A Data-driven Contact Estimation Method for Wheeled-Biped Robots

TL;DR

This work tackles ground-contact estimation for wheeled-biped robots using only inexpensive sensors, addressing the lack of dedicated contact hardware. It introduces a data-driven Bayesian filter that combines a nonparametric KDE-based measurement model, learned from real knee and wheel torque data, with a transition model learned online from vertical accelerometer signals, formalized through a recursive belief update on the binary state $S_t\in\{C,\lnot C\}$. Key contributions include (i) a learned measurement pipeline via KDE, (ii) a transition model that separates switch events from directionality using IMU spectra and median-frequency features, (iii) extensive real-robot and simulation validation showing improved accuracy and sample efficiency over a deep-learning baseline, and (iv) an open-source implementation for the Upkie platform. The approach demonstrates robust contact estimation under realistic noise levels, enabling reliable state estimation and control for wheeled-biped locomotion without dedicated contact sensors.

Abstract

Contact estimation is a key ability for limbed robots, where making and breaking contacts has a direct impact on state estimation and balance control. Existing approaches typically rely on gate-cycle priors or designated contact sensors. We design a contact estimator that is suitable for the emerging wheeled-biped robot types that do not have these features. To this end, we propose a Bayes filter in which update steps are learned from real-robot torque measurements while prediction steps rely on inertial measurements. We evaluate this approach in extensive real-robot and simulation experiments. Our method achieves better performance while being considerably more sample efficient than a comparable deep-learning baseline.

Figures (5)

• Figure 1: Robustly detecting the moments when a wheeled-biped robot makes and breaks contact is crucial for successful estimation and control. This paper proposes a contact estimator based only on inertial and torque measurements. The measurements are fed into a novel Bayesian filter formulation to robustly estimate the binary contact state. We validate our results extensively both in simulation and real-world experiments, as depicted in the bottom figure.
• Figure 2: Overview of the estimation pipeline. We use Bayesian filtering to estimate the posterior probability $P(S_t|\mathbf{m}_{0:t})$ of being in contact state $S_t$ given measurements $\mathbf{m}_{0:t}$. Internally, measurement probabilities $P(\mathbf{m}_t | S_t)$ are estimated by kernel density estimation (KDE) from knee and wheel torque sensors, while transition probabilities are estimated from IMU measurements through frequency analysis.
• Figure 3: Results of modeling torque measurements $\mathbf{m}_t$ in contact ($C$) and no-contact ($\lnot C$) states. The left two plots show the Gaussian KDEs fit to vectors of absolute knee and wheel torques $\mathbf{m}_t \in \mathbb{R}^2 : (\tau_{\text{knee}}, \tau_{\text{wheel}})$. The contact likelihood model is normalized by the marginal likelihood by assuming a flat $\overline{\text{bel}}(S_t)$ at each timestep. This gives a simple non-recursive "Measurement Only" model to estimate the contact probability directly, without any dependence on the history or prior beliefs (right-most plot).
• Figure 4: The Bullet environment used to collect contact data. The robot was driven down a flight of steps, each with a height of 0.25. The captured IMU and proprioceptive readings were used to evaluate the contact estimator against noise.
• Figure 5: Robustness study with respect to measurement noise in simulation. The heatmap shows the overall success rate of the estimator under different noise levels (standard deviation of zero-mean Gaussian measurement noise). On its right, we provide a detailed study for two representative noise settings, highlighted with black rectangles. We zoom in on the robot rolling down one step (z-coordinate in world frame shown in green) and show, from left to right, the ground truth (top) and noisy (bottom) torque measurements, the resulting contact probabilities, the STFT of the ground truth (top) and noisy (bottom) accelerometer data (including power and median frequency), and the resulting transition probabilities.