Design and control aspects for JQuadRobot.

Vatau, Steliana ; Maniu, Inocentiu ; Moldovan, Cristian Emil 等

1. INTRODUCTION

The mobile robots are equipped with a locomotion system, in order to be able to perform programmed or remote controlled movement in a very large working space (Kovacs et al., 2000). In terrestrial locomotion the following systems are used: based on rolling (wheeled and tracked), with or without air cushion lifting technique, or based on walking (Manko et al., 1992).

Numerous advantages arise when legged locomotion is chosen over tracked or wheeled methods. Most walking robots of today are quite slow and have bad payload weight-to-own-weight ratio compared to more conventional wheeled or tracked robots. The control of a walking robot has to cope with a highly nonlinear system with many degrees of freedom, changes in the system dynamics as the legs are being lifted and placed, and unknown dynamics such as the interaction of the foot with the ground. The control of walking robots also requires that the issue of stability against tipping over be treated in a more specific fashion than for wheeled robots, as there are discrete changes in the support of the robot when legs are lifted or placed (Ilg et al., 1999). In this paper, the mechanical design and some control system configuration aspects are presented.

2. JQUADROBOT DESIGN

JQuadRobot was development at University "Politehnica" of Timisoara, Mechatronics Department (see Fig.1). The robot has 12 degrees of freedom, with three degrees of freedom per leg. Each leg has hip, knee and ankle. The hip joint is actuated in vertical plane (Pitch) and horizontal plane (Roll), knee joint is actuated in vertical plane (Pitch) and ankle is not actuated (passive joint). Figure 1 shows the quadruped robot model and the real robot (Vatau, 2008).

3. KINEMATICS AND TRAJECTORY PLANNING

The quadruped cannot make another step, without bringing the support leg in the support polygon corners.

[FIGURE 1 OMITTED]

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The programmed routines elaborated to implement the configuration operations into the control software are based on the leg's inverse kinematic model (see Fig.2). The inverse kinematic model supposes that the support polygon's corner points P ([x.sub.p], [z.sub.p]) are defined. The unknown variables are the orientation angles [alpha] and [beta]. According to the algorithm (Vatau et al., 2007) the angles are determined with the relations (1).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

During the configuration, the leg's characteristic point goes through a fragmented trajectory (see Fig.3). This trajectory has the [C.sub.1] as the start point and the C2 as the stop point, in successive positions of the ankles joint, before and after the configuration operation. The fragmented trajectory contains the first rising segment [C.sub.1][Q.sub.1], the second horizontal movement segment [Q.sub.1][Q.sub.2], and the third descending segment [Q.sub.2][C.sub.2]. To obtain the [Q.sub.1] and [Q.sub.2] coordinates, from [C.sub.1] and [C.sub.2] points if is translated the axis of the points with the h height as in Fig.3.

This algorithm associates to each coordinate pair, one angle pair. With the four pair of angles ([[alpha].sub.C1], [[beta].sub.C1]), ([[alpha].sub.C2], [[beta].sub.C2]), ([[alpha].sub.Q1], [[beta].sub.Q1]), ([[alpha].sub.Q2], [[beta].sub.Q2]) the angular range, needed in the hip joint and the knee joint is defined by the relations (2).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Every configuration routines, used by the control software to change the walking method, are based to the same relations like (2).

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In the walking locomotion, the system is permanently reconfigured. This process depends on both the stepping leg's movement and on support leg's movement. In order to formulate the algorithm, that permits to include these influences into the control routine, is broke up the trajectory of the characteristic point in respect of the frame, in two branches. In the first branch is kept the stepping phase related part, and in the second the support phase related part. This operation is called brute segmentation and is presented in Fig.4a. The branch passed in the stepping phase, contains the same segments [C.sub.1][Q.sub.1], [Q.sub.1][Q.sub.2], [Q.sub.2][C.sub.2] like the configuration trajectory that was discussed for the immobile supports. Therefore the afferent movements for this branch can be controlled also by routines based on the described algorithm. The branch passed during the support phase ([C.sub.2][C.sub.1] segment), is passed in three sequences, which on duration rule has same lengths equal with L/4. In the support phase of the leg's (2), the first sequence correspond to the [C.sub.2]C' interval--when the leg (4) is stepping, the second sequence correspond to the interval C'C"--when the leg (1) is stepping, and the third sequence correspond to the interval C"[C.sub.1]--when the leg (3) is stepping. After the brute segmentation a fine segmentation is made (Fig.4b). This operation divides each support segment in subintervals, i.e. C'[C.sub.Q1], [C.sub.Q1][C.sub.Q2], [C.sub.Q2]C" having the lengths proportional with the other segments [C.sub.1][Q.sub.1], [Q.sub.1][Q.sub.2], [Q.sub.2][C.sub.2] from the stepping phase branch (because they have constant speeds).

According to the two segmentations, for the subinterval lengths, it is obtained the relations (3). These relations permit to calculate the coordination of the intermediary points [C.sub.Q1], [C.sub.Q2], and with the inverse geometrical algorithm to deduce the joints ranges, needed to correlate each support leg movement with the other stepping leg movement.

[1.sub.CCQ1] = [1.sub.Q2C"] = h x L/8h + 3L [1.sub.CQ1CQ2] = L/4 - 2 x h x L/8h + 3L (3)

These calculations must be repeated for each support interval and for each involved leg, in both the support phase and in the stepping phase. They use the same algorithm and software routine, only with changed dates (the coordinates of the trajectory points).

4. CONTROL ROBOT

For monitoring and controlling a custom mobile robot named JQuadRobot, it was development a software application named JQuadRobot (Vatau, 2008).

This application is developed in Java and is essential in development motions for the legged robot. The application is released as free software under the GNU General Public License (GPL) and was conceived modular (see Fig. 5).

[FIGURE 5 OMITTED]

The quadruped robot is controlled using the simulator JQuadRobot developed in Java and Java 3D API, which implements different diagram gait.

The simulator can be used together JQuadRobot Editor to prevent collision detection between robot's legs by running the commands before sending it to robot. Another feature is to make constrictions to prevent collision detection in some environments like walking through a pipe or through a frame with specific dimensions.

5. CONCLUSION

In the walking locomotion, the system is permanently reconfigured. This process depends on both the stepping leg's movement and on support leg's movement. In this paper it was formulate the algorithm, which permits to include these influences into the control routine, it broke up the trajectory of the leg's extremity in respect of the frame into two branches.

6. FUTURE WORK

The future advancement can be carried out in the project by going for embedded processor that can process and transmit the control signal faster to the actuators. Complex movements can be achieved by increasing the D.O.F. Vision system can help the robot to work autonomously. Remote control through wireless ethernet mode can also be considered.

7. REFERENCES

Manko, D.J. (1992). A general model of legged locomotion on natural terrain, Kluwer Academic Publishers, ISBN 0-7923-9247-7, Boston

Ilg, W.; Albiez, J.; Jedele, H.; Berns, K. & Dillmann, R. (1999). Adaptive periodic movement control for the four legged walking machine BISAM, Available from: http://ieeexplore.ieee.org. Accessed: 2008-03-10

Kovacs, Fr.; Varga, S. & Pau, V. (2000). Introduction to Robotics, Printech Publisher, ISBN 973-632-230-X, Bucuresti

Vatau, S.; Varga S. & Radulescu C. (2007). Algorithms for the quadruped mobile robot locomotion system configuration, Proceedings of International Conference Optimization of the Robots and Manipulators, Olaru, A., Ciupitu, L., (Ed.), pp. 161-167, ISBN 978-973-648-656-2, Predeal, Romania, May 2007, Bren Publishing House, Bucuresti

Vatau, S. (2008). The constructiv--functional optimization for quadruped mobile robots. Politehnica Publisher, Timisoara, ISSN 1842-7707, ISBN 978-973-625-613-4