Proprioceptive-only State Estimation for Legged Robots with Set-Coverage Measurements of Learned Dynamics
Authors: Abhijeet M. Kulkarni, Ioannis Poulakakis, Guoquan Huang
Organizations: Department of Mechanical Engineering, University of Delaware, Newark, DE, USA · Robotics Institute, Athena Research Center, Marousi, Greece; School of Mechanical Engineering, National Technical University of Athens, Greece; HERON–Center of Excellence in Robotics, Athens, Greece
Proprioceptive-only state estimation is attractive for legged robots since it is computationally cheaper and is unaffected by perceptually degraded conditions. The history of joint-level measurements contains rich information that can be used to infer the dynamics of the system and subsequently produce navigational measurements. Recent approaches produce these estimates with learned measurement models and fuse with IMU data, under a Gaussian noise assumption. However, this assumption can easily break down with limited training data and render the estimates inconsistent and potentially divergent. In this work, we propose a proprioceptive-only state estimation framework for legged robots that characterizes the measurement noise using set-coverage statements that do not assume any distribution. We develop a practical and computationally inexpensive method to use these set-coverage measurements with a Gaussian filter in a systematic way. We validate the approach in both simulation and two real-world quadrupedal datasets. Comparison with the Gaussian baselines shows that our proposed method remains consistent and is not prone to drift under real noise scenarios.
Figures & tables
Fig. 1: Proposed method uses set-coverage measurements for update.
Fig. 2: Prediction error et of the learned velocity predictor for Vision60 on the training trajectory (green) versus a test trajectory (red).
Fig. 3: A single calibrated coverage statement can remain valid for both training (green) and test (red) error distributions.
Fig. 4: Illustration of the KL-minimal belief update with a coverage constraint. (a) Prior with πt<γ . (b) Exact KL-optimal posterior: piecewise rescaling of the prior inside/outside Ct . (c) Gaussian approximation obtained by moment matching.
Samples
Timing (ms)
Prob. Error
Mean Error
Cov. Error
100
0.0125
3.12e-4
1.03e-1
2.32e-1
500
0.0372
8.07e-5
2.10e-2
6.72e-2
1000
0.0664
2.00e-5
1.48e-2
3.14e-2
5000
0.302
5.33e-6
3.46e-3
6.46e-3
10000
0.532
1.06e-6
2.06e-3
3.20e-3
(Ref.) 1e7
818.23
0
0
0
TABLE I: Runtime–accuracy for truncated-moment computations.
γ
RMSE (m) (unbiased/biased)
NEES pos (unbiased/biased)
EKF update
–
0.6133±0.2546/2.3298±1.4016
3.1139±2.5023/99.8873±121.1403
Set-coverage update
0.70
0.9063±0.3111/2.9453±1.0126
2.5220±1.1528/1.8621±1.3769
0.75
0.8500±0.2590/2.8397±1.2102
3.5934±2.4633/3.0924±3.6713
0.80
0.9402±0.2702/2.6030±1.3559
4.8568±2.4530/1.9772±2.6391
TABLE II: Unbiased/Biased noise Monte Carlo comparison.
Fig. 5: β -mixing coefficients for Vision60 (a) and Spot (b) calibration data.
Fig. 6: Two of the representative trajectories of the Spot dataset and with comparison with the baselines.
Fig. 7: Two of the representative trajectories of the Vision60 dataset and with comparison with the baselines.
Robust and accurate proprioceptive state estimation of the main body is crucial for legged robots to execute tasks in extreme environments where exteroceptive sensors, such as LiDARs and cameras, may become unreliable. In this paper, we propose DogLegs, a state estimation system for legged robots that fuses the measurements from a body-mounted inertial measurement unit (Body-IMU), joint encoders, and multiple leg-mounted IMUs (Leg-IMU) using an extended Kalman filter (EKF). The filter system contains the error states of all IMU frames. The Leg-IMUs are used to detect foot contact, thereby providing zero-velocity measurements to update the state of the Leg-IMU frames. Additionally, we compute the relative position constraints between the Body-IMU and Leg-IMUs by the leg kinematics and use them to update the main body state and reduce the error drift of the individual IMU frames. Field experimental results have shown that our proposed DogLegs system achieves better state estimation accuracy compared to the traditional leg odometry method (using only Body-IMU and joint encoders) across various terrains. We make our code and datasets publicly available to benefit the research community (https://github.com/YibinWu/DogLegs).
Yibin Wu, Jian Kuang, Shahram Khorshidi +4
Center for Robotics, University of Bonn, Germany · GNSS Research Center, Wuhan University, China · Humanoid Robots Lab, University of Bonn, Germany +1
In this paper, we propose a method that applies Inertial-Leg (IL) tokenization to an attention-based network for proprioceptive state estimation in legged robots. Unlike existing learning-based state estimators that concatenate all sensor measurements into a single flat vector, the proposed architecture represents inertial measurements and leg-wise measurements as individual tokens and uses an attention mechanism to learn the relative importance of each measurement.This design allows the network to reweight each measurement according to the current contact condition, reflecting the fact that the reliability of forward kinematic measurements depends on whether the corresponding foot is in contact. Unlike conventional contact-aided estimators, however, the proposed method learns this behavior without relying on an explicit contact estimator or on explicit measurement updates based on a stationary contact assumption. To validate the proposed method, we conducted experiments on a Unitree Go1 robot, including debris terrain not modeled in simulation and gait patterns not seen during training. Experimental results show that the proposed method achieves better estimation performance than existing learning-based state estimators under unseen gait patterns and also improves performance over contact-aided model-based methods.
Young-Rang Seo, Hajun Kim, Sangmin Kim +2
Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon 34141, Republic of Korea.
Legged robots carry an IMU, but the inertial solution drifts because consumer-grade IMUs are noisy. However, the feet create intermittent contacts with the environment that can be used to mitigate that drift. This report develops a sequence of increasingly expressive legged robot state estimators that leverage this. In all cases, the floating-base state comprises attitude, position, velocity, and IMU biases. To model foot contacts, we start from the contact-aided invariant EKF of Hartley et al., albeit at a reduced contact update rate. This is then augmented by replacing the measurement update by a small factor graph. Finally, we turn the same factors into a fixed-lag smoother with contact-episode footholds, with and without an evolving IMU bias. To facilitate reproducibility and further research in proprioceptive legged odometry, all four variants are available in GTSAM (Dellaert et. al), and we additionally provide a ROS2-compatible implementation.