Centroidal State Estimation based on the Koopman Embedding for Dynamic Legged Locomotion

In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform the robot's complex nonlinear dynamics into a linear system, by employing dynamic mode decomposition and deep learning for model construction. We evaluate both models on their linearization accuracy and capability to capture both fast and slow dynamic system responses. We then select the most suitable model for estimation purposes, and integrate it within a moving horizon estimator. This estimator is formulated as a convex quadratic program, to facilitate robust, real-time centroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits, our data-driven framework outperforms conventional filtering techniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise in highly dynamic motions and accurately recovers the centroidal states, demonstrating the adaptability and effectiveness of the Koopman-based linear representation for complex locomotive behaviors. Importantly, our model based on dynamic mode decomposition, trained with two locomotion patterns (trot and jump), successfully estimates the centroidal states for a different motion (bound) without retraining.

Perception for Humanoid Robots

Purpose of Review: The field of humanoid robotics, perception plays a fundamental role in enabling robots to interact seamlessly with humans and their surroundings, leading to improved safety, efficiency, and user experience. This scientific study investigates various perception modalities and techniques employed in humanoid robots, including visual, auditory, and tactile sensing by exploring recent state-of-the-art approaches for perceiving and understanding the internal state, the environment, objects, and human activities. Recent Findings: Internal state estimation makes extensive use of Bayesian filtering methods and optimization techniques based on maximum a-posteriori formulation by utilizing proprioceptive sensing. In the area of external environment understanding, with an emphasis on robustness and adaptability to dynamic, unforeseen environmental changes, the new slew of research discussed in this study have focused largely on multi-sensor fusion and machine learning in contrast to the use of hand-crafted, rule-based systems. Human robot interaction methods have established the importance of contextual information representation and memory for understanding human intentions. Summary: This review summarizes the recent developments and trends in the field of perception in humanoid robots. Three main areas of application are identified, namely, internal state estimation, external environment estimation, and human robot interaction. The applications of diverse sensor modalities in each of these areas are considered and recent significant works are discussed.

Visual-Inertial and Leg Odometry Fusion for Dynamic Locomotion

Implementing dynamic locomotion behaviors on legged robots requires a high-quality state estimation module. Especially when the motion includes flight phases, state-of-the-art approaches fail to produce reliable estimation of the robot posture, in particular base height. In this paper, we propose a novel approach for combining visual-inertial odometry (VIO) with leg odometry in an extended Kalman filter (EKF) based state estimator. The VIO module uses a stereo camera and IMU to yield low-drift 3D position and yaw orientation and drift-free pitch and roll orientation of the robot base link in the inertial frame. However, these values have a considerable amount of latency due to image processing and optimization, while the rate of update is quite low which is not suitable for low-level control. To reduce the latency, we predict the VIO state estimate at the rate of the IMU measurements of the VIO sensor. The EKF module uses the base pose and linear velocity predicted by VIO, fuses them further with a second high-rate IMU and leg odometry measurements, and produces robot state estimates with a high frequency and small latency suitable for control. We integrate this lightweight estimation framework with a nonlinear model predictive controller and show successful implementation of a set of agile locomotion behaviors, including trotting and jumping at varying horizontal speeds, on a torque-controlled quadruped robot.

On the Use of Torque Measurement in Centroidal State Estimation

State of the art legged robots are either capable of measuring torque at the output of their drive systems, or have transparent drive systems which enable the computation of joint torques from motor currents. In either case, this sensor modality is seldom used in state estimation. In this paper, we propose to use joint torque measurements to estimate the centroidal states of legged robots. To do so, we project the whole-body dynamics of a legged robot into the nullspace of the contact constraints, allowing expression of the dynamics independent of the contact forces. Using the constrained dynamics and the centroidal momentum matrix, we are able to directly relate joint torques and centroidal states dynamics. Using the resulting model as the process model of an Extended Kalman Filter (EKF), we fuse the torque measurement in the centroidal state estimation problem. Through real-world experiments on a quadruped robot with different gaits, we demonstrate that the estimated centroidal states from our torque-based EKF drastically improve the estimation of these quantities compared to direct computation.