New Solution for Walking Robot Tadeusz Mikolajczyk 1,a*, Tomasz Fas 1,b, Tomasz Malinowski 1,c, ukasz Romanowski 1,d 1 University of Technology and Life Sciences, Department of Production Engineering 85-876 Bydgoszcz, Kaliskiego 7 str., Poland a tami@utp.edu.pl, b tomasz-fas@wp.pl, c techniczny.tomasz@gmail.com, d romek@utp.edu.pl Keywords: mobile robot, walking robot, walking upstairs, kinematical analysis Abstract. Many designs of walking robots are based on ideas borrowed from bionics. Some of them are very similar to the original biological concept of a walker, but those are also very complicated. The purpose of this paper is to elaborate not on the bionic pattern, but our own simple idea of task managing robot with the ability to walk on flat surfaces, rotate and climb stairs. In this design, 4 degrees of freedom (DOF) were used. The paper contains a technical solution, kinematics analysis and simulation software. Introduction Nowadays, it is becoming more and more common for robots to perform their services [1-5] in most cases, they are mobile robots. For movement, wheels [2] or walking system is implemented [1,3-5]. A hybrid solution is also possible with legs and wheels [6]. Currently, among the existing solutions for walking robot systems, a large variety of forms and designs can be observed. In most cases, the main principle for robot operations is to simplify and implement the rules derived from natural living beings. There are both two - and multi-limb settings [3-5] (Fig. 1). Existing models of bionic-inspired walking robots are complex and difficult to control. Their design and manufacturing are undertaken by the leading companies with major research centers supported by sufficient financial capacity [3]. Some of the high-tech four-legged robots have the ability to outrace a cheetah. One of the most important task of a walking robot is to climb stairs. Designers came up with many solutions of bionic-inspired robots. Some of them were equipped with legs [3] or even a special wheel [7,8]. Asimo might be one of the most effective robot designs (Fig. 1b), resembling a human body. The aim of the presented study is to develop and analyse a new, simple idea of a walking robot with a small, yet significant freedom of movement. Walking robot new idea The core of the presented solution is the construction of a two-legged robot presented in figure 2. Its legs are slidably connected to the body and are moved simultaneously by a single motor, which is responsible for lifting the legs. Another two motors are then responsible for the rotation of this legs. The rotation around the legs' axes works both clockwise and counterclockwise. Rotation of the right leg is defined as 1 and of the left leg as 2. Additionally, this robot is equipped with a stabilizing mass balance to ensure stability during leg movement. The mass is controlled using yet another motor. All in all, the robot have four axes of movement. The robot body rotation allows it to execute a first step (Fig. 3). Then the robot leaves the first leg and is ready for the next step using the second leg. At the same time, a coordinated movement of the mass balances the robot. Presented
mechanism is much simpler and relatively easy to control then compared to other existing structures (Fig.1). a) b) c) d) e) f) g) h) i) Fig. 1. Selected walking robot designs: a) Rabbit [3], b) Asimo (Toyota) [3], c) Qurio (Sony) [3], d) Bear [3], e) P3 (Honda) [3], f ) Climber [3], g) watterruner - nanorobot [5], h) Aibo (Sony) [3], i) Messor [4] Fig. 2. The idea of the walking robot -front view Fig. 3. The principle of walking robot motion - top view
This method enables a possibility to regulate stride length done by the robot by changing the angle of feet rotation. This allows the robot to walk and change direction. Some examples of these abilities were presented in figure 4 and 5. Simultaneously, by using the vertical motion the robot can overcome stair-like obstacles. To ensure balance it is crucial to make the robot's center of mass be transferred properly during the process. Fig. 4. Changing the direction of the robot by rotating the right leg 1 = -45 and then of the left leg 2 = 110 Fig. 5. Changing the direction of the robot by rotating the right leg 1 = 180 Theoretical analysis of the robot movement In order to describe the movement of the legs, robot body and mass will be analysed basing on a non-inertial x'z' frame of reference. The progressive movement of the robot will be analysed basing on an inertial xyz frame of reference. Both frames of reference are shown in Fig. 6. Fig. 6. Inertial (xyz) and non-inertial (x'z') frame of reference used at kinematical analysis of the robot movement
Complete cycle of robot moves consists of the following stages (Fig. 7 and Fig. 8): mass is moved to the right (from x =0 to x = b max ), the left leg rises and goes down (from z =0 to the z =h max and back), simultaneously the right foot turns to angle 1, mass is moved back to the center (x =0), mass is moved to the left (x = -b max ), right leg rises and goes down, simultaneously the left foot turns to angle 2 (or 2 2 if the movement is continued), mass is moved back to the center. Fig. 7. The movement of legs, body and mass in a non-inertial frame of reference Fig. 8. Linear motion of the robot: a) along the y axis, b) oblique to the y axis For a straight movement of the robot along the y axis rotation of the feet must occur in the order: 1, 2, 2, 1 (Fig. 8a). A different order of rotations can cause a relocation along the x axis (Fig. 8b). The length of a single step depends on the distance (r) between legs and on the angle 1, and is equal to: Lss rsin1 (1) See Fig. 8. For linear motion of the robot along the y axis, 1 + 2 = 0 (see Fig. 8a). The average speed of the robot in linear motion is determined by the following equation (2):
rsin1 vy tl tm where: t L - time of the leg being raised and put down; t M - time of the mass being moved (see Fig. 9). (2) Fig. 9. Interrelation between the robot's angle 1 and the length of the step The movement up the stairs is possible provided the h max is higher than the H st. and Lss is equal to L st. (Fig. 10). Fig. 10. The robot is climbing stairs With the simplest control algorithm, movement of legs and mass will be similar to the one presented in Fig. 11a. However, one should aim for as fluent, harmonic solution for motion as possible (Fig. 11b) for better stability. The harmonic motion (Fig. 11b) is described by the following equation for leg: and for the mass: h 2 h z' t t 2 tl 2 2 max max sin (3)
b 2 b x t t 2 tm 2 2 max max ' sin (4) Virtual animated model Fig. 11. Movement of legs and mass in time In order to visualize the operating walking robot and its controller, it was depicted with a dedicated software in VB6 environment. The program presents two forms. The first presents the animation of robot movement from the frontal perspective - it shows the robot s leg lifting movement (Fig. 12). The second shows the robot's movement from above (Fig. 13). The software allows you to set the step frequency and the rotation angle of robot's feet at runtime step, which allows you to control the trajectory of the robot movement. After completing the software code to control stepper motors this software will be used to control a practical model. Fig. 12. Selected phases of robot leg lifting front view Fig. 13. Selected phases of a robot's step top view
Summary and further Presented design of the walking robot is a simple one as it includes only 4 DOF. This robot has the ability to move on flat surfaces, change direction, and to rotate in any direction in any angle. The robot has the ability of walking up and down the stairs. The essential element in this design is to use the additional mass for gravity movement inside the robot and perform leg rotation in a relative vertical motion. The walking robot idea can be executed in different scales. The preliminary analysis indicates a great functional potential of a robot kinematics despite its simple structure. The presented study provides a basis for further work on the robot and its control systems. More research on the launch control system including distance sensors is highly recommended. This project requires further work in order to depict the practical implementation of the robot model and serve as a new solution for future robot design. Further experiments should include two stages: firstly, to build a simple model of the robot with a small jump legs in order to verify the robot's motion on flat surface. The second step is to build the ultimate robot model with heavy traffic jump linear foot for the verification of stair climbing. This work should identify the issues related to the dynamic linear motion and rotary components. This will allow to estimate the relevant forces and the power needed to drive. Application of the machine of this type can be very wide. Due to the simple structure its cost will be low. The cost of the robots control system will depend on how is it supposed to interact with the environment, which might require the computer for control system. For simple walk procedure, a microprocessor for example of the ATMEGA type should be enough [9]. Reference [1] M. Vagaš, M. Hajduk, J. Semjon, L. Koukolová, R. Jánoš, View to the Current State of Robotics, Advanced Materials Research, vol. 463-464, (2012), 1711-1714 [2] T. Mikolajczyk, J. Musial, L. Romanowski, A. Domagalski, L. Kamieniecki, M. Murawski Multipurpose Mobile Robot, Applied Mechanics and Materials, vol. 282, (2013), 152-157 [3] www.asimo.pl (Rabbit, QRIO, Asimo, P3, Aibo, City Climber) [4] www.walkingrobots.xsk.pl/index.php?option=com_content&view=article&id=54&itemid=58 &lang=pl (Messor) [5] nanolab.me.cmu.edu/projects/waterrunner/water_runner_4leg_big.jpg (WaterRunner) [6] R. Jánoš, M. Hajduk, J. Semjon, L. Šidlovská, Design of Hybrid Mobile Service Robot, Applied Mechanics and Materials, vol. 245), (2012), 255-260 [7] M. Eich, F. Grimminger, F. Kirchner, A Versatile Stair-Climbing Robot for Search and Rescue Applications, Proceedings of the 2008 IEEE International Workshop on Safety, Security and Rescue Robotics Sendai, Japan, (2008), 35-40 [8] A. S. Boxerbaum, M. A. Klein, R. Bachmann, R. D. Quinn, R. Harkins, R. Vaidyanathan, Design of a Semi-Autonomous Hybrid Mobility Surf-Zone Robot, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Singapore, (2009), 974-979 [9] T. Malinowski, T. Mikolajczyk, A. Olaru, Control of Articulated Manipulator Model using ATMEGA16, Applied Mechanics and Materials, Submitted to print (2014)