Research Article

International Journal of Advanced

Robotic Systems
January-February 2018: 1–11
The synthesis of a segmented ª The Author(s) 2018
DOI: 10.1177/1729881417749470
stair-climbing wheel journals.sagepub.com/home/arx

Vladimir Mostyn , Vaclav Krys , Tomas Kot,

Zdenko Bobovsky and Petr Novak

Abstract
The article describes the process of development of an essentially new wheel suitable both for moving on flat ground and
for travelling on stairs. The stair-climbing wheel is composed of rotary circular segments arranged around a shared carrier
with arms to form a complete circular profile of the wheel adapted for moving on flat ground; for travelling on stairs,
individual segments are rotated by an appropriate angle to touch down tangentially on the stepping surface of the stairs.
The dimensions of individual segments, the centre of rotation of individual segments and the angle of their partial turn have
been chosen so that the length of the arc along which the circular segment rolls is equal to the length of the stepping
surface of an average stair, and, at the same time, the circular segment touches down tangentially on the stepping surface
while the wheel turns around the edge of the previous segment. Using the rotation angle of the turnable segments, the
wheel can be adapted to the height of non-standard stairs. The segments can be inclined in both directions for bidirec-
tional movement of the wheel up and down the stairs. An undercarriage equipped with these wheels can be used in the
field of exploratory robots and for the transportation of persons and materials on stairs.

Keywords
Locomotion, mobile robot, mechanism design, conceptual design, stair-climbing wheel

Date received: 28 July 2017; accepted: 20 November 2017

Topic: Special Issue – Mobile Robots

Topic Editor: Nak-Young Chong
Associate Editor: Michal Kelemen

Introduction Belt undercarriages or combined belt undercarriages

with sliding wheels, auxiliary belts for running up the
The development of a wheel that would be able, besides
first stair and a lifting mechanism as appropriate –
moving on flat ground, to travel on stairs or to run up a curb
also belts with the configurable circumference’s
has a long history in the field of engineering, and thousands
shape belong to this group.
of different technical solutions have been patented. The Wheel undercarriages with large wheels, alternatively
development of a wheel providing the advantages of
completed with a lifting mechanism.
smooth movement on flat surfaces at a relatively high speed
and with low energy demands along with the possibility of
safe and relatively smooth travelling on stairs and problem-
free running up the first stair has continued, as documented Department of Robotics, VSB – Technical University of Ostrava, Ostrava,
by the relatively recent solution patented in 2011 (see Fig- Czech Republic
ure 1). The wheel is fitted with small turnable protrusions
Corresponding author:
that can be reclined inside the wheel. Vladimir Mostyn, Department of Robotics, VSB – Technical University of
Current technical solutions of a wheel adapted for tra- Ostrava, 17. listopadu 2172/15, Ostrava 70833, Czech Republic.
velling on stairs can be categorized into six major groups: Email: vladimir.mostyn@vsb.cz

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open-access-at-sage).
2 International Journal of Advanced Robotic Systems

Figure 2. The WIPO patent WO2004108045 with a crawler and

wheels.6
Figure 1. The US patent US 20110127732 of the stair-climbing
wheel.1 Wheel undercarriages are usually designed either with
wheels sufficiently large to be able to overcome the stair
Multiple-arm wheels with two, three (Weinstein wheel, height, such as the mobile robot Orpheus,7 or to utilize a
tri-star concept) and four arms, equipped with smaller solution known as the rocker-bogie mechanism8; alterna-
driven wheels at the ends. tively they are equipped with various auxiliary mechanisms
Hybrid walking systems: mechanical legs combined with for lifting the wheel up to the stair, for example the solution
wheels for moving on the ground. described in the patent of Carstens9 and the solution of the
Polymorphous wheels whose shape changes from a cir- lifting mechanism with an eccentric paddle mechanism that
cular profile for moving on the ground to a shape was introduced in Sun et al.10 A wheelchair with manual
matching the stair. lever propulsion of the lifting mechanism was introduced in
Special profiles of solid wheels: The wheel is equipped Sasaki et al.11 The solution with a group of two or more
with a varied number of protrusions (usually three or driven wheels placed on a turnable carrier has become more
four) with a cycloid-shaped, logarithmic or Archime- widespread. When moving on the flat ground, only the
dean spiral profile. The solid protrusions are used for driven wheels turn while the carrier only copies the terrain;
moving on stairs; when moving on flat ground, the when moving on stairs, the wheels are braked and the car-
protrusions are covered with circular segments, or, rier turns with the wheels in a manner so that the profile of
alternatively, auxiliary wheels are slid out. the stairs falls between individual wheels of the carrier. A
number of solutions exist for this design; for example, two
The widest range of applications for travelling on stairs wheels on a turnable arm are used by the robotic wheel-
and over obstacles was achieved by a group of solutions chair12; the principle of the two wheels on the flipped car-
based on reconfigurable belt undercarriages.2 A very rier is also used for stairclimbing in Wang et al.13; a variant
interesting principle with reconfigurable belt’s outer cir- of the known Segway principle with pairs of wheels on
cumference between wheel and track was introduced in each side is used by the powered wheelchair iBot.14 Three
Xueshan et al.3 Some of these belt undercarriages are wheels on a carrier have been known as the wheel cluster,
completed with auxiliary mechanisms to raise the under- Weinstein-wheel or tri-star wheel concept; the Loper robot
carriage up to the first stair. To this group belong also the undercarriage15 can be mentioned as an example. The four
undercarriages with belts on swinging arms.4,5 Higher wheels on a shared carrier are also the subject of a patented
energy demands of the tracks while moving both on flat solution.16 A solution introduced in Sugahara et al.17 with
ground and on stairs, problems with shear control of transformable wheeled four-bar linkages belongs partially
movement direction and problems due to small objects to the next group with wheels combined with legs.
getting wedged between the belt and the wheels are the The robot leg-wheel ASTERISK H18 with wheels at the
disadvantages of the belt undercarriages. The aforemen- ends of the legs is a representative of a group of solutions
tioned technical solutions attempt to remove the disad- utilizing a hybrid combination of legs and wheels. An inter-
vantages of belt undercarriages using sliding wheels for esting solution is provided by the hybrid platform Quat-
moving on the ground, for example, as indicated by the troped; this platform transforms two semicircular wheel
patented solution illustrated in Figure 2.6 parts into a leg.19 Another hybrid solution with lifting
Mostyn et al. 3

opposite requirements for the wheel mechanism. The

wheel should have a full and perfect circular shape for
travelling on flat ground, and at the same time a shape
with rounded protrusions, showing the logarithmic spiral
profile at best, or a circular profile on both sides of
the projection. In addition, there is a requirement for
relative simplicity of the wheel mechanism, which is at
variance with the requirement for integrating both of the
main functions – travelling on flat ground and travelling
on stairs – in a single mechanism.

Conceptual design
Figure 3. Logarithmic spiral wheel for the stair-climbing vehicle. Such opposing technical requirements can be approached
using TRIZ (the Russian acronym for the Theory of Inven-
mechanism and wheels on some kind of mechanical legs tive Problem Solving) methodology and its tools for sol-
was introduced in Chocoteco et al.20 Although technical ving technical contradictions: heuristic principles27 built
solutions utilizing polymorphous and deformable wheels21 based on an analysis of a large quantity of patented tech-
are used, these usually find applications only as research nical solutions in various fields, and summarized in the
projects. The last group of principles is based on wheels so-called Altshuller’s table. Altshuller’s table can be used
with solid protrusions; although such wheels are able to to formulate and overcome technical contradictions based
move on stairs and over obstacles, their movement on flat on problem categorization in 39 categories that should be
ground is too ‘bumpy’. The best results for the movement resolved; for example, the shape of the wheel should
on stairs are shown by wheels with protrusions shaped as a be circular as well as having protrusions; complexity of
logarithmic spiral 5, as illustrated in Figure 3, where the the device leads to larger dimensions; and complexity of
centre of wheel 1, while rolling over the stepping surface 4 the device increases energy losses. In order to solve such
of the stair, moves at least partially along a line 6 in the contradictions, the table offers 40 innovative principles
stairs’ rising direction, and therefore the movement is very for resolving any given technical contradiction. The fol-
smooth.22 Protrusion 2 can be covered using auxiliary cir- lowing principles follow from recommendations based on
cular segment 7 for moving on the flat ground, as shown in Altshuller’s table:
Figure 3 on the right.
The wheel with rigid protrusions is also introduced in Principle 1 – segmentation, that is, the division of the
the contribution of Castillo et al.23 and solution of a wheel circle of the wheel to the individual segments.
with flexible protrusions can be mentioned as an example Principle 5 – merging, that is, merging areas used for
in Eich et al.24 Interesting solution of the ‘bumping’ prob- rolling on flat ground and rolling up the stepping
lem, introduced in Pan et al.,25 is a foldable wheel that surfaces of the stairs in a single body.
consists of two incomplete wheels on arms; these two Principle 6 – universality, that is, the use of the same
wheels form protrusions necessary for moving on stairs and objects for rolling on flat ground as well as for rolling
can be folded up into one circular wheel to move on the flat on the stepping surfaces of the stairs.
surface. The hybrid platform Quattroped, mentioned above
in Chen et al.,19 belongs also to this group of the foldable Based on these recommendations, the circle was divided
wheels. The transformation mechanism of this wheel com- into segments installed as turnable segments on the arms of
bines two half-circles as a leg with the two degrees of the carrier; when travelling on stairs, these segments would
freedom in case of stair-climbing and it can combine these allow reconfiguration to obtain a shape approaching the
half-circles also as a circular wheel. The well-done com- requirement for the wheel rolling on solid protrusions (see
parison of various stair-climbing principles including their Figure 4 on the left); for movement on flat ground, the
stability analysis is carried out in Tao et al.26 circular segments form a perfect and full circle (see Figure
4 on the right).
However, identification of the basic principle of the
solution for a wheel travelling on stairs – segmentation
Synthesis of a wheel with circular
of the circular shape in multiple turnable circular seg-
turnable segments ments – is only the beginning of the technical solution.
The new solution seeks to remove the disadvantages of The purpose is to find such a kinematic structure of the
existing solutions, particularly the structural complexities wheel that will enable the circular segment to touch down
and energy demands, in short, to adapt a simple wheel for tangentially on the stepping surface of a standard stair
smooth movement also on stairs. Clearly, these are quite while the wheel turns around the edge of the previous
4 International Journal of Advanced Robotic Systems

Figure 4. Basic principle of segmented wheel. 1 – carrier;

2 – arms; 3 – segments.

segment. Dimensions of individual segments, the centre Figure 5. Calculation scheme of the geometric analysis.
of rotation of individual segments and the angle of their
partial turn must be such that the length of the arc along Geometric analysis of the wheel mechanism
which the circular segment rolls is equal to the length of
the stepping surface of an average stair. The wheel can be An ideal number of circular turnable segments will follow
adapted to the height of the stairs using the angle of from the geometric analysis of mutual positions of the
partial turn of the turnable segments. This technical solu- partially turned segments towards the standard stair. The
tion of the wheel provides advantages both for movement standard dimensions of the stair are a riser height of 170
on flat ground where the wheel exhibits an ideal circular mm and tread width of 290 mm according to the so-called
shape, disturbed only by possible transitions between the average stair according to the Czech national standard
segments, and for travelling on stairs where a suitable ČSN 73 4130 ‘Staircases and Inclined Ramps’, which
choice of the segment’s angle provides motion with only specifies the design of staircases and inclined ramps as
a little swaying. The segment’s turn angle can be con- footpaths. Considering that the ideal number of segments
trolled using a suitable control algorithm based on the is unknown at this moment, the kinematic structure of the
measurement of the stair dimensions using sensors. In wheel with three circular segments is used for the deriva-
terms of smoothness of the movement on stairs, it would tion (see Figure 5).
be better if the contact area of the turned segments on The purpose of the analysis of the geometric conditions
which the wheel rolls on the stairs could have the shape is to calculate the distance v that must correspond to the
of a logarithmic spiral, which is advantageous for the stair height of 170 mm and to calculate the length of the
movement of the wheel centre along a line parallel to the rolling curve L that must correspond to the stepping
staircase inclination, but the circular shape also provides length of the stair of 290 mm for two variable parameters
a very smooth movement along stairs with a deviation of of the segment: distance d of the segment rotation axis
the wheel centre position from the line of the order of from the wheel centre and the partial turn angle of the
millimetres. The issue of synthesis of such a wheel gives segment . The number of segments is defined by the
rise to the following basic unknowns: variable s. The control circle of the segment is defined
by the points A; B and C of each segment. Segments 2
number of turnable segments; and 3 according to Figure 5 are used to calculate the
position of the segment rotation axis – symmetric or height v and the length of the rolling curve L. Transfor-
asymmetric; mation matrices between the global coordinate system
suitable distance of the segment rotation axis from the GCS and local coordinate systems LCS2 and LCS 3 of
wheel centre; segments 2 and 3 are used to calculate the positions of
the range of diameters of the wheel for the given number the points A 2 ; B 2 and C 2 as well as A 3 ; B 3 and C 3 . The
of segments; Denavit–Hartenberg principle was conveniently used for
optimal diameter of the wheel for the smallest sway the placement of the local coordinate systems and for the
amplitude while travelling on stairs; setup of the transformation matrices. Then the homoge-
implementation of the inner mechanism for partial neous transformation matrix Tb2 between the global
rotation of the segments and the related number coordinate system GCS and the local coordinate system
of drives. LCS 2 has the form
Mostyn et al. 5

2 3
cðSÞ  cðÞ  sðSÞ  sðÞ cðSÞ  sðÞ  sðSÞ  cðÞ 0 d  cðSÞ
6 cðSÞ  sðÞ þ sðSÞ  cðÞ cðSÞ  cðÞ  sðSÞ  sðÞ 0 d  sðSÞ 7
6 7
Tb 2 ¼6 7 ð1Þ
4 0 0 1 0 5
0 0 0 1

where the goniometric function sinðSÞ and cosðSÞ are where r is the radius of the wheel. Segments 2 and 3 will be
abbreviated as sðSÞ and cðSÞ, respectively, to shorten the used to calculate the distance v and the length of the arc L
expression. The angle variable S is the angle of rotation of for various numbers of segments, as illustrated in Figure 5.
the local coordinate system LCS 2 against the global coor- Then the following equations can be applied to the homo-
dinate system GCS at  ¼ 0 (all segments form circular geneous coordinates of the points of segments 2 and 3
wheel), so S can be expressed as expressed in the reference coordinate system GCS.
p  ð3s  4Þ A 2 ¼ Tb2 :A22 B2 ¼ Tb2 :B 22 C 2 ¼ Tb2 :C22 ð7Þ
S ¼ ð2Þ
2s
A 3 ¼ Tb3 :A33 B3 ¼ Tb3 :B 33 C 3 ¼ Tb3 :C33 ð8Þ
where s is number of segments, here s ¼ 3. Angle  is the
angle of rotation of the segment, d is distance between the Based on the calculations of positions of the points A2 ,
segment rotation axis and the centre of the wheel and wheel B2 and C2 of the second segment in global coordinate
radius is r. The homogeneous transformation matrix Tb3 system, the position of the centre S2 of the arc of this
between the global coordinate system GCS and the local segment is calculated, as well as the position of the inter-
coordinate system LCS 3 has the form section point P of the line between the points A3 , S2 and
2 3 the circle given by the points A2 , B 2 and C 2 . Finally the
sinðÞ cosðÞ 0 0
6  cosðÞ sinðÞ 0 d 7 length L of the arc between the points A2 , B2 and P is
6 7
Tb3 ¼ 6 7 ð3Þ calculated based on expression of the angle between the
4 0 0 1 0 5
vectors ½S 2 P T and ½S2 A2  T .
0 0 0 1
However, the task of the wheel dimensions synthesis,
The homogeneous coordinates of the points A 2 , B2 and finding the radius r, a suitable distance d of the segment’s
C 2 of the segment 2, as well as the coordinates of the points turning centre from the wheel axis and a suitable angle ()
A3 , B 3 and C 3 of the segment 3, expressed in their local of the segment’s rotation is an inverse task. We know the
coordinate systems LCS 2 and LCS 3 are fixed; they are normalized height of the stair riser v ¼ 170 mm and the
indexed as A 22 , B 22 and C22 and A33 , B33 and C 33 , respec- normalized stepping length (tread width) L ¼ 290 mm,
tively, and can be expressed as and we need to obtain the range of possible wheel dimen-
2 0 1 3 sions D ¼ 2r, for which there is at least one solution for the
p pair of d and  that satisfies the given condition, and more-
6 r  cos@ A  d 7
6 s 7 over, does so for various numbers of segments s. An
6 7
6 0 1 7 attempt at designing an analytical solution and at creating
6 7
6 pA 7
A 22 ¼ A 33 ¼6 @ 7 ð4Þ inverse functions of individual relationships would lead to
6 r  sin 7
6 s 7 expressions that are too large and difficult to solve. Given
6 7
6 7 that this is a typical optimization task, an iterative heuristic
4 0 5
1
optimization method was used to solve this task, pro-
grammed in Matlab; for the chosen number of segments s
2 3
rd and for the chosen wheel diameter D ¼ 2r, this method
6 0 7 seeks all combinations of the pair of the d and  parameter
6 7
B 22 ¼ B 33 ¼6 7 ð5Þ values in the chosen intervals of d ¼ hd min ; d max i and
4 0 5
1  ¼ h min ;  max i, for which the minimum of the target
2 0 1 3
function F obj approaches the zero value. The target (objec-
p tive) function in the form
6 r  cos@ A  d 7
6 s 7
6
6
7
7 F obj ¼ ðv  170Þ 2 þ ðL  290Þ 2 ð9Þ
6 0 1 7
6 pA 7
C22 ¼ C33 ¼6 @ 7 ð6Þ was conveniently created as a quadratic functional of the
6 r  sin 7
6 s 7 deviations of v and L from the desired values, for which the
6 7
6 7 method converges to a solution very well and rapidly. At
4 0 5
first, we tried to obtain a solution of the wheel with three
1
6 International Journal of Advanced Robotic Systems

Figure 7. Range of possible solutions for a wheel with four

Figure 6. Range of possible solutions of a three-segment wheel. segments.

segments, that is, for s ¼ 3. Based on the iteration optimi-

zation calculation, it was found that for the given wheel
diameter D ¼ 2r, there is always a single pair of the d and
 values that satisfies the required stair height v and the
length of the stepping surface L with the preset accuracy,
while the value of 1 mm was set as satisfactory accuracy.
The range of the wheel diameter D values, for which the
error of setting the height v and the length L is within the
given range, lies in the interval D ¼ h 303 mm; 410 mmi.
There is no solution for wheel diameter values outside the
given interval; that is, there is no pair of the parameters
d and  satisfying the required stair height v and length of
the stepping surface L with the required accuracy of 1 mm.
The optimization results – possible values of the distance d
and angle  for given diameter D – are shown in Figure 6.
In order to find an optimal value of the wheel diameter D
based on the values of the distance d of the segment rota-
tion axis and of the segment inclination angle , it is appar- Figure 8. Theoretical solution for a wheel with two segments.
ent that values in the left part of the graph are more
advantageous, as the partial turn angle of individual seg- diameters of a wheel with four segments is indicated by
ments is relatively small in this part of the graph, which is vertical lines in Figure 7 and falls in the range of
convenient especially for the use of pull rods to incline the D ¼ h 410 mm; 479 mmi.
segments. However, marginal values such as the wheel We also succeeded in finding a solution for a two-
diameter D ¼ 303 mm cannot be used either, given that segment wheel for travelling on stairs; the calculation
the distance of the segment rotation axis from the wheel determined suitable values of d and , as illustrated in
axis is d ¼ 151 :5 mm, and the segment rotation axis is Figure 8 on the left. Although segment inclination of the
thus found on the outer profile of the segment, providing wheel is not feasible due to an intersection of the seg-
no space for the placement of the relatively robust rotation ments with the stair, a solution of the inner mechanism
joint. Practical values of the wheel diameter start from the with a parallelogram is possible, as illustrated in Figure
value of D ¼ 307 mm. Higher values of the wheel diame- 8 on the right.
ter cannot be used, either, for construction reasons. The Similarly, a solution can be found for five or more seg-
partial turn angle of the segments is too large for these ments; a higher number of segments leads to a larger diam-
values, which complicates the inner mechanism for partial eter of the wheel, but also to increased complexity of the
rotation of the segments. The range of up to  ¼ 90 was partial turning mechanism of the segments. For these rea-
preliminarily determined as applicable. Figure 6 illustrates sons, solutions with three and four segments were included
a practical range of values of d and , delimited by vertical in further analysis. Further, the optimal radius of a wheel in
lines, falling in the range of D ¼ h 307 mm; 347 mmi. the ranges delimited in graphs in Figures 6 and 7 is inves-
A similar optimization calculation was also performed for tigated. As mentioned above, smaller wheel diameters
the wheels with four segments, which led to the determi- seem more convenient and lead to smaller angles of partial
nation of similar dependencies. The applicable range of turn of the segments for a normalized stair and thus to
Mostyn et al. 7

Figure 10. The course of wheel centre x and y positions while the
wheel rolls on stairs in MSC ADAMS.

Figure 9. Simulation of the wheels with different diameters,

rolling on stairs in MSC ADAMS.

simpler relationships in the turning mechanism of the seg-

ments. On the contrary, larger wheel diameters are more
convenient for moving on flat ground while overcoming
points of minor unevenness.

Simulations
Finding the optimal wheel diameter is a further step and is
based on the evaluation of the quality of movement on
stairs and on the amount of swaying by the vehicle while
travelling on stairs. To answer this question, simulation-
based verification of the behaviour of various wheel dia-
meters in the given range while travelling on stairs was
undertaken in the software MSC ADAMS (multibody
dynamics simulation software by the MSC Software Corp.) Figure 11. Evaluation of the deviation of the wheel centre from a
that can suitably model the contact of individual wheels line; S3 and S4 are the sums of the squares of the differences for
three-segment and four-segment wheels, respectively.
with standard stairs. The segmented wheels of various dia-
meters, with three and four segments, were rolled concur-
rently on stairs, and the trajectory of the centres of height of 170 mm and the tread depth of 290 mm of the
individual wheels and its deviation from the ideal move- stair, and the offset value 1180.8 mm was calculated using
ment along a line were evaluated. The arrangement of the optimization method based on the ordinary least squares
simulation experiment is shown in Figure 9. method and minimization of the sum of the squares S3 and
The course of the simulated trajectory of a wheel’s cen- S4 of the vertical differences between measured value and
tre with four segments and with the diameter D ¼ 410 mm, reference line values for the 3 and 4 segments, respectively.
while travelling on stairs, is illustrated as an example in Based on the values of these sums of vertical differences
Figure 10. squares, various wheels diameters were also compared, and
The course of the simulated trajectory exhibits certain the results are shown in Figure 11.
swaying while travelling on stairs; however, this swaying The simulation results indicate that the best results are
motion is relatively small as apparent, reaching maximum provided by the wheel with four inclinable segments, with
difference about 20 mm in the direction of the vertical the wheel diameter D ¼ 430 mm with simulated maximal
axis y from the reference line y ¼ 0:586x þ 1180:8. The deviation about 14 mm. Wheels with three segments are
parameters of this reference line were obtained by comput- also satisfactory, and the best result is provided by the
ing the stairs slope value 0.586, that is defined by the rise wheel with the minimal feasible diameter D ¼ 304 mm,
8 International Journal of Advanced Robotic Systems

Figure 12. Travel of the testing undercarriage on stairs. Figure 14. Processed coordinates of points while travelling on
stairs.

Figure 13. Travel of the testing undercarriage on flat ground.

Figure 15. Processed vehicle angles while travelling on stairs.
which produces maximal deviation about 18 mm. How-
ever, these deviations are not large and pose no limitations
on the use of a different wheel diameter. undercarriage frame was evaluated in a simplified manner
as is shown in Figure 14.
The positions of the first and third LED diodes were
used to calculate the deviation of the undercarriage frame
Experimental verification angle while travelling on stairs from an ideal line in the
Experimental verification of the segmented wheel principle rising direction of the stairs, whose value ranges within one
for travelling on stairs was carried out using a scaled degree and it proves that the presented principle of the
testing model with stairs of the height of 64 mm, and wheel with the rotational segments operates properly (see
with the stepping surface length of 110 mm, as shown in Figure 15). Visible vibrations are caused by tolerances of
Figures 12 and 13. the printed parts and shafts play and by skidding the seg-
Individual parts of the wheel were produced using the ments on the surfaces of the stairs; skidding was caused by
rapid prototyping technology, using the 3D printer Fortus inaccurate velocity control of the wheels.
360mcL (Stratasys Ltd.); they were made of polycarbo- A number of related problems were addressed as part of
nate, and the pivots are metal. Each wheel is fitted with the experimental verification of the functionality of the
two Maxon drives with EPOS control units. The experi- main principle, both those related to the wheel mechanism
ments were used to verify the quality of movement on itself and those related to controlling the wheel movement
stairs, especially the swaying motion of the wheels in the on the stairs. Major mechanical problems include high
vertical direction. For this purpose, the testing undercar- loads exerted on the axes of individual segments caused
riage was equipped with colour LED diodes whose trajec- by differential steering control of the vehicle and also the
tories were scanned using a camera. Based on processing problems of locking the segments with respect to the seg-
the image from the camera, the trajectory of the ment carrier in the given position while travelling on the
Mostyn et al. 9

stairs, which is necessary for saving energy. In addition,

optimization of the pull rod mechanisms for segment incli-
nation must be addressed, which is also needed to reduce
the load exerted on the parts; a lower weight of the wheel
and related energy savings should be also achieved.
Regarding the control of the wheel movement on stairs, the
problem of continuous scanning of the stairs profile should
be addressed to achieve an optimal opening of the segments
while moving on the stairs and to perform any corrections
of their opening as needed to prevent slippage of the seg-
ment to the lower stair while travelling. There exist many
methods for detecting the stairs and scanning their dimen-
sions using LIDAR28; solution with laser scanners was
introduced in previously mentioned article of Chocoteco
et al.20 and in Zheng et al.29 in connection with a hexapod Figure 16. A virtual prototype of the mobile robot undercarriage
robot. The solution based on cameras with three- in the MSC ADAMS environment.
dimensional measurement possibilities (RGB-D cameras)
was introduced in Pérez-Yus et al.30 Among the equipment
that is successfully used for scanning the stairs is also
known Xbox 360 Kinect (Microsoft) as is shown in Li et
al.31 The problem of rising up the first stair is also relatively
complex with respect to the proper distance from the first
stair at the moment of opening the wheel. Here is the prob-
lem of synchronizing the partial turn of the wheels on the
left and right sides, which exhibits different values of par-
tial turn when approaching the stairs due to the skid steer-
ing principle. The same applies to proper partial turn of the
wheels on the front and rear axles with respect to the stairs’
profile and their mutual distance.
Furthermore, there is a need to control the angular speed
of individual wheels so that the translational speed of the
wheel centres, when rolling with a variable rotation radius
while travelling, remains constant. The second very impor-
tant reason for the precise angular velocity control of the
wheels is prevention of the push–pull forces between front Figure 17. Simulation of the torques of drives for the front and
and rear wheels, which has the essential influence on the rear wheels in the MSC ADAMS environment.
torques of drives. The essential simulations were performed
using the MSC ADAMS simulation software to properly
size the drives power and torque. The movement of a vir-
tual undercarriage with the weight of 195 kg was simulated
on the stairs with rise height of 170 mm and the tread depth
of 290 mm during the design stage of the real mobile robot.
The simplified virtual prototype with the wheels diameter
412 mm and the front and rear axles distance 600 mm is
shown in Figure 16.
The simulation results for the demanded translational
velocity 100 mm/s and with the angular velocity control
of the wheels are shown in Figure 17.
The simulation in Figure 17 shows that the allowed
continuous torque of the drives should be around 70 Nm
with maximal allowed values above 90 Nm. The
necessary power consumption for the demanded transla-
tional speed 0.1 m/s was simulated and result is shown in
Figure 18. The simulated average power value about 100 Figure 18. Simulation of the power consumption of the all drives
W corresponds with the necessary power for movement of for the translational speed 0.1 m/s in the MSC ADAMS
a box of the weight of 195 kg along the inclined plane with environment.
10 International Journal of Advanced Robotic Systems

ORCID iD
Vladimir Mostyn http://orcid.org/0000-0002-2588-0804
Vaclav Krys http://orcid.org/0000-0002-4840-6961

References
1. Mann K, Klatt W and Barnes N. Stair climbing wheel with
multiple configurations. Patent US 20110127732, 2011.
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