We present a highly effective approach for the calibration of vehicle models. The approach combines the output error technique of system identification theory and the convolution integral solutions of linear systems and stochastic calculus. Rather than calibrate the system differential equation directly for unknown parameters, we calibrate its first integral. This integrated prediction error minimization (IPEM) approach is advantageous because it requires only low-frequency observations of state, and produces unbiased parameter estimates that optimize simulation accuracy for the chosen time horizon. We address the calibration of models that describe both systematic and stochastic dynamics, such that uncertainties can be computed for model predictions. We resolve numerous implementation issues in the application of IPEM, such as the efficient linearization of the dynamics integral with respect to parameters, the treatment of uncertainty in initial conditions, and the formulation of stochastic measurements and measurement covariances. While the technique can be used for any dynamical system, we demonstrate its usefulness for the calibration of wheeled vehicle models used in control and estimation. Specifically we calibrate models of odometry, powertrain dynamics, and wheel slip as it affects body frame velocity. Experimental results are provided for a variety of indoor and outdoor platforms.

Abstract-When GPS, or other absolute positioning, is unavailable, terrain-relative velocity is crucial for dead reckoning and the vehicle's pose estimate. Unfortunately, the positiondenied accuracy of the inertial navigation system (INS) is governed by the performance of the linear velocity aiding sources, such as wheel odometry, which are typically corrupted by large systematic errors due to wheel slip. As a result, affordable terrestrial inertial navigation is ineffective in estimating position when denied position fixes for an extended period of time. For mobile robots, the mapping between inputs and resultant behavior depends critically on terrain conditions which vary significantly over time and space which cannot be pre-programmed. Past work has used Integrated Perturbative Dynamics (IPD) to identify successively systematic and stochastic models of wheel slip, but treated the pose filter only as input without improving the odometry measurements used for vehicle navigation. We present a unique approach of a predictive vehicle slip model in a delayed state extended Kalman filter. The relative pose difference between the current state and delayed state is used as a measurement update to the vehicle slip model. These results create an opportunity to compensate for wheel slip effects in terrestrial inertial navigation. This paper presents the design, calibration, and verification of such a system and concludes that the position-denied performance of the compensated system is far superior.

The motions of wheeled mobile robots are largely governed by contact forces between the wheels and the terrain. Inasmuch as future wheel-terrain interactions are unpredictable and unobservable, high performance autonomous vehicles must ultimately learn the terrain by feel and extrapolate, just as humans do. We present an approach to the automatic calibration of dynamic models of arbitrary wheeled mobile robots on arbitrary terrain. Inputs beyond our control (disturbances) are assumed to be responsible for observed differences between what the vehicle was initially predicted to do and what it was subsequently observed to do. In departure from much previous work, and in order to directly support adaptive and predictive controllers, we concentrate on the problem of predicting candidate trajectories rather than measuring the current slip. The approach linearizes the nominal vehicle model and then calibrates the perturbative dynamics to explain the observed prediction residuals. Both systematic and stochastic disturbances are used, and we model these disturbances as functions over the terrain, the velocities, and the applied inertial and gravitational forces. In this way, we produce a model which can be used to predict behavior across all of state space for arbitrary terrain geometry. Results demonstrate that the approach converges quickly and produces marked improvements in the prediction of trajectories for multiple vehicle classes throughout the performance envelope of the platform, including during aggressive maneuvering.

Abstract-This paper presents an online approach to calibrating vehicle model parameters that uses the integrated dynamics of the system. Specifically, we describe the identification of the time constant and delay in a first-order model of the vehicle powertrain, as well as parameters required for pose estimation (including position offsets for the inertial measurement unit, steer angle sensor parameters, and wheel radius). Our approach does not require differentiation of state measurements like classical techniques; making it ideal when only low-frequency measurements are available. Experimental results on the LandTamer and Zoë rover platforms show online calibration using integrated dynamics to be fast and more accurate than both manual and classical calibration methods.

We present an approach to the problem of real-time identification of vehicle motion models based on fitting, on a continuous basis, parametrized slip models to observed behavior. Our approach is unique in that we generate parametric models capturing the dynamics of systematic error (i.e. slip) and then predict trajectories for arbitrary inputs on arbitrary terrain. The integrated error dynamics are linearized with respect to the unknown parameters to produce an observer relating errors in predicted slip to errors in the parameters. An Extended Kalman filter is used to identify this model on-line. The filter forms innovations based on residual differences between the motion originally predicted using the present model and the motion ultimately experienced by the vehicle. Our results show that the models converge in a few seconds and they reduce prediction error for even benign maneuvers where errors might be expected to be small already. Results are presented for both a skid-steered and an Ackerman steer vehicle.