An official website of the United States government
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.
more »
« less
Invariant Extended Kalman Filtering for Human Motion Estimation with Imperfect Sensor Placement
This paper introduces a new invariant extended Kalman filter design that produces real-time state estimates and rapid error convergence for the estimation of the human body movement even in the presence of sensor misalignment and initial state estimation errors. The filter fuses the data returned by an inertial measurement unit (IMU) attached to the body (e.g., pelvis or chest) and a virtual measurement of zero stance-foot velocity (i.e., leg odometry). The key novelty of the proposed filter lies in that its process model meets the group affine property while the filter explicitly addresses the IMU placement error by formulating its stochastic process model as Brownian motions and incorporating the error in the leg odometry. Although the measurement model is imperfect (i.e., it does not possess an invariant observation form) and thus its linearization relies on the state estimate, experimental results demonstrate fast convergence of the proposed filter (within 0.2 seconds) during squatting motions even under significant IMU placement inaccuracy and initial estimation errors.
more »
« less
- PAR ID:
- 10395706
- Date Published:
- Journal Name:
- American Control Conference
- Page Range / eLocation ID:
- 3012 to 3018
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
Legged robots require knowledge of pose and velocity in order to maintain stability and execute walking paths. Current solutions either rely on vision data, which is susceptible to environmental and lighting conditions, or fusion of kinematic and contact data with measurements from an inertial measurement unit (IMU). In this work, we develop a contact-aided invariant extended Kalman filter (InEKF) using the theory of Lie groups and invariant observer design. This filter combines contact-inertial dynamics with forward kinematic corrections to estimate pose and velocity along with all current contact points. We show that the error dynamics follows a log-linear autonomous differential equation with several important consequences: (a) the observable state variables can be rendered convergent with a domain of attraction that is independent of the system’s trajectory; (b) unlike the standard EKF, neither the linearized error dynamics nor the linearized observation model depend on the current state estimate, which (c) leads to improved convergence properties and (d) a local observability matrix that is consistent with the underlying nonlinear system. Furthermore, we demonstrate how to include IMU biases, add/remove contacts, and formulate both world-centric and robo-centric versions. We compare the convergence of the proposed InEKF with the commonly used quaternion-based extended Kalman filter (EKF) through both simulations and experiments on a Cassie-series bipedal robot. Filter accuracy is analyzed using motion capture, while a LiDAR mapping experiment provides a practical use case. Overall, the developed contact-aided InEKF provides better performance in comparison with the quaternion-based EKF as a result of exploiting symmetries present in system.more » « less
-
Variational system identification is a new formulation of maximum likelihood for estimation of parameters of dynamical systems subject to process and measurement noise, such as aircraft flying in turbulence. This formulation is an alternative to the filter-error method that circumvents the solution of a Riccati equation and does not have problems with unstable predictors. In this paper, variational system identification is demonstrated for estimating aircraft parameters from real flight-test data. The results show that, in real applications of practical interest, it has better convergence properties than the filter-error method, reaching the optimum even when null initial guesses are used for all parameters and decision variables. This paper also presents the theory behind the method and practical recommendations for its use.more » « less
-
This paper considers the self-localization of a tethered drone without using a cable-tension force sensor in GPS-denied environments. The original problem is converted to a state-estimation problem, where the cable-tension force and the three-dimensional position of the drone with respect to a ground platform are estimated using an extended Kalman filter (EKF). The proposed approach uses the data reported by the onboard electric motors (i.e., the pulse width modulation (PWM) signals), accelerometers, gyroscopes, and altimeter, embedded in the commercial-of-the-shelf (COTS) inertial measurement units (IMU). A system-identification experiment was conducted to determine the model that computes the drone thrust force using the PWM signals. The proposed approach was compared with an existing work that assumes known cable-tension force. Simulation results show that the proposed approach produces estimates with less than 0.3-m errors when the actual cable-tension force is greater than 1 N.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.23919/ACC53348.2022.9867745
