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Proprioceptive Invariant Robot State Estimation

Tzu-Yuan Lin, Tingjun Li, Wenzhe Tong, Maani Ghaffari

TL;DR

This work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots.

Abstract

This paper reports on developing a real-time invariant proprioceptive robot state estimation framework called DRIFT. A didactic introduction to invariant Kalman filtering is provided to make this cutting-edge symmetry-preserving approach accessible to a broader range of robotics applications. Furthermore, this work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots, enabling a significant capability on a variety of robotics platforms to track the robot's state over long trajectories in the absence of perceptual data. Extensive real-world experiments using a legged robot, an indoor wheeled robot, a field robot, and a full-size vehicle, as well as simulation results with a marine robot, are provided to understand the limits of DRIFT.

Proprioceptive Invariant Robot State Estimation

TL;DR

This work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots.

Abstract

This paper reports on developing a real-time invariant proprioceptive robot state estimation framework called DRIFT. A didactic introduction to invariant Kalman filtering is provided to make this cutting-edge symmetry-preserving approach accessible to a broader range of robotics applications. Furthermore, this work dives into the development of a proprioceptive state estimation framework for dead reckoning that only consumes data from an onboard inertial measurement unit and kinematics of the robot, with two optional modules, a contact estimator and a gyro filter for low-cost robots, enabling a significant capability on a variety of robotics platforms to track the robot's state over long trajectories in the absence of perceptual data. Extensive real-world experiments using a legged robot, an indoor wheeled robot, a field robot, and a full-size vehicle, as well as simulation results with a marine robot, are provided to understand the limits of DRIFT.
Paper Structure (53 sections, 2 theorems, 47 equations, 11 figures, 6 tables)

This paper contains 53 sections, 2 theorems, 47 equations, 11 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Contributions
  3. Outline
  4. Literature Review
  5. Symmetry in Robot State Estimation
  6. Legged Robots
  7. State Estimation
  8. Contact Estimation
  9. Wheeled Robots
  10. Marine Robots
  11. Preliminaries and notation
  12. Process Dynamics on Lie Groups
  13. Associated Noisy System
  14. Invariant Observation Model
  15. Invariant Kalman Filtering
  16. ...and 38 more sections

Key Result

Theorem 1

A system is group affine if the dynamics, $f_{u_t}(\cdot)$, satisfies: for all $t>0$ and $X_1, X_2 \in \mathcal{G}$. Furthermore, if this condition is satisfied, the right- and left-invariant error dynamics are trajectory-independent and satisfy:

Figures (11)

  • Figure 1: Estimated trajectory from DRIFT overlapped with the satellite image at the University of Michigan North Campus. A Clearpath Robotics Husky robot was driven on the sidewalk for $55$ minutes, with a total path of around 3 kilometers. Consuming proprioceptive measurements only, DRIFT can produce highly accurate estimations for long-horizon operations. This experiment demonstrates the potential of DRIFT to be a reliable odometry system in perceptually degraded situations.
  • Figure 2: DRIFT takes measurements from an IMU and encoders as inputs. The angular velocities and linear accelerations are used in the propagation model. The encoder measurements are passed through kinematic functions and applied in the correction model. Two optional modules, a contact estimator and a gyro filter, are provided for low-cost robots to enhance their performance.
  • Figure 3: Left: The configuration of an MIT Mini Cheetah robot for contact data collection. Right: Different terrain types in the contact data set.
  • Figure 4: The estimated trajectories from DRIFT using different contact estimation methods on the Mini Cheetah data set. The robot walks on a grassy field with a motion capture system, which is used for ground truth capturing. With the proposed contact estimator, DRIFT produces the best trajectory. Contrarily, the two baseline methods introduce significant drift in the height ($z$) axis. This figure is generated with the aid of the Python package evo grupp2017evo.
  • Figure 5: A Fetch robot used in the indoor experiments. The figure shows the robot at the Department of Naval Architecture and Marine Engineering on the University of Michigan campus. Fetch is a differential drive robot that is commonly used for indoor service robot research.
  • ...and 6 more figures

Theorems & Definitions (4)

  • Definition 1: Left and Right Invariant Error
  • Theorem 1: Autonomous Error Dynamics barrau2017invariant
  • Theorem 2: Log-Linear Property of the Error barrau2017invariant
  • Remark 1