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.