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Physics-based virtual environments for autonomous earthmoving and mining machinery.

Authors:
  • Autonomous Intelligent Driving GmbH

Abstract and Figures

The scientific foundation for constructing virtual environments (VE) that support the development of earthmoving and mining machinery with autonomous capabilities is summarized. It is explained how the physics simulation engine AGX Dynamics support this. Finally, a methodology for computational design exploration of an autonomous load-haul-dump machine in a physics-based VE is described.
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Physics-based virtual environments for
autonomous earthmoving and mining machinery
Martin Servin1,2and Michael Brandl1
1Algoryx Simulation AB, Kuratorvägen 2, SE-90736 Umeå, Sweden
2Umeå University, SE-90187 Umeå Sweden
martin.servin@umu.se
Abstract. The scientic foundation for constructing virtual environ-
ments (VE) that support the development of earthmoving and mining
machinery with autonomous capabilities is summarized. It is explained
how the physics simulation engine AGX Dynamics supports this. Finally,
a methodology for computational design exploration of an autonomous
load-haul-dump machine in a physics-based VE is described.
Keywords: Physics Engine, Autonomous Mining, Multibody, Granular, LHD.
1 Introduction
Increased automation in the eld of earthmoving and mining is important for
economic, environmental and safety reasons. It is however challenging to nd
solutions that are both ecient and robust. The machines move in unstructured
and dynamic environment, and handle fragmented material whose behavior is
dicult to predict. In a physics-based virtual environment it is possible to ex-
plore many alternative solutions in dierent scenarios and generate suciently
large and varied data sets to train autonomous systems. Such a virtual environ-
ment requires reliable physics integrated with computational algorithms for the
many subsystems: mechanics, materials, actuators and sensors. The performance
and precision must be sucient for the intended use. Real-time performance is
often required when the simulation involves human- or hardware in-the-loop.
The virtual environment needs also be modiable with interoperability between
the software and engineering tools used to compose it, so that validated models
are easy to share and reuse within and between organizations.
2 Scientic foundation
Avirtual environment (VE) is a visual interactive computer-simulated world
whose elements have geometric and physical attributes, and evolve according to
a given set of physical laws. To the virtual world there are interfaces in the form
of 3D visualization, signal inputs and outputs for sensors and actuators that are
used for control - that may be manual, semiautonomous or fully autonomous.
The hardware for running VEs range from an ordinary laptop to distributed
over a cluster of powerful computers. It may include advanced VR systems such
as motion platforms and haptic feedback.
VEs are designed to be very general. All possible states and courses of events
that may occur with the given elements can be simulated as long as they are
consistent with the physics laws that are implemented. The core of a VE is a so-
called physics engine. That is a software library with dedicated data structures
and algorithms for representing physical objects, managing their interaction and
solving the dynamic system’s equations of motion to evolve the VE forward
in time. The scientic foundation of modern physics engines for industrial and
scientic applications is described below, with the design and control of earth-
moving and mining machinery particularly in mind.
2.1 Multi-domain nonsmooth multibody dynamics
A physics engine must support faithful multi-domain and multibody dynamics,
while ensuring a fast and stable simulation. The presence of contacts, controllers
and human or hardware in-the-loop means that the connectivity between the
system variables varies frequently and unpredictably during simulation. Artic-
ulated rigid and exible bodies are therefore modeled on descriptor form3and
Lagrangian formulation in terms of dierential algebraic equations (DAEs) [15].
This can be extended to include dynamic models of other physics domains - such
as hydraulics, electronics and drivetrain - and multidomain couplings in terms of
eort and ow variables [19]. Stable numerical steppers, designed to preserve the
fundamental physical invariants, are constructed with discrete-time mechanics
and variational integrators [21]. The integration of the DAEs of motions requires
solving large block-sparse linear systems of equations. This can be done with high
performance codes for direct factorization that exploit parallelism using graph
partitioning and block operations with optimized BLAS3 kernels [25].
It has been realized that contacts, dry friction, limits on joint and actuators
are best treated in terms of inequality constraints and complementarity prob-
lems [28] and considering the time-discrete system as a nonsmooth dynamics
system [1]. This means that velocities may change discontinuously in accor-
dance with some contact and impact law giving rise to impulses that propagate
instantaneously throughout the system. This enables xed-step time integration
with large time-step. Many VEs with heavy machines run with time-step size
120 ms. The alternative is to do exact event detection (in time) or to use ne
enough temporal resolution for all the dynamics to appear smooth and modeled
in terms of continuous DAEs and ordinary dierential equations alone. That is
an intractable approach for full-system simulations of mechatronics system with
any substantial complexity.
The time-stepping subproblem in the nonsmooth dynamics approach be-
comes a nonlinear complementarity problem (NCP) or quadratic programming
problem (QP) in place of nonlinear system of equations. This is often linearized
3All the degrees of freedom are represented and no coordinate reduction is done.
into a mixed complementarity problem (MCP) [12]. The strict computational
budget of most VEs means that one-stage methods of rst or second order are
favored. Popular methods include reformulating the NCP constraint equations
as Fischer-Burmeister or Fischer-Newton NCP function [10], Alart-Curnier func-
tion [2] or proximal (prox) function. The PATH solver [9] has been widely used
in solving MLCPs. Constraint regularization and stabilization are important to
reduce errors that may occur from high-velocity impacts and to improve numeri-
cal solvability [4]. The SPOOK stepper is derived from a variational formulation
of nonholonomic and compliant constraints, and has been proven to be linearly
stable [17]. The regularized constraints may be viewed as Legendre transforms
of a potential or a Rayleigh dissipation function. This enables modeling of ar-
bitrarily sti elastic and viscous interactions in terms of constraint forces with
direct mapping between the regularization and stabilization terms to physical
material parameters. The physics engine AGX Dynamics is one instance of the
described computational technology, summarized in Fig. 1.
,
,,
,
,,,
,,
Constraint compliance potential and dissipation function
Regularization and stabilization mapped to compliance and damping
Fig. 1: The mathematical building blocks of the physics engine AGX Dynamics
- from equations of motion to the discrete-time integrator and its mixed com-
plementarity problem following the contact laws and joint and actuator limits.
2.2 Computational granular dynamics
Rocks and soil are granular matter, which is dened as a large collection of dis-
crete macroscopic particles interacting locally by interfacial contact forces that
are highly dissipative. There is a multitude of methods for simulating these ma-
terials [22]. The widely used discrete element method (DEM) is popular for its
versatility. It can be used for simulating granular matter in all its three phases:
gaseous, liquid as well as solid. With DEM the bulk dynamics emerge naturally
from the collective behavior of the particles with no need for constitutive mod-
eling other than the local contact law and particle properties such as shape,
viscoelasticity and surface friction. When the dynamics of a machine and gran-
ular material are strongly coupled, it is advantageous to treat them both as
nonsmooth dynamics systems to achieve a fast and stable simulation by means
of time-implicit integration. Several versions of nonsmooth DEM (NDEM) have
been provided [24,27] that enable time-step up to 1000 times larger than for
conventional DEM. Each solve is, however, computationally intense, why iter-
ative solvers that may be truncated at a desired precision are preferred. Many
techniques for computational acceleration have been developed [23,29,26,30].
2.3 Computational robotics and machine vision
There is a growing interest in using virtual environments as complement to phys-
ical experiments for machine learning and intelligent task and motion planning
for machines handling objects in a cluttered or rough terrain environments [5].
There are also promising results of using physics driven virtual environments
in-the-loop for object motion tracking [7] and path planning of terrain vehicles
[8]. These motivate integration with software libraries for robotic control and
machine vision, e.g., Robotic Operating System (ROS), OpenCV, Point Cloud
Library (PCL) or VANE [13]. The open source robotics simulation software
Gazebo [16] supports this integration and has a generic physics API.
2.4 Co-simulation
The term co-simulation describes a setup where the full system is composed
of two or more subsystems that share dynamic variables, yet are simulated as
black boxes in a distributed manner. The main reasons for doing co-simulation
are that the subsystems rely on distinct simulation software and solvers, or in
order to avoid disclosing condential models. The subsystems are coupled either
by sharing physical forces at the boundaries or by algebraic constraints. The
Functional Mockup Interface (FMI) [3] provides a tool independent standard
for creating and interconnecting subsystem software components, and several
runtime environments with master steppers are available [11,18].
3 AGX Dynamics
AGX Dynamics from Algoryx Simulation AB is a multi-purpose physics engine
for simulators, VR applications, engineering and scientic simulation of mecha-
tronics, materials and industrial processes. Typical systems include robots, vehi-
cles, cranes and other complex mechanisms found in manufacturing, transporta-
tion, construction and bulk material processing. The customer’s purpose of use
Fig. 2: AGX Dynamics is a multi-purpose physics engine for simulators, VR
applications, engineering and scientic simulation enabling VE:s as stand-alone
simulation application or integration into other software and hardware.
ranges from simulation based design, control and optimization to testing with
human- or hardware-in-the-loop, operator training, sales and marketing.
The software is architectured as a Software Development Kit (SDK), see
Fig. 2. It consists of hundreds of C++ classes of highly optimized and portable
code for integration with simulator software and hardware, or for stand-alone
simulation applications. The core library is oriented around rigid multibody sys-
tems with nonsmooth dynamics, numerical time integration based on SPOOK
[17] and high-performance parallel equation solvers that provide robust and
valid simulations even for systems with extreme loads and mass ratios, kine-
matic loops, redundant constraints, frictional contacts and impulsive dynamics.
A number of library modules support high-level modeling and simulation of ca-
ble and wire, drivetrain, hydraulics, hydrodynamics, granular materials, terrain
and tires. User code can be injected for event handling, virtual sensors, actua-
tors and controllers. Simulations can be authored and managed either directly
through the C++ API, through high-level scripting via Python, C# or Lua, or
through the graphical user interface in the 3D modeling environments AGX Mo-
mentum and the VR and simulator development platform Unity. AGX supports
FMI export and co-simulation with other software tools that support the FMI
standard [3,18]. It also supports direct coupling with Matlab/Simulink.
AGX has both direct and iterative MCP solvers that are tailored for the
sparse linear algebra operations of contacting multibody systems. A hybrid
direct-iterative solver and smart splitting scheme supports the simultaneous use
of both direct and iterative solver kernels for solving dierent parts of the sys-
tem with dierent precision. This enables simulations that combine high per-
formance, accuracy and scalability. This is essential for ecient and reliable
simulation of heavy machinery excavating or transporting granular materials.
The direct solver is applied to the vehicle mechanics and hydraulics and is ex-
act to machine precision, while the scalable iterative solver provides a fast and
approximate solution of the granular dynamics. The coupling can be solved ei-
ther using a direct or iterative method, or a combination. With the NDEM
approach to granular materials, the viscoelastic material parameters can be
mapped to the constraint compliance and damping parameters of the SPOOK
stepper [27]. For small relative contact velocities, or in the limit of small time-
steps, the normal constraint force coincides with the Hertz contact law, i.e.,
GTλk[δ3/2+1/2˙
δ]n, with overlap δ, normal stiness k=E2d/3in
terms of the eective Young’s modulus E, the particle diameter d, and the
viscocity c. NDEM granular sub-systems are solved using a parallel projected
Gauss-Seidel algorithm with domain decomposition. The computational speed
is further accelerated using adaptive model reduction [26] and warmstarting [30].
4 Computational exploration of an autonomous LHD
For demonstration purpose, we describe a method for computational exploration
of an autonomous load-haul-dump (LHD) machine using a virtual environment.
An LHD is a four-wheeled vehicle designed to operate in underground mines
along narrow paths. It has an articulation steering joint that separates the rear
driving unit from the front loading unit, which is equipped with a loading boom
arm and bucket. LHDs are still not fully automated but rely on a human operator
for controlling the loading task, normally by remote. The haul and dump tasks
have been successfully automated, but loading of fragmented rock remains a
challenge [6]. The diculty lies in perceiving the state of the pile, making a
dig plan and controlling the machine movement to ll the bucket in short time,
avoiding damage on the vehicle, and leaving the pile in a state well-suited for
continued loading.
Autonomous loading can be divided into pile analysis, dig planning and mo-
tion control during approach, entry, digging and breakout. We propose using
VEs for systematic exploration of the design space for dig planning and load-
ing control. The method is outlined in Fig. 3. The idea is to rst construct a
detailed simulation model for the rock pile and the machine equipped with sen-
sors, powertrain and actuators, using the method in Fig. 1. The next step is to
provide the system with a generic dig plan and loading control algorithm that
are functions of a set of design variables, x, as well as of the sensor data and
the kinematics of the machine, see Fig. 4. The planned bucket motion depends
on four design variables, x= [α, β, γ, κ], that parametrize the target ll ratio
(α), the dig depth (β), entry point (γ) and bucket curl during lling (κ). One
shallow and one deep dig trajectory, relative to the estimated pile surface, are
indicated in Fig. 4. A large set of simulated loading operations are carried out
with dierent values on the design variable and dierent rock piles. A loading
performance, ϕ(x), is measured in each simulation according to a specied set
of objective functions for the productivity, machine damage and resulting pile
state. A surrogate model is constructed, using the SUMO Toolbox [14], for how
the loading performance depends on the design variables for dig planning and
dig plan
control plan
loading simulation
pile dynamics
machine dynamics
internal sensors
performance
input output
surrogate model
Pareto optimal solutions
Autonomous loading with dig planner and controller
trained on Np piles and Nl simulated loadings
planning
design space
design variable
pile vision &
analysis
machine model
new pile vision &
analysis
response surface
simulation model
design space exploration and multiobjective optimization
Fig. 3: Illustration of the proposed method for computational exploration of dig
planning and loading control with sample results from [20].
loading control. The evaluation time for the surrogate model is negligible com-
pared to the time for physics-based simulation. The surrogate model enables
systematic exploration of the design space and visualization of the response sur-
faces. A set of Pareto optimal solutions can be determined using multiobjective
optimization, for which the genetic algorithm NSGA-II in Matlab’s gamultiobj
is used.
The described method for computational exploration was applied in a recent
study [20] considering the dig planning task for loading at the draw point in
a narrow tunnel (Scenario 1). Nearly 5000 loading cycles where simulated with
a muck pile consisting of approximately 5000 rocks. A surrogate model with
accuracy of 518% was built, analysed and a set of Pareto optimal solutions for
the dig plan design variables were found. Sample results are shown in Fig. 3 and
videos are found at http://umit.cs.umu.se/loading. The objective function
for damage was based on critical twisting forces in the joint connecting the boom
and the bucket. The objective function for the resulting pile state was based on
the amount of rock spill in front of the pile. A set of dig planning design variables
where identied that combine high productivity with low damage and rock spill.
These variables correspond to shallow dig trajectories, attempting to overll the
bucket by 30 %, applying a large bucket curl and entering the pile at a point
compute loading perforance
(x)
(x)
x
x
x
x
y
y
Fig. 4: Illustration of automated loading and algorithm for force-based control.
The operations that depend on the design variable are colour highlighted.
with center of mass closer to the front. Force-based loading control was not used
in [20] and the present powertrain model is more evolved.
The LHD is modelled as a rigid multibody system consisting of 18 bodies
and 24 joints, primarily hinge and prismatic constraints with joint limits on the
extensions of hydraulic cylinders. The geometry, mass and powertrain charac-
teristics are those of a Sandvik LH6214, which has an operating weight of 56
tonnes, is 12 m long and 3 m wide. The key bodies are listed in Fig. 5, where
the LHD and the powertrain system are also illustrated.
The rock pile is modeled as contacting rigid bodies of dierent convex shapes
and size. The material parameters are listed in Fig. 5. Two scenarios are created.
Scenario 1 represents loading at the draw point in the end of a narrow tunnel
where the pile stretches further back and up [20]. Scenario 2 is a pile in front
of a static wall. For vision, a virtual 3D imaging device is assumed mounted on
top of the machine. The 3D imaging sensor consists of a simulated camera and
a laser scanner modeled as a point-based source of rays with angular density of
about 1K rays per steradian and a point-based receiving unit placed 100 mm
from the source. The sensor outputs 2D images from the simulated camera as
well as a 3D point cloud in the coordinate system of the mine. Sample data is
displayed in Fig. 6. A pile analysis algorithm transforms the points representing
a pile surface into a mass distribution from which the center of mass can be
estimated and projected to the pile front on the ground to obtain a pile entry
point to which the LHD can be steered.
4Sandvik Technical Specication LH621-18,http://unitedminingrentals.com/pdf/
trucks/LH621.pdf and 3D model from https://www.cgtrader.com/3d-models/
vehicle/industrial/sandvik-underground-loader-toro- 0011.
power
distribution
system
ω
rl
ω
d
ω
d
ω
fl
d
df
hp
dhpshpb
em
dems
ω
fr
gb hm
ω
m
emb
em
power
distribution
system
Fig. 5: Illustration of the LHD, equipped with a 3D vision sensor (center point
and view frame illustrated) and electric-hydraulic power distribution system.
The described method for computational exploration can also be applied to
the loading control only. For this purpose a simple force-based loading control
algorithm, mimicking the more sophisticated admittance control [6], was de-
veloped and examined. The idea, illustrated in Fig. 4, is to control the bucket
motion based on the wheel slip and pile resistance, measured as the moving av-
erage [fl(t)]τof the lift cylinder force over a time window tτto t. The pile
resistance increases as the LHD enters the pile. This may cause loss of traction.
If any wheel starts spinning, [ωij]τ> ωspin , the boom lifting is activated to in-
crease the normal and traction force until the wheel spinning ceases. The bucket
tilting is activated when the force in the lift cylinder exceeds a threshold. This
is to prevent excessive slip, bucket under- or overlling and prolonged loading
time. The bucket tilting is held constant while [fl(t)]τ> fmin cbcMbcgacc and
otherwise ωbt(t) = ωmax
bt (1 fmin/[fl(t)]τ), where Mbc is the loading capacity
of the bucket and cbc is determined experimentally and considered as a control
design variable in addition to ωmax
bt .
A simplied electric-hydraulic powertrain model is assumed to distribute
the total available power, Pmax =Pmax
d(t) + Pmax
s(t) + Pmax
b(t), to the sub-
systems for drive (d), articulated steering (s) and for lifting and tilting the
bucket (b). The power limits may be distributed dierently during entry of
the pile, bucket lling and breakout. Each actuator is modeled by an eort
constraint, e.g., εmλm+ωm=ωtarget
m(t)for the hydraulic motor driving the
Fig. 6: The imaging sensor produce a 2D camera image (top left) and a 3D point
cloud (middle and lower left). A pile analysis algorithm transform the surface
points into a mass distribution that is input to a dig planning algorithm.
motor shaft at target target speed ωtarget
m(t)that is set by the control system
(or operator). The applied torque and power, τm=λmand Pm=τmωm, depend
on the dynamics of the full system and follow from the numerical computations
carried out by the physics engine, as described in Fig. 1. The hydraulic motor
is assumed to be fed by hydrostatic transmission, with hydraulic pump (hpd),
and an electric motor (emd) such that the total power for actuating the motor
shaft is Pd=ηdepmPmwhere ηdepm is the combined energy eciency of the
power transmission between the electric motor and hydrostatic transmission.
A gearbox (gb) couples the motor shaft to the main drive shaft and provides it
with velocity and torque pair [ωd, τd]and with gear ratio constraint ωd=cgbωm.
The drive shaft is then connected to the four wheel axes with angular velocity
[ωfl, ωf r , ωrl , ωrr ]via a front and rear dierential (ddand dr) modeled by the
constraints ω+ωfr =ωdand ωrl +ωrr =ωd. A power limit, Pmax
d, on the
drive system thus translates to a constraint limit |λm| ≤ Pmax
ddepmωm. The
articulated steering is similarly modeled as an actuator that attempts to drive the
articulation joint at a desired rotational speed (ωs) given a limit on the constraint
multiplier, |λs| ≤ Pmax
ssepcωs, set by available power for steering and eciency
ηsepc of the electric motor (ems) and hydraulic pump (hps). The loading unit
connects the boom arm and bucket through a Z-bar linkage mechanism with one
hydraulic cylinder for lifting (l) the boom and one for tilting (t) the bucket. The
two cylinders share the power supplied by a hydraulic pump (hpb) and electric
motor (emb). This is modeled as two linear actuators with eort constraint
εbiλbi+vbi=vtarget
bi(t)with i=l,t. Since the two actuators share a common
power source, the constraint limits are |λbi| ≤ (Pmax
bPbj)b epmvbi for j̸=i
and actuator power Pbi =λbivbi. The joints and actuators are equipped with
force sensors and motion encoders producing signals for controlling the machine.
Three samples of simulations for Scenario 2 with dierent control design
variables, x= [cbc, ωmax
bt ]are presented in Fig. 7. The bucket lling was measured
to 8.7,11.0and 12.7tonnes, the respective loading time 10,11 and 12 s. The lift
bucket fill
8.7 ton
0 2 4 6 8 10 12
t [s]
0
0.5
1
1.5
force [N / 106]
-0.1
0
0.1
0.2
0.3
extension [m]
[cbc,max
bt ] = [2.0,0.4]
fl(t)
cyllift(t)
cyltilt(t)
bucket fill
11.0 ton
0 2 4 6 8 10 12
t [s]
0
0.5
1
1.5
force [N / 106]
-0.1
0
0.1
0.2
0.3
extension [m]
[cbc,max
bt ] = [4.0,0.35]
fl(t)
cyllift(t)
cyltilt(t)
bucket fill
12.7 ton
0 2 4 6 8 10 12
t [s]
0
0.5
1
1.5
force [N / 106]
-0.1
0
0.1
0.2
0.3
extension [m]
[cbc,max
bt ] = [8.0,0.3]
fl(t)
cyllift(t)
cyltilt(t)
Fig. 7: Dierent design variable, [cbc, ω max
bt ], give dierent bucket lling and load-
ing time. The right subplots show the cylinder extension and force.
force and cylinder extensions, as function of time, are also shown in Fig. 7. The
respective peak force value in the lift cylinder was 750,1000 and 1300 kN. The
most aggressive loading caused wheel slip that was eciently reduced by the
lifting of the boom for increased traction, but the loading time was nevertheless
prolonged. The target speed into the pile was 1m/s. Videos from simulations
can be accessed from http://umit.cs.umu.se/LHD.
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... This enables simulations that combine high performance, accuracy and scalability. This is essential for efficient and reliable simulation of systems where the reaction force from the particulate material on the machinery doing transport and processing affect the dynamics of the machine such that it cannot be represented by a kinematic model [8,9]. ...
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