A Digital Twin based Approach to Structural Mechanics: New

Perspectives for Robotics in Forestry and Beyond

Dorit Kaufmann, Tobias Osterloh and Jürgen Rossmann

Institute for Man-Machine Interaction at RWTH Aachen University, Ahornstrasse 55, 52074 Aachen, Germany

Keywords: Finite Element Analysis (FEA), Digital Twin (DT), Holistic Simulation Framework.

Abstract: Computational simulations are nowadays crucial for the development of any complex mechatronic system.

This holds especially true when it comes to robots acting in a highly dynamic environment, such as robots

used as mobile machinery in forestry. The ever changing loads acting on these robots result from different

weather conditions, ground stability, leverage forces of falling trees during cutting etc. Thus, the structural

layout of the robot is rather sophisticated. Nevertheless, it is usually done once in the beginning of the design

process and the dynamic loads can only be estimated, leading to huge safety margins. Regarding the ecological

consequences every operation in forestry involves, it is of uttermost importance not only to do a neat structural

design, but also to computationally analyse the mobile machinery directly in its actual environment. This

work proposes a Digital Twin (DT) based approach to structural mechanics. Every feature of the environment

(every tree, the soil etc.) as well as the robot itself can be represented by a DT. An existing Rigid Body

Dynamics (RBD) is used to record all acting forces and momentums during an operation. They serve as input

for a Finite Element Analysis (FEA) thus enabling a holistic simulation framework.

1 INTRODUCTION

Forestry is an important branch of economics for

many countries such as Canada, US, Germany, the

Baltic and the Scandinavian countries. While the

requirements for improvements in mobile machinery

for timber harvesting are the same as for any other

robot regarding mechanics, electrics, communication

etc., there is one further aspect that needs to be

considered and which is of utmost importance: the

direct impact on the environment of every work step.

Interesting challenges arise in the mechanical

layout of mobile machinery for forestry, as it interacts

with an ever-changing and sometimes even “hostile”

environment, and – even more important – the

ecological consequences of this interaction have to be

considered and optimized to sustain a strong, healthy

forest for future generations.

While the planning of e.g. thinning strategies and

the manual hand-on work is usually done by

experienced forest workers who take ecological

consequences into account, powerful tools are

required to create concrete guidelines further

automation can follow to determine specific actions.

Thus, using computational simulation is inevitable

for improvements in forestry. Nowadays, there are

many sophisticated and tested tools to consider both

ecological and economical aspects in forestry, some

of them even creating a whole “Virtual Forest”.

The design of mobile machinery for forestry (such

as harvesters, forwarders etc.) highly benefits from

these simulation frameworks, since it reduces

otherwise tremendous prototyping costs of any such

complex robot with relatively small number of units.

Despite the continuous progress in simulation

technology, it remains difficult to optimize the

robotic layout, as the estimation of dynamic loads is

challenging due to e.g. different soil conditions and

high leveraging forces of falling trees. Thus, the

structural design of the robot is usually still carried

out with forces that are assumed to occur during the

application and hence have accordingly huge safety

margins, leading to unnecessary large weight or

limitation in the applications.

This work presents a Digital Twin (DT) based

approach to structural mechanics, where structural

simulations are performed directly after a work step

is executed in the Virtual Forest, where all

environmental aspects and different application

scenarios may be taken into account. During this

process, Rigid Body Dynamics (RBD) calculates the

actual dynamic loads serving as an input for a Finite

274

Kaufmann, D., Osterloh, T. and Rossmann, J.

A Digital Twin based Approach to Structural Mechanics: New Perspectives for Robotics in Forestry and Beyond.

DOI: 10.5220/0012755500003758

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2024), pages 274-280

ISBN: 978-989-758-708-5; ISSN: 2184-2841

Element Analysis (FEA). Following this approach,

DTs become the crystallization point in the design

and engineering process.

To test this concept, an exemplary application

scenario of a harvester cutting a tree was examined

(see Fig. 1).

2 RELATED WORK

The need for simulation in forestry was recognized

many years ago. The improvements in mobile

machinery for forestry and the awareness for

environmental consequences following their usage

grew simultaneously, leading to new thinning and

reforestation strategies (Rautio et al, 2023). Thus,

there are nowadays powerful computational tools to

describe forestry processes. The Virtual Forest is one

of these concepts. It combines aerial survey

technologies, aspects of Virtual Reality and robotics

to simulate an actual existing forest and the ongoing

forestry in all its facets (Rossmann et al, 2009).

Some authors focus on quantifying the economic

and ecological consequences of certain forestry

operations with mobile machinery (Losch et al,

2017), but a lot of research is done to improve the

mobile machinery itself. In (Cheng et al, 2023) a

more general point of view on agricultural robots is

presented, while in (Visser et al, 2021) especially

automation for harvesting operations is considered,

stating that the software requirements for an

autonomous felling robot are still in their infancies.

The approach developed in the presented work

uses DTs. DTs are seen as a core feature of Industry

4.0, but the general concept has expanded to nearly

all engineering applications. The authors of (Negri et

al, 2017) give an overview of several different

definitions of DTs. The way of defining and using

them in this work is similar as described in (Atorf et

al, 2018), where DTs represent their real twins and

“are brought to life” by multi-domain 3D simulation

systems.

The interaction of RBD and FEA becomes more

and more important with decreasing safety margins

and complex robots working in highly dynamic

environments (e.g. man-machine interaction). Thus

there is a wide range of views on this subject: either

rather theoretical ones, that deal with the mathematics

of coupling (Busch, 2012) and ways of combining the

different underlying models (Kaufmann et al, 2018)

or approaches being developed for one single

application, as “classical” robotics (Chung et al,

2010) or automotive engineering (Dietz et al, 2001).

3 KEY METHODS

In order to perform structural design for robots used

as mobile machinery in forestry, the two principles of

RBD and FEA need to be captured by the DT. Both

form the mathematical and computer scientific base

for this work and thus will be briefly explained in the

following section.

3.1

Structural

Simulations via Finite

Element Analysis (FEA)

FEA is a validated and sophisticated method for

structural mechanics, described in many textbooks,

e.g. (Bathe, 1996). External influences serve as input

variables (forces, temperature, etc.) in order to

calculate the behaviour of the structure

(deformations, stresses, temperature distributions,

etc.) as output variables. The material and the shape

of the examined structure set the relation between

both.

First, the structure is meshed and hence

mathematically discretized, i.e. divided into m

individual elements. Nodes connect these elements.

During the so-called preprocessing, boundary

conditions (BCs) are defined in the form of loads and

supports. The next step of solving describes the

solution of the mathematical problem, which can be

simplified as follows:



𝒌

𝟏

⋱

𝒌

𝒎

⋅

𝒖

𝟏

⋮

𝒖

𝒎



𝒇

𝟏

⋮

𝒇

𝒎

≡𝒌⋅𝒖

𝒇

(1)

Here, u



describes the displacement of the

elemental nodes of element i, 𝒇

𝒊

is the corresponding

acting force and the matrix entries 𝒌

𝒊

reflect material-

Figure 1: Real-life application scenario for the developed

concept and implementation: A harvester is cutting a tree.

The DT of the mobile machinery builds the base fo

enhanced structural mechanics.

A Digital Twin based Approach to Structural Mechanics: New Perspectives for Robotics in Forestry and Beyond

275

specific elastic moduli. In descriptive terms, during

the solution, all external acting forces must be

translated into deformations, while the nodes couple

neighbouring elements to move accordingly. Thus, a

system of coupled differential equations is created,

which in general cannot be solved analytically. The

crucial parameters for numerical solving have also

been specified during the preprocessing (required

accuracies of the solution, termination criteria, etc.).

Depending on the complexity of the model and the

computing power used, the calculation of the solution

requires a few seconds up to several weeks.

Afterwards, the results can be visualized and

analysed in the subsequent postprocessing.

3.2 Rigid Body Dynamics (RBD)

The simulation of RBD is a well-established tool for

the development and analysis of mechanical systems.

Depending on the use case, several approaches like

the Composite-Rigid-Body Algorithm (generalized

coordinates) (Featherstone, 2012) and the 𝐽𝑀𝐽𝑇

approach (maximal coordinates) (Baraff, 1996) are

applied. RBD aims for a macroscopic simulation of

the system, replicating the kinematic and dynamic

properties of the system. In addition, several

extensions to RBD exist, allowing for a simulation of

deformable objects and compliant mechanisms

(Bender et al, 2014). The approaches are capable of

visually replicating structural deformations but are

not yet sufficient for the realization of high-fidelity

DTs, since the fundamental models are just

simplifications of the structural properties of the

bodies and do not provide the required level of detail.

The envisaged coupling of RBD with detailed

FEA poses some requirements on the pursued RBD

simulation approach. The RBD simulation must

allow for detailed introspection capabilities in order

to capture the bearing forces within the system, which

will then be passed to the FEA simulation.

Additionally, the implicit interaction of a DT with its

environment must be possible, setting this DT-based

approach apart from other simulation approaches like

Modelica or Simscape. (Both only allow to describe

the explicit interaction – e.g. joints – between bodies.

Collisions have to be modelled explicitly, which is

not feasible for DTs interacting with complex

environments.)

Consequently, we build upon a rigid body

simulation in maximal coordinates, following the

𝐽𝑀𝐽𝑇 approach. The kinematic constraints are

described by position-based constraints C and are

implemented by the constraint Jacobian 𝐽= 𝜕𝐶/𝜕𝑥 ,

forcing the relative velocity of two connected rigid

bodies at the joint position to zero, see (2).

𝐽

⋅𝑥=0

(2)

This way, complex systems can be described

easily. For each joint within the system, additional

lines are added to the Jacobi matrix J. Based on the

kinematic constraints captured by the Jacobi matrix 𝐽,

the constraint forces λcan be calculated by an

impulse-based approach (Stewart et al, 2000), see (3).

-



⋅dt ⋅

J ⋅ [x+ M

-

⋅ dt ⋅





]=b

(3)

The mass matrix is described by 𝑀, the external

forces (e.g. gravitation) are described by 𝑓



and

finally the vector 𝑏 is used for stabilization purposes

(Baumgarte, 1972).

The interactions of the DT with its environment

(i.e. contact forces and friction) are realized based on

complementarity constraints, resulting in a Linear

Complementarity Problem (LCP) (Anitescu et al,

1997). Therefore, a slack variable 𝑎 is introduced to

the right side of (3), allowing to formulate the

complementarity condition (4).

𝑎≥0 , 𝜆



≥0 , 𝑎⋅𝜆



(4)

Either two colliding bodies are separating (𝑎>0)

and no contact force needs to be applied

(𝜆



= 0), or a contact exists (𝑎=0) and a

contact force prevents penetration of both colliding

rigid bodies

(

𝜆



)

The final building block in the RBD tool chain is

the handling of kinematic loops. Kinematic loops

introduce redundant constraints to the simulation,

resulting in a reduced row rank of the Jacobi matrix

𝐽. Consequently, the system matrix 𝐴= 𝐽𝑀



𝐽



becomes singular and (3) will not have a unique

solution for the constraint forces 𝜆. In order to cope

with such singular systems and achieve an

unambiguous solution for the constraint forces 𝜆, a

Constraint Force Mixing based regularization of the

system matrix 𝐴 is performed (Smith, 2019).

Subsequently, a small amount of compliance is

introduced to the simulated system that can be

controlled by the magnitude of the regularization

parameter, resulting in an efficient calculation of the

inverse dynamics problem.

Once the constraint forces 𝜆 are calculated, the

forward dynamics can be solved.

M ⋅x







⋅

(5)

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

276

Applying this simulation approach allows to

efficiently analyse the dynamic loads occurring when

a DT interacts with its environment. The

introspection to the bearing loads is given by default

and thus allows to effortlessly generate the required

inputs for a detailed FEA of arbitrary structures

within the DT.

4 CONCEPT: ENABLING A

HOLISTIC SIMULATION

FRAMEWORK

Every single operation in forestry (such as cutting a

tree, reforestation, etc.) is subject to a forestry plan.

In this way it is ensured, that both economic and

ecological aspects are taken into account. The

different work steps are favourably done with mobile

machinery, whose structural design has been defined

with the help of FEA (see left side of Fig. 2). Today,

there are sophisticated simulation methods to

examine the outcome an operation will have and thus

to estimate its economic and ecologic consequences.

As both the robot itself and the environment are rather

complex and highly interact with each other, there are

many different aspects to consider. Thus, all of them

and their connections should be represented virtually,

creating a whole “Virtual Forest” (Rossmann et al,

2009). Every part of the system gets a DT. This holds

true for e.g. every tree, the ground, stones, the forestry

workers, and of course the mobile machinery. With

this, one can answer specific questions (e.g. “Is it

possible to cut this tree if the harvester is in this

position?”) and develop whole forestry strategies

(e.g. “If we want our forest to have this structure and

tree assortment in X years, what do we need to do

now?”).

Nevertheless, this already very elaborated picture

is still missing a direct link to the structural design of

the deployed robots. In general, the structural layout

of a robot is created with the help of FEA. The forces

and torques required to perform a structural analysis

are usually estimated or based on real life experience

of other structures. But the loads in a forest are highly

dynamic, due to weather conditions, leverage effects

of falling trees, ground stability etc. The ultimate

value for structural design is the safety for the present

forestry workers and the durability of the robot.

Thus, a neglect of structural analyses for an

individual operation leads to omission of possibilities

on the one hand (“this tree could have been cut, as the

estimated leverage effect was to high due to its actual

shape of the treetop”) or a to high ecological impact

on the other hand (“the used mobile machinery could

have been way lighter, thus the soil is unnecessarily

compressed”).

In this work, a concept was developed to do a

more flexible and neater structural design, as RBD is

performed for the DT of the mobile machinery and

the recorded loads serve as input for a FEA. Thus, a

holistic simulation framework is enabled.

As the actual dynamic loads are considered, this

builds a solid foundation for optimizations (of the

robot and work processes) and finally even

automation, as specific instructions for every

situation can be defined from the holistic simulation

framework (see right side of Fig. 2).

Please note, that the general concept also holds

true for completely different fields of application,

where complex robots encounter highly dynamic

environments (such as robots collaborating with

humans or space robotics).

Figure 2: Comparison of a classic sequential design and

engineering process for forestry (a) and the developed

interlaced concept building on DTs and a Virtual Forest (b):

usually a forestry plan leads to the individual operations,

which are performed with mobile machinery. The robots

were developed beforehand, where the structural design

was based on assumptions (a). There already exist

elaborated simulation tools to virtually represent this

workflow: the mobile machinery is represented as DT in the

Virtual Forest. The new concept adds structural design to

this scheme (left side of b)), thus enabling a holistic

simulation framework, which finally allows to do

optimization and automation (right side of b)).

5 REALIZATION VIA A DIGITAL

TWIN (DT)

In context of this paper, we present an in-depth

analysis of a harvester that is used to cut and segment

trees in forestry applications. The analysis is focused

on systems level mechanical aspects and detailed

structural analysis of selected elements. We created a

Forestry Plan

(thinning strategies)

Virtual Forest

Individual Operations

(cut this tree)

Mobile Machinery

(harvester)

leads to

Structural Design

(FEA)

determines

Forestry Plan

(thinning strategies)

Individual Operations

(cut this tree)

Digital Twin

(harvester)

Structural Design

(FEA)

enables

Holistic

Simulation

Framework

Possibilities for optimization and automation

a) b)

A Digital Twin based Approach to Structural Mechanics: New Perspectives for Robotics in Forestry and Beyond

277

virtual test scenario that highlights the interaction of

the harvester with its environment (i.e. cutting trees).

The DT of the harvester is shown in Fig. 3. It

consists of a detailed RBD model that models the

relevant parts of the harvester. The mechanical model

is parametrized according to estimated masses and

information provided by CAD data. The kinematics

of the crane and harvesting head are also extracted

from CAD data. Since we are not interested in the

hydraulic design of the crane, we can neglect the

hydraulic aspect in the DT and approximate the

hydraulic cylinders by two actuated rigid bodies. In

addition, we did not model the actuators based on

external forces 𝑓



but based on constraints

𝐽⋅ 𝑥= 𝑣



imprinting a desired velocity 𝑣



to the system. This way, it is easy to realize desired

motions of the crane without the need to emulate the

control software, leading to a more efficient DT.

Figure 3: DT of a Harvester.

Since the mechanical stresses in the telescope arm are

expected to cause the most structural stress on the

crane, we decided to analyse these stresses in detail.

Therefore, the bearing forces and torques are

measured in a RBD simulation and are injected to the

FEA at defined injection points, as shown in Fig. 4.

We intentionally realized a unidirectional coupling,

since the expected deformations will be very small,

and the material will either withstand the mechanical

loads or burst entirely. This way, complex and

computationally demanding bidirectional coupling

between RBD and FEA can be avoided.

Figure 4: Interface between RBD Simulation and FEA

Simulation.

In addition to the DT of the harvester, we realized

a DT of a forest environment (as shown in Fig. 5).

The Virtual Forest is built from GIS data. In the direct

neighbourhood of the harvester, the trees have been

replaced by their DTs, meaning that they include a

full RBD model approximating their collision shape

and mass distribution. The interaction between the

harvesting head and the trees is described by a spring-

damper model with Coulomb friction, approximating

contact and friction forces. Additionally, the ground

contact of the harvester is modelled by individual

spring-damper models and Coulomb friction

allowing to roughly estimate the mechanical stress to

the soil surface.

By fusing all DTs in a holistic scenario, we are

able to simulate the interaction of the harvester with

its environment via contact forces and friction. This

way, the dynamic loads that occur during cutting a

tree can be simulated and predicted easily. Emerging

from these DTs, we are able to realize the intended

application.

6 EXAMPLE APPLICATION

SCENARIO: DISPLACEMENTS

ON CRANE DURING

HARVESTING

In order to test not only the DTs, but also the whole

concept, a specific application scenario was chosen.

As it is displayed in Fig. 5, the harvester is cutting and

segmenting a tree in the holistic simulation

framework.

Figure 5: DT of a harvester in a forest environment cutting

a tree.

Fig. 6 shows the forces and torques calculated by

RBD on the top end of the last crane arm segment,

which were taken as input for the FEA (see Fig. 4).

Several points of the recorded curves (green

arrows in Fig. 6) can be assigned clearly to specific

SIMULTECH 2024 - 14th International Conference on Simulation and Modeling Methodologies, Technologies and Applications

278

work steps of the task shown in the lower row of Fig.

7. First of all, there is a time span without any

recognizable forces on the crane arm, when the

harvester is moving to a suitable position for cutting

the tree (point 1 in Fig. 6 and Fig. 7). Then there are

two force peaks: one, when it’s connecting to

(“hitting”) the tree and the second one, when the

cutting is done and the tree falls over (point 2). This

is where a huge torque is starting to be recorded, as

the tree is now hold horizontally by the harvester.

During the segmentation process, this torque (and the

force) declines, as the leverage effect decreases with

an ever shorter tree trunk (point 3).

As expected, the deformation of the crane arm

segment behaves accordingly (upper row of Fig. 7)

with no deformation without force (point 1), a

deformation peak at point 2 during the cutting and a

slightly deformation during the segmentation process

(point 3).

It has to be clarified again, that this application

scenario is exemplary and e.g. no hydraulic effects

were considered, thus the results of the FEA are

qualitatively right, but cannot be quantified.

Nevertheless, if the missing information is provided

(e.g. by the manufacturer), this can be easily

implemented. This is another advantage of the

realization via DT, as the same model gets more and

more sophisticated while using the same holistic

simulation framework.

Figure 7: The upper row shows different deformations of

the crane arm. As this was an exemplary study, the results

are qualitatively and not absolutely. The time points 1, 2, 3

from Fig. 6 can be directly assigned to characteristic actions

of the harvester and the resulting deformations of the crane.

Furthermore, it is even possible to focus on different

aspects of the Virtual Forest in this small example:

from an ecological point of view, the impact on the

environment might be analysed as compression of the

ground or destruction of the undergrowth. On the

other hand, for economics, it might be interesting to

collect all information about the cut tree or to

examine, whether a neighbouring tree was damaged

during the process. The respective focus can be easily

analysed by choosing different visualization styles,

while the underlying simulation stays the same: e.g.

Fig. 5 for the ecological point of view and Fig. 7 for

the economic one.

7 CONCLUSION

In this work, a holistic simulation framework was

enabled by taking a DT based approach to structural

mechanics. This concept leads to a more profound

structural design of robots in highly dynamic

environments, as the underlying FEA may be

performed directly after a certain operation is done

virtually. This is achieved by creating DTs of the

robot itself and the whole environment and

calculating the explicit forces acting on the robot with

the help of RBD.

Especially in forestry, neat structural layout is

crucial, as any operation with mobile machinery has

not only economic consequences, but might have a

huge ecological impact as well. Thus, in this work,

the developed concept was directly interlaced with a

Virtual Forest and an exemplary application scenario

of a harvester cutting and segmenting a tree was

successfully performed.

Figure 6: Recorded forces and torques for joint 1 during the

performed task of cutting and segmenting a tree. (The x-

axis is displaying simulation time and therefore without

unit). The green arrows mark specific points in time (see

Fig. 7).

A Digital Twin based Approach to Structural Mechanics: New Perspectives for Robotics in Forestry and Beyond

279

8 OUTLOOK

In future work, the execution of the developed

concept could be automated and – subject to the

condition that required computing time and hardware

is available – made bidirectional concerning RBD and

FEA. This would allow to perform parameter studies,

do even more sophisticated optimizations or to

integrate continuative concepts such as structural

health monitoring.

Even more important, there will be a sophisticated

test of the presented work during an upcoming

project. The involved industry partner will build a

completely new type of harvester crane and its

structure is designed with the help of the developed

holistic simulation. As all preliminary work is done,

real life data (exceeding simple experiments) will

directly be used to further analyse this ansatz,

quantify its limits and validate the concept and

implementation in general.

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