performance analysis of constant speed local obstacle...

2017 NDIA GROUND VEHICLE SYSTEMS ENGINEERING AND TECHNOLOGY SYMPOSIUMModeling & Simulation, Testing and Validation (MSTV) Technical Session

August 8-10, 2017 – Novi, Michigan

PERFORMANCE ANALYSIS OF CONSTANT SPEED LOCALOBSTACLE AVOIDANCE CONTROLLER USING AN MPC

ALGORITHM ON GRANULAR TERRAIN

Nicholas HarausDept. of Mechanical Engineering

Marquette UniversityMilwaukee, WI

Radu SerbanDept. of Mechanical Engineering

University of Wisconsin - MadisonMadison, WI

Jonathan FleischmannDept. of Mechanical Engineering

Marquette UniversityMilwaukee, WI

ABSTRACT

A Model Predictive Control (MPC) LIDAR-based constant speed local obstacle avoidance algorithmhas been implemented on rigid terrain and granular terrain in Chrono to examine the robustness ofthis control method. Provided LIDAR data as well as a target location, a vehicle can route itselfaround obstacles as it encounters them and arrive at an end goal via an optimal route. Using Chrono, amultibody physics API, this controller has been tested on a complex multibody physics HMMWV modelrepresenting the plant in this study. A penalty-based DEM approach is used to model contacts on bothrigid ground and granular terrain. We draw conclusions regarding the MPC algorithm performancebased on its ability to navigate the Chrono HMMWV on rigid and granular terrain.

1 INTRODUCTION

Obstacle avoidance is a crucial capability for Au-tonomous Ground Vehicles (AGVs) of the future.This refers to a ground vehicle’s ability to sense itssurrounding environment, develop an optimal patharound the obstacles in the environment, gener-ate optimal control commands to satisfy that path,and physically navigate around the obstacles safelyand to a desired endpoint. Safety is defined asavoiding collisions as well as enforcing limitations

on excessive sideslip or tire lift-off. An ideal controlalgorithm is one that is capable of pushing a vehi-cle to its performance limits by using knowledge ofits dynamic capabilities and surrounding environ-mental conditions, while still enforcing strict safetyrequirements. Although previous work has demon-strated use of Model Predictive Control (MPC)algorithms for obstacle avoidance on wheeled ve-hicles, more work is required to test the fidelityof these algorithms and determine where improve-ments are needed. One area in which MPC al-

Proceedings of the 2017 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS)

gorithms have yet to be tested is their ability tocontrol a wheeled vehicle on granular terrain. Upto this point, the terrain has been assumed to berigid and flat. Performance of MPC algorithms ondeformable terrain raise additional questions. Dothe current most commonly used vehicle modelsperform successfully within an MPC algorithm ondeformable terrain? The present work evaluates,through numerical simulation, the robustness andvalidity of an MPC algorithm with different vehiclemodels in an environment more similar to what anoff-road military vehicle would experience in com-bat.

The goal of this paper is to present the results ofthis study to understand how model fidelity of thecontroller model affects overall performance of theobstacle avoidance controller. Simulating a vehicleon granular terrain in such scenarios introduces ad-ditional challenges related to the sheer number ofnecessary particles required to properly model thedesired terrain patch. This challenge has been ad-dressed by employing a simulation framework forgranular terrain described later in this paper.

The present study has the following three objec-tives:

1. Study the performance of the MPC Controlleron granular terrain as compared to that onrigid terrain.

2. Analyze the impact of fidelity of the internalcontroller model on speed and performance ofthe obstacle avoidance controller.

3. Showcase the potential of controller testing ina high fidelity virtual test environment withChrono to assist with initial control algorithmdevelopment before physical implementationfor vehicular applications.

The remainder of this paper is organized asfollows. In Section 2 we provide overviews ofthe MPC-based local obstacle avoidance algorithmand the Chrono multiphysics package used as the

test environment. In Section 3 we describe theChrono::Vehicle HMMWV vehicle model used inthis study as the plant model to be controlledand our proposed method for simulating a vehicledriving on deformable terrain over large distances.Then, the specific MPC LIDAR-based local ob-stacle avoidance controller used for this study ispresented. We introduce the different simplified,lower-fidelity analytical vehicle models used in theMPC algorithm to predict the Chrono vehicle be-havior. We also provide descriptions of the testcases considered for this study and a summaryof the metrics used to compare performance ofthe various tested combinations. In Section 4 wepresent the results of the tests outlined in the pre-vious section and provide comparisons when the in-ternal controller vehicle model is varied and whenthe terrain is changed from rigid to granular. Sec-tion 5 wraps up the paper and presents potentialfuture work based on the results of this study.

2 BACKGROUND

2.1 MPC Based Local Obstacle Avoidance

The concept of MPC is to use an internal modelof the system one desires to control to predict andoptimize future system behavior from the currentsystem state and inputs [1]. The system behavioris predicted over some defined finite time horizonand the optimal control sequence over the predic-tion horizon is output. The control sequence isexecuted for an execution time smaller than theprediction horizon, and the whole process is re-peated. The repetition of this process over timecreates a feedback loop which continually controlsthe system, pushing it towards an optimal path.

For this study, the system to be controlled isan AGV. Consider an AGV located in a level en-vironment without roads or any other structuresto guide its motion and assume the AGV has aknown global target position. Between the target

Performance analysis of obstacle avoidance algorithm on granular terrain of 17


Figure 1: Schematic of MPC LIDAR-Based Constant Speed Local Obstacle Avoidance Controller

position and the current vehicle position there mayor may not be obstacles of unknown size. Using theMPC formulation outlined in [2], the vehicle cannavigate from the current position to the providedtarget position while avoiding obstacles as they areencountered. Obstacle information is assumed tobe unknown a priori and only obtained througha planar LIDAR sensor. The MPC schematic ispresented in Fig. 1.

The planar LIDAR sensor, mounted at the frontcenter location of the vehicle, returns the closestobstacle boundary in all radial directions of thesensor at an angular resolution ε. The sensor has amaximum range past which it cannot sense any ob-stacles. Therefore, if the closest obstacle boundaryis greater than the LIDAR radius RLIDAR, then thesensor returns RLIDAR. The LIDAR sensor rangeis [0◦, 180◦], with 90◦ being the vehicle headingdirection. Since the AGV considered here is driv-ing along level ground, whether granular or rigid,a planar LIDAR sensor is sufficient. The sensoris assumed to have no delay and zero noise andcan therefore instantaneously generate a safe areapolygon assembled from the returned points fromthe LIDAR. An overhead view of the AGV encoun-tering an obstacle and the generated LIDAR safearea polygon are presented in Fig. 2.

For the purpose of these simulations, the onlyoutputs of the MPC algorithm are the steering sig-

(a) 3D Visualization of LIDAR Encountering Obstacle

(b) LIDAR Sensed Safe Area

Figure 2: Sample obstacle field and LIDAR output



nals. As shown in Fig. 1, the MPC algorithm ismade up of the internal controller vehicle model,the cost function and constraints, and the dynamicoptimizer. The internal controller vehicle modelpredicts the future states of the AGV for a givensteering sequence. Herein, the internal controllervehicle model is varied from test to test between a2-DOF vehicle model and a 14-DOF vehicle model,as detailed in further sections. Cost functions andconstraints are used to formulate the optimal con-trol problem using the equations from the vehiclemodel, and the resulting optimal control problemis solved using dynamic optimization.

Since the ability of finding and executing an op-timal solution, rather than solution speed, is theprimary focus here, an exhaustive search is used tofind the optimal solution to the problem at hand.With this method, the steering sequence is dis-cretized and a finite set of path possibilities aretested and weighed by a cost function.

2.2 Chrono Multibody Physics Package

The physics modeling and simulation capabilitiesare provided by the multiphysics open-source pack-age Chrono [3]. The core functionality of Chronoprovides support for the modeling, simulation, andvisualization of rigid multibody systems, with ad-ditional capabilities offered through optional mod-ules. These modules provide support for additionalclasses of problems (e.g., finite element analysisand fluid-solid interaction), for modeling and simu-lation of specialized systems (such as ground vehi-cles and granular dynamics problems), or providespecialized parallel computing algorithms (multi-core, GPU, and distributed) for large-scale simu-lations.

2.2.1 Vehicle Modeling

Built as a Chrono extension module,Chrono::Vehicle [4] is a C++ middleware li-brary focused on the modeling, simulation, and

visualization of ground vehicles. Chrono::Vehicleprovides a collection of templates for varioustopologies of both wheeled and tracked vehiclesubsystems, as well as support for modeling ofrigid, flexible, and granular terrain, support forclosed-loop and interactive driver models, andrun-time and off-line visualization of simulationresults.

Modeling of vehicle systems is done in a mod-ular fashion, with a vehicle defined as an assem-bly of instances of various subsystems (suspen-sion, steering, driveline, etc.). Flexibility in mod-eling is provided by adopting a template-based de-sign. In Chrono::Vehicle, templates are parameter-ized models that define a particular implementa-tion of a vehicle subsystem. As such, a templatedefines the basic modeling elements (bodies, joints,force elements), imposes the subsystem topology,prescribes the design parameters, and implementsthe common functionality for a given type of sub-system (e.g., suspension) particularized to a spe-cific template (e.g., double wishbone). Finally, aninstantiation of such a template is obtained byspecifying the template parameters (hardpoints,joint directions, inertial properties, contact mate-rial properties, etc.) for a concrete vehicle (e.g.,the HMMWV front suspension).

For wheeled vehicle systems, templates are pro-vided for the following subsystems: suspension(double wishbone, reduced double wishbone usingdistance constraints, multi-link, solid-axle, McP-hearson strut, semi-trailing arm); steering (Pitmanarm, rack-and-pinion); driveline (2WD and 4WDshaft-based using specialized Chrono modeling ele-ments, simplified kinematic driveline); wheel (sim-ply a carrier for additional mass and inertia ap-pended to the suspension’s spindle body); brake(simple model using a constant torque modulatedby the driver braking input).

In addition, Chrono::Vehicle offers a variety oftire models and associated templates, ranging fromrigid tires, to empirical and semi-empirical models



(such as Pacejka and Fiala), to fully deformabletires modeled with finite elements (using either anAbsolute Nodal Coordinate Formulation or a co-rotational formulation). Driver inputs (steering,throttle, and braking) are provided from a driversubsystem with available options in ChronoVehi-cle including both open-loop (interactive or data-driven) and closed-loop (e.g., path-following basedon PID controllers).

2.2.2 Granular Mechanics

In this work, the focus is on modeling and simu-lating the terrain and the tire-terrain interactionusing high-fidelity, fully-resolved granular dynam-ics simulations, employing the Discrete elementMethod (DEM). Meaningful mobility simulationsrequire large enough terrain patches and smallenough particle dimensions that result in DEMproblems involving frictional contact with millionsof degrees of freedom.

Unlike continuum-based deformable terrainmodeling approaches, DEM treats all componentparticles separately, as distinct entities, by main-taining and advancing in time their states whiletaking into account pair-wise interaction forces dueto frictional contact. Broadly speaking, compu-tational methods for DEM at this scale can becategorized into two classes: penalty-based (alsoknown as a compliant-body approach; denotedhere by DEM-P) and complementarity-based (alsoknown as a rigid-body approach; denoted here byDEM-C). While differing in the underlying formu-lation employed for modeling and generating thenormal and tangential forces at the contact inter-face, and thus leading to different mathematicalmodels and different problem sizes, both meth-ods rely crucially on efficient methods for prox-imity calculation. This common algorithmic stepprovides a complete geometric characterization ofthe interaction between neighboring bodies, takinginto account the current system state and specifi-

cation of the contact shapes associated with allinteracting bodies.

Penalty methods begin with a relaxation of therigid body assumption [5]. A regularization ap-proach, DEM-P assumes local body deformationat the contact point. Employing the finite elementmethod to characterize this deformation would in-cur a stiff computational cost. Instead, an ap-proximation is employed, using information gen-erated during the collision detection stage of thesolution, and the local body deformation is relatedto the depth of inter-penetration between two oth-erwise rigid contact shapes. In order to apply re-sults from Hertz contact theory, valid for sphere-sphere interactions, the contact shapes are furtherapproximated by their local radius of curvature atthe contact point [6]. This approach yields a gen-eral methodology for computing the normal andtangential forces at the contact point. For granu-lar dynamics via DEM-P, the equations of motionneed not be changed. Indeed, normal and tan-gential contact forces are treated as any externalforces and directly factored in the momentum bal-ance. For details on the specific DEM-P implemen-tation in Chrono, see [7]. In this work, we employedthe DEM-P capabilities in Chrono, leveraging themulti-core, OpenMP-based parallelization featuresoffered by the Chrono::Parallel module.

3 TECHNICAL APPROACH ANDMETHODOLOGY

3.1 Full-Vehicle Multibody Model

The model to be controlled (the plant) is a full-vehicle Chrono::Vehicle model of an HMMWV,which includes multi-body subsystems for the sus-pensions, steering, driveline, and powertrain, andis available in the Chrono package.

This vehicle model (see Fig. 3) has a curb weightof 2, 550 kg. It includes independent front andrear double wishbone suspensions and a Pitman



Figure 3: Full-vehicle HMMWV multibody model.

arm steering mechanism. The shock absorber andcoil spring, mounted between the lower control armand the chassis, are modeled with Chrono nonlin-ear force elements and include the effects of bumpstops.

The AWD driveline is modeled using Chronoshaft elements and includes three power split-ting elements (a central differential and front/reardifferentials), as well as conical gears connectedthrough 1-dimensional shaft elements which carryrotational inertia. The powertrain is also modeledusing 1-dimensional shaft elements and includesmodels for a thermal engine specified throughspeed-torque maps for power and engine losses, atorque converter specified via maps for the capac-ity factor and the torque ratio, and an automatictransmission gearbox with three forward gears anda single reverse gear. The connection betweenpowertrain and driveline is a force-displacement in-terface at the driveshaft (with torque applied fromthe powertrain and angular velocity provided bythe driveline).

For mobility studies on deformable terrain, pro-vided that the tire inflation pressure is compara-ble or larger than the average ground pressure,according to the postulate by Wong [8] the tirecan be considered in a so-called rigid regime. As

Figure 4: Relocating Granular Patch that follows thevehicle

such, tire deformation can be ignored and the vehi-cle’s tires modeled using rigid contact shapes. TheHMMWV tire model used here is thus representedby a cylinder with a radius of 0.47 m (18.5 in) anda width of 0.254 m (10 in).

3.2 Relocating Granular Patch

Due to the large-scale nature of the simulationsin this study, generating granular particles dis-tributed across the entire obstacle field is bothcomputationally exhausting and unreasonable. In-stead, we adopt a moving-patch approach. Con-sider an AGV on a large terrain patch of 100 by 100meters. Since we are primarily interested in the ve-hicle behavior and performance and not explicitlyin the terrain behavior, we assume only a smallpatch of granular terrain underneath and aroundthe vehicle is significant. This idea promoted thedevelopment of a relocating granular patch whichenables simulations of a vehicle traversing granularterrain over a large area, without the need to gen-erate particles everywhere throughout that area.

This mechanism allows a user to generate gran-ular particles within a specified distance of the ve-hicle’s CoG. Figure 4 presents the patch of granu-lar terrain underneath the Chrono HMMWV thatmoves with the vehicel. The particles are con-



tained within four rigid walls to prevent them fromescaping the desired terrain area. As the vehi-cle moves across the terrain, this patch maintainsgranular material underneath the vehicle by con-sistently relocating particles that are too far awayfrom it. When the vehicle location comes withina certain predefined distance of any of the walls,a band of particles from the opposite end of thegranular patch are relocated past the closest walland all of the walls are shifted in that direction.Each of these relocation steps keeps the vehicle ontop of granular terrain at all times. Dependingon the vehicle, this granular patch can be resizedfor both computational efficiency and to guaranteethe vehicle maintains a reasonable distance fromthe walls to prevent any boundary effects. Thisnewly developed method of simulating granularterrain for AGV’s is omnidirectional in the groundplane, allowing the vehicle to move in any direc-tion while the terrain patch relocates and respondsto that movement, thus enabling simulations overarbitrarily large areas.

For our simulations, the granular patch wasmaintained at a size of roughly 6.6 by 6.6 meters.This number was assigned as two times the largestdimension of the vehicle. The dimensions of thepatch are not constant, however, since the patchexpands in the direction of relocation by two timesthe largest particle radius every time the advanc-ing wall is shifted. This is done in order to avoidparticle overlap, since the relocated particles aremoved to a position that is shifted one largest par-ticle radius ahead of the particles adjacent to theadvancing wall. After relocation, the walls of thegranular patch are given a recovery velocity suchthat the granular patch regains its original dimen-sions in 0.1 seconds. This recovery time should besmall relative to the duration of the simulations,and in general it will also depend on the velocityof the vehicle, since the granular patch should com-pletely recover its dimensions between subsequentrelocations.

Within the granular patch, the granular terrainwas modeled by 55, 931 uniform spherical particles,with a micro-scale inter-particle sliding friction co-efficient of µ = 0.8, and particle diameter of 0.1 m.Previous studies [9] have shown that a randomlypacked assembly of as few as 3, 000 - 30, 000 uni-form spheres will exhibit macro-scale bulk granularmaterial yield behavior (due to inter-particle slid-ing) that closely matches the Lade-Duncan yieldsurface, which is a well-established yield criterionin the field of geomechanics, where the macro-scalefriction angle φ for the bulk granular material canbe determined as a function of the inter-particlefriction coefficient µ.

Referring to Fig. 10 of [9], a randomly packedassembly of uniform spheres with an inter-particlefriction coefficient of µ = 0.8 will exhibit macro-scale yield behavior corresponding to a bulk gran-ular material with a macro-scale friction angle be-tween roughly 35◦ ≤ φ ≤ 40◦ if particle rotation isallowed (6 DOF particles), or with a macro-scalefriction angle between roughly 65◦ ≤ φ ≤ 70◦ ifparticle rotation is prohibited (3 DOF particles).Since the granular patch used in our simulationscontains more than 50, 000 uniform spheres, wecan reliably conclude that it is accurately mod-eling the yield behavior of a true granular mate-rial on the macro-scale: either with a macro-scalefriction angle of 35◦ − 40◦ if particle rotation isallowed, which is typical of a wide range of drynatural and crushed sands [10]; or with a macro-scale friction angle of 65◦− 70◦ if particle rotationis prohibited, which is typical of crushed or frag-mented rock, such as railway track ballast [11].

We note that in the case of the HMMWV, thevehicle tire width is equal to only approximately2.5 particle diameters in the granular patch. Thisis less than ideal. However, a more suited value of10 particle diameters per tire width would increasethe number of particles in the granular patch tomore than 3 million, which would result in pro-hibitively slow simulations, particularly for events



corresponding to physical time durations on theorder of 10 seconds or more.

3.3 MPC LIDAR-Based Local ObstacleAvoidance

The MPC controller as formulated in [2] is usedfor this study. The cost function and constraintsneed to be specified to avoid collisions with obsta-cles and guarantee vehicle dynamical safety. Theoptimal control problem solved at each MPC timestep consists of the following set of equations:

J = sT + wd (1)

ξ = v [ξ (t) , ζ (t)] (2)

ξ (0) = ξ0 (3)

S [x (t) , y (t)] ≤ 0 (4)

|δf (t)| ≤ δf,max (U0) (5)

|ςf (t)| ≤ ςf,max (6)

t ∈ [0, TP ] . (7)

Equation (1) defines the cost function for thisoptimal control problem. This equation is a softrequirement which defines how the separate pathpossibilities are weighed against each other andhow to determine which path is actually optimal.The cost function is comprised of two terms de-fined as:

sT =

√[xG − x (TP )]2 + [yG − y (TP )]2 (8)

d =

TG∫0

|ς (t)| dt . (9)

Here, sT seeks to minimize the distance betweenthe prediction end-location and the target posi-tion. A prediction path that guides the vehi-cle towards the closest location to the target willhave the smaller sT term. The second term, d,aims to minimize the change in steering angle so

that smoother, straighter paths are preferred overwindy paths. A weighting factor w is used to scalethe influence of d in the total cost.

Equations (2-7) are the constraints for this op-timal control problem and represent hard require-ments for vehicle safety and collision avoidance.Any paths that violate these constraints are notconsidered safe paths and are eliminated as po-tential options in this prediction window. Equa-tion (2) defines a set of differential equations thatdescribe the internal controller vehicle model, withthe initial conditions of Eq. (3).

Equation (4) defines a safe area polygon, con-structed from LIDAR data and including an addi-tional safety buffer to account for vehicle size andto prevent collisions of the vehicle corners. Allpoints along paths found from Eqs. (2)-(3) mustfall inside this safe area polygon.

Equation (5) imposes a maximum limit on thesteering angle, based on vehicle speed. This valueis obtained from a lookup table which can be gen-erated either experimentally or from simulation.Equation (6) imposes a maximum limit on steer-ing rate. Equation (7) defines the time limits overwhich this optimal control problem is solved.

As noted above, Eq. (2) refers to an analyti-cal vehicle model expressed as a set of differen-tial equations which allow the controller to predictvehicle performance within the prediction hori-zon. The accuracy of the internal vehicle controllermodel should directly influence the driven vehicle’scontrolled performance. If the internal vehicle con-troller model poorly predicts a vehicle’s responseto inputs from the driver or the environment, thenthese deficiencies will be witnessed when attempt-ing to control the driven vehicle and result in in-correct trajectories that may lead to collisions. Onthe other hand, a highly complex internal vehi-cle controller model may provide accurate trajec-tory and vehicle response predictions, but with anunacceptable time required to solve the optimalcontrol problem. An ideal controller should not



only accurately predict vehicle responses, but alsodo it quickly enough to insure vehicle safety. Inthis study we consider two separate internal con-troller vehicle models to approximate the dynamicsof the driven Chrono HMMWV vehicle (describedin Section 3.1). The first controller uses a sim-ple 2-DOF vehicle model to predict the trajectoryfor different series of steering sequences and is pre-sented in detail in Section 3.4.1. The second con-troller, described in Section 3.4.2, uses a more com-plex 14-DOF vehicle model. These two models arecompared in their ability to successfully navigatethe driven HMMWV vehicle through two obsta-cle fields, on rigid flat terrain and then granularterrain.

As mentioned previously, exhaustive searchspace [2] is used to solve the optimal control prob-lem at each time step. The steering space is dis-cretized into five possible steering angles, while theprediction horizon is split into four intervals. Thisresults in 625 different steering sequence possibil-ities and therefore 625 different path possibilitiesthat are weighed by the controller to determinethe optimal steering sequence and resulting for-ward path. A sample visualization of the differ-ent predicted trajectories from the 2-DOF modelis presented in Fig. 5 where, for visualization pur-poses, only three steering angles over three inter-vals were considered. A point in polygon algorithmis used to determine which trajectories remain in-side of the safe area polygon visualized in Fig. 2and therefore should be compared to the other pos-sibilities using Eq. (1).

3.4 Internal Controller Vehicle Models

The vehicle models embedded in the MPC are sim-plifications of the full, multi-body based, Chronowheeled vehicle model which is being controlled.We consider two such models, providing differentlevels of fidelity, as described below.

Figure 5: Potential Paths predicted by 2-DOF Inter-nal Vehicle Controller Model

3.4.1 2-DOF Vehicle Model

The standard vehicle model used in recently de-veloped MPC obstacle avoidance algorithms suchas [2] is the 2-DOF yaw plane vehicle model. Thesemodels normally either assume constant corneringstiffness or the nonlinear Pacejka Magic FormulaTire Model [12] to predict the ground tire inter-action forces. For this study, the Pacejka MagicFormula is used to predict tire forces in the vehiclemodels.

A visual representation of the 2-DOF yaw planevehicle model can be found in Fig. 6. The 2-DOFmodel is described by the following first-order or-dinary differential equations:

V = (Fy,f + Fy,r) /M − U0r (10)

r = (Fy,f − Fy,r) /Izz (11)

ψ = r (12)

x = U0 cosψ − (V + Lfr) sinψ (13)

y = U0 sinψ + (V + Lfr) cosψ , (14)

where Fy,f and Fy,r are the lateral tire forces atthe front and rear axles, respectively. U0 and Vare the longitudinal speed and lateral speed of the



Figure 6: 2-DOF Vehicle Model

vehicle in the vehicle’s coordinate frame. ψ is theyaw angle and r is the yaw rate. (x, y) representthe front center location of the vehicle expressedin global coordinates. M is vehicle mass, Izz is themoment of inertia of the vehicle, Lf is the distancefrom the front axle to the vehicle CoG, and Lr

is the distance from the rear axle to the vehicleCoG. For this study, the model is constrained toa constant longitudinal speed. Then the planar3-DOF body with one constraint results in the 2-DOF model used for this study.

3.4.2 14-DOF Vehicle Model

A 14-DOF model is often used in studies such asthese to test the obstacle avoidance controller witha higher fidelity vehicle model [2, 13]. A bene-fit of using the 14-DOF in the controller is themodel’s ability to predict tire liftoff and accountfor dynamic effects from suspension systems. Forthis paper, it is appropriate to also compare per-formance of the local obstacle avoidance controllerrunning an internal 14-DOF on rigid terrain versusgranular terrain.

The 14-DOF vehicle model consists of onesprung mass connected above four unsprung

masses [14]. The sprung mass is allowed to roll,pitch, and yaw while also displacing laterally, ver-tically, and longitudinally. This sprung mass con-tributes six DOF to the model. Each of the fourwheels are allowed to bounce vertically and ro-tate about the wheel horizontal axis. The fronttwo wheels are also free to steer. Each wheel thencontributes two DOF to the fourteen DOF model.The model is constrained at a constant longitudi-nal speed of 8.1 m/s. The equations used for thismodel, as well as their derivation can be foundin [14].

3.5 Evaluation Metrics

Five evaluation metrics will be used to compareone test performance to the other. First, all testruns will be compared based on the time to reachthe target, Ttarget to determine which controllerleads the vehicle to the target point quickest. Sec-ond, the closest distance the vehicle reaches to anyobstacle, dmin, will be measured. Third, the con-trol effort will be calculated and compared betweentest cases. The better test case will have a lowercontroller effort value. Finally, the maximum andaverage lateral accelerations will be calculated andcompared. The accelerations are calculated at thedriver’s position in the chassis. Using the DEM-Pmethod of simulation results in noisy accelerationdata. To address this, acceleration data is filteredto remove noise. These five evaluation metrics pro-vide a consistent methodology for comparing onetest case with another, regardless of the terraintype and underlying analytical controller model.

3.6 Numerical Simulation Setup

Simulations on both rigid and granular terrainwere compared to understand how the controllerperforms on non-ideal surfaces. The two inter-nal controller vehicle models studied in these testswere the previously described 2-DOF and 14-DOFvehicle models. All other controller parameters



Test Terrain Controller VehicleNumber Type Model

1 Rigid 2-DOF2 Rigid 14-DOF3 Granular 2-DOF4 Granular 14-DOF

Table 1: Individual Simulation Test Information

(a) Field 1 (b) Field 2

Figure 7: Obstacle fields.

were kept unchanged over all tests. Referring toTable 1, the effect of model fidelity on controllerperformance was gauged by comparing test 1 with2 and test 3 with 4, for rigid flat and granular ter-rain, respectively. Similarly, comparing test 1 with3 and test 2 and 4 allowed evaluating the perfor-mance of each internal vehicle model on rigid andgranular terrain.

Each of the above four tests consisted of runson two fields with different obstacle distributions.The first one, depicted in Fig. 7a, contains a sin-gle large circular obstacle located along the initial

x y Radius(m) (m) (m)

Field 1Target Location 200.0 0.0 -

Obstacle 1 100.0 0.0 15.0

Field 2Target Location 550.0 0.0 -

Obstacle 1 100.0 0.0 15.0Obstacle 2 200.0 -50.0 30.0Obstacle 3 300.0 55.0 30.0Obstacle 4 425.0 0.0 50.0

Table 2: Obstacle Field Parameters

heading of the vehicle, with the target location ata large distance behind the obstacle. The secondobstacle field (see Fig. 7b) consists of four circu-lar obstacles of varying sizes placed in the vehicle’sinitial heading direction, and provides a more real-istic obstacle-avoidance scenario. Table 2 summa-rizes the obstacle locations and dimensions, as wellas the target location for the above two scenarios.

The following vehicle parameters are maintainedthroughout all of the executed tests. A PID speedcontroller is used to maintain a near constant speedof 8.1 m/s longitudinally for the simulated plantChrono wheeled vehicle. This constant speed is alsoenforced in the analytical models internal to theMPC controller. The LIDAR sensor has a max-imum range RLIDAR = 129.6 m and is sampledinstantaneously at increments of 2.5◦. The vehicleis limited to a maximum steering angle of 10◦, witha maximum steering rate of 70◦/s.

4 SIMULATION RESULTS

This section summarizes the results of the fourtests listed in Table 1.

The trajectories for the four performed tests arepresented in Figs. 8a and 9a, for obstacle fields 1



Test Number 1 2 3 4Controller Model 2-DOF 14-DOF 2-DOF 14-DOFTerrain Rigid Rigid Granular GranularTime to Target (s) 26.67 26.15 28.32 28.03Minimum Obstacle Distance (m) 0.897 5.462 3.491 4.721Controller Effort 0.0340 0.0340 0.0340 0.0306Max. Lateral Acceleration (m/s2) 2.78 1.57 2.47 2.33Avg. Lateral Acceleration (m/s2) 0.54 0.51 0.55 0.46

Table 3: Test Evaluation Metrics Summary on Obstacle Field 1

Test Number 1 2 3 4Controller Model 2-DOF 14-DOF 2-DOF 14-DOFTerrain Rigid Rigid Granular GranularTime to Target (s) 73.85 71.55 76.64 74.70Minimum Obstacle Distance (m) 0.331 2.599 1.083 1.152Controller Effort 0.0510 0.0680 0.0714 0.0612Max. Lateral Acceleration (m/s2) 2.92 2.51 2.55 2.45Avg. Lateral Acceleration (m/s2) 0.41 0.43 0.53 0.58

Table 4: Test Evaluation Metrics Summary on Obstacle Field 2.

and 2, respectively. The associated steering com-mands generated by the controller are presented inFigs. 8b and 9b. The evaluation metrics for eachtest, as defined in Section 3.5, are tabulated foreach obstacle field in Tables 3 and 4.

4.1 Influence of model fidelity

Assessing the effect of internal vehicle model fi-delity on controller performance when the vehiclenavigates on rigid terrain (comparison of tests 1and 2), we make the following observations:

• the 14-DOF model leads to marginally fastertravel to the target location;

• the 2-DOF model leads to trajectories withlower obstacle clearance;

• the two models result in the same controllereffort on the first obstacle course; however, the

higher-fidelity 14-DOF model requires 33%more controller effort on the second obstaclecourse, a consequence of its decision of per-forming a course change to negotiate the lastobstacle;

• the two models result in approximately thesame number of command changes on bothobstacle courses;

• the 14-DOF model results in lower maximumlateral accelerations.

Overall, while the higher-fidelity internal modelleads to marginally better performance, the 2-DOFmodel is perfectly suitable for use in MPC-basedlocal obstacle avoidance on rigid terrain at non-extreme speeds, as it can safely navigate the ve-hicle to its end goal. These results support thefindings and conclusions in [2] even though a dif-ferent AGV is considered here.



(a) Vehicle trajectories.

(b) Steering commands.

Figure 8: Test results on obstacle field 1.

(a) Vehicle trajectories.

(b) Steering commands.

Figure 9: Test results on obstacle field 2.



A similar comparison can be made for the case ofobstacle avoidance on granular terrain (tests 3 and4). As on rigid terrain, the higher fidelity modelleads to faster travel to the end goal, larger clear-ances to the obstacles, and lower maximum lat-eral accelerations. However, on granular terrain,the controller effort required by using the 14-DOFmodel is always lower than that required by the2-DOF model. We again conclude that using ahigher-fidelity internal controller model leads tooverall marginally better performance.

The 2-DOF and 14-DOF internal vehicle mod-els were derived using rigid ground assumptions,yet they are still capable of successfully and safelynavigating the simulated vehicle through an ob-stacle field on granular terrain. The monitoredmetrics indicate a slight drop in controller per-formance when using the 2-DOF model. How-ever, these gains are outweighed by the benefits,in terms of required computational effort, offeredby implementing the lower-fidelity 2-DOF model.

4.2 Influence of terrain type

Turning next to evaluating the 14-DOF internalcontroller model when navigating on rigid versusgranular terrain (comparison of tests 2 and 4), wedraw the following conclusions:

• on both obstacle courses, the target can bereached faster when navigating on rigid ter-rain;

• the resulting trajectories are slightly closer tothe obstacles when navigating on granular ter-rain;

• the required controller effort is lower whennavigating on granular terrain;

• the maximum lateral accelerations are similaron both types of terrain.

A similar analysis can be performed on the 2-DOF model when used to control a vehicle on ei-ther rigid or granular terrain (comparison of tests1 and 3). Unlike the 14-DOF model, the simpler2-DOF model does a better job of approaching theobstacles more closely when controlling a vehicleon rigid rather than on granular terrain. Relatedto this, the controller effort on rigid terrain (test1) is lower than that required on granular terrain(test 3).

The forces the vehicle experiences from drivingon granular terrain can be much different thanforces on simple rigid ground. Examining Figs. 8aand 9a, the vehicle navigating on granular terraindoes not turn as sharply for a given steering com-mand as the vehicle does on rigid ground terrain.To understand the different behavior between a ve-hicle driving on rigid and granular terrain, a para-metric study should be performed analyzing thevehicle driving on a variety of granular terrainswith different granular parameters.

Tests 3 and 4 were performed on granular ter-rain modeled as randomly packed uniform sphereswith an inter-particle friction coefficient of µ = 0.8,diameter of 0.1m, and a macro-scale friction an-gle roughly in the range 65◦ ≤ φ ≤ 70◦, withparticle rotation prohibited. This granular mate-rial resembles railway track ballast. These sametests were attempted on the the same randomlypacked uniform spheres with particle rotation al-lowed resulting in a macro-scale friction angle be-tween 35◦ ≤ φ ≤ 40◦. This granular material re-sembles a dry sand. The results of this second setof tests on dry sand are not plotted or tabulatedbecause the vehicle failed to move from the ini-tial position. Instead, the vehicle spins its wheelsin place at its initial location, making no progressforward as the wheels slowly dig themselves downinto the granular terrain. However, this may bedue to the too large diameter spheres used for thisstudy for computational reasons. Generally theMPC LIDAR-based constant speed local obstacle



avoidance controller used in this study is not ap-propriate for use on all granular terrains. Thereare situations where a combined speed and steer-ing controller similar to that described in [15], oreven some new speed and steering controller whichaccounts for terrain parameters and mobility infor-mation to better predict vehicle movement, wouldbe required. Neither of the models used in thepresent study, the rigid ground 2-DOF yaw planemodel nor the rigid ground 14-DOF vehicle mod-els, were appropriate for predicting vehicle behav-ior and performance on dry sand.

5 CONCLUSIONS

In this study, using the multibody physics packageChrono, we developed a simulation of a HMMWVdriving through a user-specified obstacle field to-wards a defined target location. Within this simu-lation, an MPC LIDAR-based local obstacle avoid-ance controller was implemented to navigate thevehicle around obstacles as it encounters them.The controller uses a simplified analytical vehi-cle model to predict the controlled vehicle stateswithin a finite prediction horizon in order to de-termine the optimal path and steering sequence,forward from the current vehicle state. Two MPCalgorithms were developed, one that uses an un-derlying 2-DOF vehicle model to predict vehiclestates and a second one based on a higher-fidelity14-DOF model. These two controllers were usedto navigate a Chrono HMMWV through two ob-stacle courses, on both rigid and granular terrain.The results were compared to understand the influ-ence of internal vehicle model fidelity on the con-troller performance and to identify improvementsthat need to be made to the MPC LIDAR-basedlocal obstacle avoidance controller to successfullycontrol a vehicle on granular terrain.

The controller using the 14-DOF internal vehi-cle model performs marginally better than the onebased on the 2-DOF vehicle model in all situa-

tions, confirming the findings reported in [2]. How-ever, tests with the 2-DOF controller prove thatthis controller can still successfully navigate a ve-hicle through an obstacle field when the vehicle ismoving at non-extreme speeds. Using the 2-DOFcontroller also allows for faster calculation of op-timal steering sequences, hence better suited fora possible physical implementation with real-timerequirements. As expected, both controllers per-form worse on granular terrain than on rigid ter-rain. This study also highlights the complexitiesintroduced to vehicle control when the terrain isno longer rigid. Examining the vehicle trajecto-ries and lateral accelerations on granular terrain,there are clear differences in tire–ground interac-tions. The granular material parameters affect theturning characteristics of the vehicle, its accelera-tion abilities, and overall vehicle dynamic perfor-mance which is not control predictive with the cur-rently used 2-DOF and 14-DOF analytical vehiclemodels. For consistency with the approach usedin [2], the internal controller models used in thepresent study relied on a Pacejka tire model re-volving on rigid flat terrain. Based on the findingsof this study, it becomes clear that future devel-opments should include in the internal controllermodel an approximation for the deformable ter-rain to more accurately predict the tire – granularterrain interaction.

The results of this study are promising, as itindicates that a controller based on a simplified 2-DOF internal vehicle model is sufficient for predict-ing vehicle behavior and performance well enough,even when the controlled vehicle navigates on de-formable, granular terrain, as long as the granularmaterial characteristics are close to that of rail-road ballast. At the same time, these results alsoemphasize the need for future research relating tovehicle control and simulation on granular terrain,and for further parametric studies on a compre-hensive set of deformable terrains, with differentgranular material characteristics. From there, new



internal analytical model should be investigatedand developed, models that are ideally not morecomplex than the 14-DOF model used here, butthat also take into account granular parameterssuch as the friction angle. From simulations onrailway track ballast and dry sand, this study alsoemphasizes the need for a speed and steering con-troller which uses information about the currentterrain and powertrain to better predict vehicleperformance on a wider variety of terrains.

Acknowledgments

Chrono development was supported in part by U.S.Army TARDEC Rapid Innovation Fund grant No.W911NF-13-R-0011, Topic No. 6a, “Maneuver-ability Prediction”. Support for the developmentof Chrono::Vehicle was provided by U.S. ArmyTARDEC grant W56HZV-08-C-0236.

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