Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation (1805.10410v1)

Abstract: This paper derives a contact-aided inertial navigation observer for a 3D bipedal robot using the theory of invariant observer design. Aided inertial navigation is fundamentally a nonlinear observer design problem; thus, current solutions are based on approximations of the system dynamics, such as an Extended Kalman Filter (EKF), which uses a system's Jacobian linearization along the current best estimate of its trajectory. On the basis of the theory of invariant observer design by Barrau and Bonnabel, and in particular, the Invariant EKF (InEKF), we show that the error dynamics of the point contact-inertial system follows a log-linear autonomous differential equation; hence, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system's trajectory. Due to the log-linear form of the error dynamics, it is not necessary to perform a nonlinear observability analysis to show that when using an Inertial Measurement Unit (IMU) and contact sensors, the absolute position of the robot and a rotation about the gravity vector (yaw) are unobservable. We further augment the state of the developed InEKF with IMU biases, as the online estimation of these parameters has a crucial impact on system performance. We evaluate the convergence of the proposed system with the commonly used quaternion-based EKF observer using a Monte-Carlo simulation. In addition, our experimental evaluation using a Cassie-series bipedal robot shows that the contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in the system dynamics.

• The paper derives an InEKF for legged robot state estimation by exploiting system symmetries to manage nonlinear dynamics.
• It introduces online IMU bias estimation and validates performance using simulations and experiments on a Cassie-series bipedal robot.
• The open-source implementation and improved convergence metrics demonstrate its potential for robust navigation in dynamic, contact-rich environments.

Summary and Insights on "Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation"

Overview

The paper "Contact-Aided Invariant Extended Kalman Filtering for Legged Robot State Estimation" addresses the development of a nonlinear observer to improve legged robot navigation using an Invariant Extended Kalman Filter (InEKF). By leveraging contact-aided inertial sensor data, the authors seek to enhance the accuracy and robustness of state estimation in dynamic environments. The paper emerges from the groundwork laid by theories on invariant observer design, notably by Barrau and Bonnabel. This work extends the capabilities of inertial navigation systems by formulating an observer that accounts for the symmetries inherent in robotic dynamics.

Key Contributions

The paper builds on an existing theoretical framework to design an observer that operates effectively within the domain of legged robotic systems. The authors introduce a contact-aided inertial navigation observer that deviates from traditional Extended Kalman Filters (EKFs) by using InEKF principles. The key contributions outlined in the paper are:

1. Derivation of InEKF for Legged Robots: The paper presents the derivation of an InEKF suited for state estimation in legged robots, facilitating better handling of nonlinearities in system dynamics due to its exploitation of system symmetries.
2. Introduction of IMU Bias Estimation: The paper augments the state with Inertial Measurement Unit (IMU) biases, recognizing their impact on performance, and proposes methods for their online estimation.
3. Simulation and Experimental Validation: Using a Cassie-series bipedal robot, the paper empirically evaluates the proposed system, showcasing improved performance over traditional quaternion-based EKFs in simulations and hardware experiments.
4. Open Source Implementation: The publication provides a GitHub repository for an open-source implementation, allowing other researchers to replicate and build upon the work.

Numerical Results

The authors present a systematic comparison through Monte-Carlo simulations, illustrating the faster and more reliable convergence of the InEKF-based approach compared to the quaternion-based EKF. The InEKF demonstrates improved initial convergence rates in both simulation scenarios and real-world experiments, highlighting its efficacy in handling large initial errors and maintaining robust state estimation.

Implications and Future Directions

The theoretical and empirical advancements presented pave the way for more robust navigation and control systems in mobile robotics. By addressing the inherent challenges posed by nonlinear observer design in dynamic environments, this methodology could have substantial implications not only for legged robots but also across various robotic platforms that rely on precise state estimation.

Practical implications include improved real-time performance in environments with unpredictable dynamics and contact. The mathematical formulation utilizing Lie groups and symmetries suggests potential applications in other domains where similar mathematical structures are present.

Looking ahead, the integration of InEKF with complementary sensory modalities such as vision or LiDAR could further enhance robustness in diverse terrain and conditions. Future research may explore extending these principles to larger systems, such as multi-legged robots, or conceptual advances regarding system identification and adaptive control mechanisms in robotic systems. There is also scope for developing higher-level frameworks that incorporate learning-based elements into these estimation tools to enhance adaptation to novel dynamic conditions.