Perspectives in Science (2016) 7, 329—332
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Synthesis of action variable for motor controllers of a mobile system with special wheels for movement on stairs夽,夽夽 y, Tomᡠs Kot, Jiˇ rí Marek Václav Krys ∗, Zdenko Bobovsk´ Department of Robotics, VSB — Technical University of Ostrava, Czech Republic Received 6 November 2015; accepted 23 November 2015 Available online 12 December 2015
KEYWORDS Locomotion subsystem; Service robotics; Simulation; Stairs climbing
Summary The article presents a procedure of obtaining waveform of angular velocities for special segmented wheels required for smooth movement of a stair-climbing chassis on stairs. The waveform was determined for a specified velocity of the chassis using a dynamic contact analysis in the CAD system SolidWorks. The main part of the work was to verify whether real motors on a testing chassis are capable of producing the required angular velocity with its significant step changes. The values of angular velocities were sent to drive control units from a software control system of the chassis. The chassis was recorded during the movement on stairs on a video camera and the resulting video was then analyzed by a special single-purpose image processing algorithm, which detected key points in individual frames. Outcome of the algorithm are tables with positions and velocities of individual key points during time. Tests proved that with lower velocities it is possible to achieve very good results with the chassis moving almost steadily. © 2015 Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Introduction 夽 This article is part of a special issue entitle ‘‘Proceedings of the 1st Czech—China Scientific Conference’’. 夽夽 This article has been elaborated in the framework of the project Pre-seed activities VSB — TUO — Security, reg. no. CZ.1.05/3.1.00/14.0316, supported by Operational Programme Research and Development for Innovations and co-financed by the European Social Fund and the state budget of the Czech Republic. This article has been also supported by specific research project SP2015/152 and financed by the state budget of the Czech Republic. ∗ Corresponding author. E-mail addresses:
[email protected] (V. Krys),
[email protected] (Z. Bobovsk´ y),
[email protected] (T. Kot),
[email protected] (J. Marek).
On our department we have been dealing with design of a special wheel for movement on stairs (Krys et al., 2014) for a long time. A possible solution seems to be a wheel with rotary segments which is capable of smooth driving both on a flat ground and on stairs without oscillation of the chassis centre of mass. The main considered application field was transport of handicapped people and unstable loads, where typically is used a combination of wheeled and tracked chasses with stabilizers (TGR, 2015; SANO, 2015) and wheeled chasses with combined wheels (Morales et al., 2013; Quaglia et al., 2011; Le Masne de Chermont, 2004). Another potential field of application are reconnaissance
http://dx.doi.org/10.1016/j.pisc.2015.11.050 2213-0209/© 2015 Published by Elsevier GmbH. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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Figure 1
V. Krys et al.
Simulation model in CAD system SolidWorks.
and manipulation mobile robotic systems, where are predominantly used tracked chasses in various modifications (tEODor, 2015; OSCAR, 2015; iRobot, 2015; Li et al., 2013; Liu and Liu, 2009). The principles applied for prototypes with special wheels or with rocker-bogie mechanisms do not provide movement of the chassis without oscillation of its centre of mass in vertical direction (Herbert et al., 2008; Eich et al., 2008; Hong et al., 2013; Boxerbaum et al., 2009). Our design of a wheel with rotary segments is capable of linear movement of the chassis with almost eliminated oscillation. The variable radius of contact surface of the wheel segments however causes fluctuating velocity of the chassis relatively to the stairs if the wheel rotation speed is constant. The article presents a way of elimination of this phenomenon by using variable angular velocity of wheels; and also presents verification that this is practically possible to achieve on a physical robot with real motors.
Simulation Contact kinematic simulation in the CAD system SolidWorks 2012 was used to determine the course of wheel angular velocity required to produce constant movement velocity of the chassis when driving on stairs. The simulation model (Fig. 1) was tuned for constant angular velocity of the wheel 6◦ /s, cosinusoidal acceleration and deceleration with the total running time 60 s. Using this setup, velocity of the chassis relatively to the stairs was examined (Fig. 2). The simulation model was simplified to only one half of the chassis. Afterwards the simulation model was modified so that the chassis moved with a defined velocity relatively to the stairs (constant with cosinusoidal acceleration and deceleration, Fig. 3) while preserving contact and rolling of the segments on stairs. To achieve this, a line parallel with the flight of steps was created in the simulation model. One of the translational axes of a planar kinematic constraint was oriented parallel to the created line. A drive was then defined on this translational axis with the specified values of chassis velocity (Fig. 3).
Figure 2 Velocity of the chassis in a direction parallel to the flight of stairs.
The next step was to set the maximal possible coefficients of friction in the contacts between wheels segments and the staircase to eliminate potential slipping. Already the first tests showed a significant step change in the wheel angular velocity. For this reason the simulation of climbing up four stairs was configured for 60 s (that means a quite low translational speed), to increase the chance that real mechanism with motors will be able to accomplish the movement as accurately as possible. The subsequent simulation generated the required waveform of angular velocity of wheels for the defined speed of the chassis (Fig. 4). The step changes (peeks) mentioned above are clearly visible on the graph. The process is analogue of inverse kinematics used for manipulators with serial kinematic structure.
Verification on a scaled prototype The values of required angular velocities determined by the simulation were exported to a table which was then used as input for the drive control units of motors of a scaled-down chassis prototype. A special rigid version of the wheels (with the segments locked in the optimal angle) was manufactured for these tests. The wheels are made from polycarbonate PC-10 with break-away support material, supplied by STRATASYS. Previous tests showed that
Figure 3 stairs.
Required velocity of the chassis during travelling on
Synthesis of action variable for motor controllers
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Figure 4 Required angular velocity of the wheel to achieve smooth velocity of the chassis in a direction parallel to the flight of stairs.
Figure 6
wheels with rotary segments made using the FDM technology on the machine FORTUS 360 MCL are not rigid enough and their deformation under load significantly affects the test results. During design and manufacturing of the parts we applied our knowledge acquired by tests on samples made by the technology (Lipina et al., 2014a,b, 2015). A very simple chassis was used for the tests, as can be seen in Fig. 5. The frame consists of aluminium profiles connected by screws. Bearing houses fixed to the frame were made using the additive technology FDM and the same material as the wheels. Each wheel is driven by 90 W Maxon motor RE35 in combination with gearbox GP42C with ratio i = 113 and encoder with 500 pulses per revolution. Control unit of each drive is EPOS 70/10. For subsequent image analysis, a black board with three LEDs was mounted on the chassis so that the LEDs were parallel with connecting line between both axles. The chassis was then during the testing movement captured on a video camera in a slightly darkened room. LEDs created very bright spots on the video frames with colour equal to clean white. To detect these spots in the video frames, a special application was programmed in Visual C++ using the image processing library OpenCV. For each frame of the video, a
temporary empty (black) image of the same size as the video frame is created with just 2 bit colour depth. Then all pixels in the original image with colour vector close to white colour (255, 255, 255) are set to white also in the temporary image. Because the video was not filmed in a fully dark room, there were some small areas around the robot that were white too, so these areas were masked-out by drawing black rectangles over them. This did not affect the important area of the image at all. With the temporary image containing all black pixels except for the three white spots corresponding to the LEDs, the next step was to use OpenCV function cvFindContours three times to find the individual spots. Each spot at this moment was just a group of pixels, so the function cvMinEnclosingCircle was then used to find a minimal circumscribed circle for each spot. Output of this function is radius of the circle and especially the coordinates of its centre (x, y). All these coordinates (six per frame) were written to a text file together with frame number. Positions of the LEDs in pixel units could later be converted to millimetres and also velocity and acceleration of the chassis was calculated using the delta time between frames. Fig. 6 shows one frame of the video. Fig. 7 shows graph of translational velocity of the chassis relatively to the stairs with variable angular velocity
Figure 5 Scaled prototype of the chassis with adjustable segmented wheels.
Figure 7 Graph of translational velocity of the chassis relatively to the stairs—output of the image processing application.
A snapshot from the video made during the test.
332 of wheels (acquired by the testing of the scaled prototype described above).
Discussion By comparing the two graphs it is obvious that by using variable angular velocities of the wheels, the required waveform of chassis velocity when driving up and down the staircase was acquired with some small error. By the tests we proved that it is technically possible to obtain smooth velocity of the chassis equipped by segmented wheels when driving on stairs. However, a problem of this approach is that it was a fixed pre-defined movement sequence. By setting the required velocity of the chassis quite low, it was ensured that the physical motors will be able to react to step changes in the waveform. By further tests we will have to find out where is the maximal allowed velocity, for which the drives are able to accept the values. Another question that will require our attention is comparison of energy demands of the movements with constant and table-defined angular velocities of wheels; and also the ability of available power-sources to cover the peek currents during the step changes.
Conclusion Simulations of a chassis equipped with shaped wheels for movement on stairs showed that with constant revolution speed of wheels, the chassis moves on the stairs with oscillating velocity relatively to the flight of steps. By using contact simulations in the CAD system SolidWorks, simulation models of a longer and a shorter variant of the chassis were created, to discover the required waveform of angular velocity of the shaped wheel to produce constant chassis translational velocity. The waveform of required velocity contains four step changes during one wheel revolution, which in practise is impossible to achieve, because of dynamical limitations. By tests on a lower-scale prototype it was proved that for lower target velocities it is possible to get close to the required waveform and achieve almost constant velocity of the chassis. The tested principle however is not applicable in the case of dynamically changing velocity of the chassis during movement, because the data are pre-calculated by a simulation for a single setup. Even with the limitation of a constant velocity selected from a list of supported velocities, the stair-climbing mechanism would have to be equipped with a very sophisticated sensor system capable of accurate detection of position on the stairs. Other significant problems on which we are working nowadays are related to entering and exiting the staircase.
Conflicts of interest The authors declare that there is no conflict of interest.
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