracy, with equivalent model size. FBNetV2 models are open-sourced at https://github.com/facebookresearch/mobile-vision.