Neal Seegmiller

Vehicle model identification by integrated prediction error minimization

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.

Aiding off-road inertial navigation with high performance models of wheel slip

When GPS, or other absolute positioning, is un-available, terrain-relative velocity is crucial for dead reckoning and the vehicles pose estimate. Unfortunately, the position-denied 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.

Optical flow odometry with robustness to self-shadowing

An optical flow odometry method for mobile robots using a single downward-looking camera is presented. The method is robust to the robots own moving shadow and other sources of error. Robustness derives from two techniques: prevention of feature selection on or near shadow edges and elimination of outliers based on inconsistent motion. In tests where the robots shadow dominated the image, prevention of feature selection near shadow edges allowed accurate velocity estimation when outlier rejection alone failed. Performance was evaluated on two robot platforms and on multiple terrain types at speeds up to 2 m/s.

A Vector Algebra Formulation of Mobile Robot Velocity Kinematics

Typical formulations of the forward and inverse velocity kinematics of wheeled mobile robots assume flat terrain, consistent constraints, and no slip at the wheels. Such assumptions can sometimes permit the wheel constraints to be substituted into the differential equation to produce a compact, apparently unconstrained result. However, in the general case, the terrain is not flat, the wheel constraints cannot be eliminated in this way, and they are typically inconsistent if derived from sensed information. In reality, the motion of a wheeled mobile robot (WMR) is restricted to a manifold which more-or-less satisfies the wheel slip constraints while both following the terrain and responding to the inputs. To address these more realistic cases, we have developed a formulation of WMR velocity kinematics as a differential-algebraic system—a constrained differential equation of first order. This paper presents the modeling part of the formulation. The Transport Theorem is used to derive a generic 3D model of the motion at the wheels which is implied by the motion of an arbitrarily articulated body. This wheel equation is the basis for forward and inverse velocity kinematics and for the expression of explicit constraints of wheel slip and terrain following. The result is a mathematically correct method for predicting motion over non-flat terrain for arbitrary wheeled vehicles on arbitrary terrain subject to arbitrary constraints. We validate our formulation by applying it to a Mars rover prototype with a passive suspension in a context where ground truth measurement is easy to obtain. Our approach can constitute a key component of more informed state estimation, motion control, and motion planning algorithms for wheeled mobile robots.

A Unified Perturbative Dynamics Approach to Online Vehicle Model Identification

The motions of wheeled mobile robots are governed by non-contact gravity forces and 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.

Online calibration of vehicle powertrain and pose estimation parameters using integrated dynamics

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.

Control of a passively steered rover using 3-D kinematics

This paper describes and evaluates a 3-D kinematic controller for passively-steered rovers. Passively-steered rovers have no steering motors, but rely on differential wheel velocities to change the axle steer angles. This passive steering design is reliable and efficient but more challenging to control than powered steering designs, especially when driving on rough terrain. A controller based on 2-D kinematics fails to accurately maintain the desired trajectory when traversing obstacles. The presented 3-D kinematic controller uses inertial and proprioceptive sensing to modify commanded steer angles and wheel velocities, greatly improving steering accuracy. Validation in simulation and physical experiments is presented. These results are significant because they establish the viability of the passive-steering configuration for precise navigation.

Modular Dynamic Simulation of Wheeled Mobile Robots

This paper presents a modular method for 3D dynamic simulation of wheeled mobile robots (WMRs). Our method extends efficient dynamics algorithms based on spatial vector algebra to accommodate any articulated WMR configuration. In contrast to some alternatives, our method also supports complex, nonlinear wheel-ground contact models. Instead of directly adding contact forces, we solve for them in a novel differential algebraic equation (DAE) formulation. To make this possible we resolve issues of nonlinearity and overconstraint. We demonstrate our method’s flexibility and speed through simulations of two state-of-the-art WMR platforms and wheel-ground contact models. Simulation accuracy is verified in a physical experiment.

Recursive kinematic propagation for wheeled mobile robots

The problem of wheeled mobile robot kinematics is formulated using the transport theorem of vector algebra. Doing so postpones the introduction of coordinates until after the expressions for the relevant Jacobians have been derived. This approach simplifies the derivation while also providing the solution to the general case in 3D, including motion over rolling terrain. Angular velocity remains explicit rather than encoded as the time derivative of a rotation matrix. The equations are derived and can be implemented recursively using a single equation that applies to all cases. Acceleration kinematics are uniquely derivable in reasonable effort. The recursive formulation also leads to efficient computer implementations that reflect the modularity of real mechanisms.

Enhanced 3D Kinematic Modeling of Wheeled Mobile Robots

Most fielded wheeled mobile robots (WMRs) today use basic 2D kinematic motion models in their planning, control, and estimation systems. On uneven or low traction terrain, or during aggressive maneuvers, higher fidelity models are required which account for suspension articulations, wheel slip, and liftoff. In this paper we present a simple, algorithmic method to construct 3D kinematic models for any WMR configuration. We also present a novel enhancement to predict the effects of slip on bodylevel motion. Extensive experimental results are presented to validate our model formulation. We show odometry improvement by calibrating to data logs and modeling 3D articulations. We also show comparable predictive accuracy of our enhanced kinematic model to a full dynamic model, at much lower computational cost.