Extended Kalman Filter (EKF) SLAM for Duckiebots

Project Resources

Objective: Implement an Extended Kalman Filter (EKF) SLAM system to estimate accurate Duckiebot pose and landmark positions in Duckietown environments.
Approach: Fuse odometry and AprilTag landmark detections using EKF to achieve robust localization and mapping for small-scale autonomous Duckiebots.
Authors: Amir Hossein Zamani, Léonard Oest O'Leary, Kevin Lessard from the University of Montreal.

Project highlights

In SLAM, everything that can drift will drift, and the role of the filter is to drift more slowly than entropy.

Extended Kalman Filter (EKF) SLAM system architecture overview — Figure 1. EKF-SLAM Architecture Overview

Extended Kalman Filter (EKF) SLAM input and output fusion diagram — Figure 2. Extended Kalman Filter (EKF) SLAM input and output flow diagram

Extended Kalman Filter (EKF) SLAM odometry before incorporating landmarks — Figure 5. Odometry before incorporating landmarks

Extended Kalman Filter (EKF) SLAM improved versus simple interpolation for trajectory estimation — Figure 6. EKF-SLAM Trajectory Interpolation

The equations describe how the Duckiebot's position and orientation (x,y,θ) evolve over time based on its linear velocity (v) and angular velocity (ω). — Figure 7. EKF's prediction-correction workflow

The diagrams illustrates the coordinate transformations and the pose estimation workflow. — Figure 9. EKF-SLAM AprilTags Pose Estimation

The visual illustrates the EKF's prediction-correction workflow, showing how odometry data predicts the next state and April tag measurements refine it. By iteratively fusing these data sources, the EKF achieves accurate localization and mapping, even under noisy or incomplete sensor inputs. — Figure 10. EKF-SLAM Motion Model Equations

Figure 11. EKF-SLAM full version (motion+measurement model)

Figure 12. EKF-SLAM measurement model (without motion model)

Figure 13. EKF-SLAM motion model (without measurement model)

Figure 14. Pose estimation using a circular interpolation

Figure 15. Pose estimation using a circular interpolation_DELTA_TIME=2

Figure 16. Pose estimation using a linear interpolation

Figure 17. Pose estimation using a linear interpolation_DELTA_TIME=2

: Figure 1. EKF-SLAM Architecture Overview

: Figure 2. Extended Kalman Filter (EKF) SLAM input and output flow diagram

: Figure 3. Incorporating landmarks into the odometry problem

: Figure 4. Odometry after incorporating landmarks

: Figure 5. Odometry before incorporating landmarks

: Figure 6. EKF-SLAM Trajectory Interpolation

: Figure 7. EKF’s prediction-correction workflow

: Figure 8. EKF-SLAM AprilTags Detection

: Figure 9. EKF-SLAM AprilTags Pose Estimation

: Figure 10. EKF-SLAM Motion Model Equations

: Figure 11. EKF-SLAM full version (motion+measurement model)

: Figure 12. EKF-SLAM measurement model (without motion model)

: Figure 13. EKF-SLAM motion model (without measurement model)

: Figure 14. Pose estimation using a circular interpolation

: Figure 15. Pose estimation using a circular interpolation_DELTA_TIME=2

: Figure 16. Pose estimation using a linear interpolation

: Figure 17. Pose estimation using a linear interpolation_DELTA_TIME=2

Extended Kalman Filter (EKF) SLAM for Duckiebots - the objectives

This SLAM-Duckietown project addresses a famous challenge in robotics: concurrently estimating the agent’s pose and mapping the environment under uncertainty.

This project implements an Extended Kalman Filter (EKF) SLAM algorithm on Duckiebots (DB21-J4), combining odometry from wheel encoders and landmark observations from April tags.

The objective is to maintain an evolving posterior over the Duckiebot’s pose (x,y,θ) and landmark positions by recursively integrating noisy control inputs and observations.

This upgrade shifts Duckiebots from open-loop dead reckoning units into closed-loop, state-estimating agents. For Duckietown, it reinforces its use as an experimental ground for real-world robotics challenges, including data association, observability, filter consistency, and multi-sensor fusion.

The challenges and approach

The system applies the EKF-SLAM pipeline in two stages: motion prediction and measurement correction.

Prediction propagates the robot’s belief through a non-holonomic kinematic model under process noise, using arc-based interpolation to reduce discretization error.

Correction incorporates April tag detections via a Perspective-n-Point (PnP) solution, updating the state with landmark-relative observations under observation noise. The state vector grows dynamically as new landmarks are observed, and the covariance matrix tracks both robot and landmark uncertainty.

The technical challenges include maintaining filter consistency under linearization errors, ensuring landmark observability despite partial fields of view, and synchronizing asynchronous data from wheel encoders, camera frames, and Vicon ground-truth captures.

Moreover, AprilTag detection is constrained by lighting artifacts and pose ambiguity at shallow viewing angles, introducing non-Gaussian errors that the EKF must approximate linearly.

Moreover, tuning noise parameters presents the classical tradeoff: too little noise leads to overconfidence and divergence; too much noise leads to filter paralysis. Deployment exposes the systemic difference between simulation and physical experiments: real Duckiebots do not move with perfect kinematics, cameras suffer from radial distortion, and computation suffers from non-deterministic latency.

In SLAM, everything that can drift will drift, and the role of the filter is to drift more slowly than entropy.

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Extended Kalman Filter (EKF) SLAM for Duckiebots: Authors

AmirHossein Zamani was a former Duckietown student, and currently, he is pursuing his Ph.D. in Computer Science at Mila (Quebec AI Institute) and Concordia University, Canada. He is also working as an AI Research Scientist Intern at Autodesk in Montreal, Canada.

Léonard Oest O’Leary was a former Duckietown student, and currently, he is pursuing his Master of Science in Computer Science at the University of Montreal, Canada.

Kevin Lessard was a former Duckietown student, and currently, he is pursuing his Master of Science in Machine Learning at Mila – Quebec AI Institute in Montreal, Canada.

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Duckietown is designed to teach, learn, and do research: from exploring the fundamentals of computer science and automation to pushing the boundaries of knowledge.

These spotlight projects are shared to exemplify Duckietown’s value for hands-on learning in robotics and AI, enabling students to apply theoretical concepts to practical challenges in autonomous robotics, boosting competence and job prospects.