Cooperative coevolutionary approach to dual arm robots' operation.

Curkovic, Petar ; Jerbic, Bojan ; Stipancic, Tomislav 等

1. INTRODUCTION

Dual arm robots exhibit behaviours similar to humans in terms of manipulating objects in highly coordinated fashion. To achieve such a coordination is a task difficult to solve for its inherent complexity (Fei et al., 2004). The task is naturally distributed--two arms, two robots, yet tightly coupled through high level of coordination required.

Coevolutionary algorithms draw their inspiration from the phenomena widespread in nature that involve the evolution of one species in close relation to another (Eiben & Smith, 2007). There are many examples of coevolution in nature, ranging from collaborational behaviours observable in relations of flowers and insects for pollination, competitive coevolution of predator and prey strategies, or relationships of host--parasite type. Coevolutionary algorithms are augmentation of traditional evolution algorithms in the sense that individuals fitness is assigned on the base of interaction of that particular individual with other individuals from the same population and/or other populations.

Most of the work in evolutionary robotics considers competitive approach to coevolution based on predator-prey relationship (Mermigikis & Petrou, 2006), (Cai & Peng, 2002). Work directed toward cooperative coevolution is mainly demonstrated in various robo-soccer applications (Uchibe et al., 1998).

The idea of this paper is to present some insight in possibilities of application of cooperative coevolutionary algorithm to a dual arm robot system as a cooperative coevolutionary architecture. The task of such a system is to explore the environment and find an object positioned in the environment. The hands have to coordinate at the location of the object since (i.e. the object is too heavy for one arm) and in coordinated fashion transport the object to the destination position. The paper will present simplified kinematics' structure adopted for initial research (Kasac & Novakovic, 2001) definition of individuals representation in genotypic space, fitness function and collaboration strategy between individuals from different populations.

2. KINEMATIC STRUCTURE OF A DUAL-ARM ROBOT SYSTEM

The environment of the dual-arm robotic system is organized under following restrictions:

* The robots operate in an environment without obstacles

* Positions of the two robots are known in every time step

* Collisions of the robots' arms are not allowed

* Positions of the object and target position are known

The cinematic structures of the robots are for simplicity reasons chosen as structures with two degrees of freedom, with one rotational and one translational degree of freedom. In such manner, each point in the work space is reachable, if there are no obstacles present in the environment. Fig.1. presents simplified robotic arm with two degrees of freedom.

[FIGURE 1 OMITTED]

Setup with two robots is presented in Fig. 2. The dimensions of the environment are known.

[FIGURE 2 OMITTED]

3. REPRESENTATION

One of the crucial steps in design of an evolutionary-based algorithm is to choose proper representations of the individuals. Complete evolutionary process is taking place in the genotypic space and it is important to enable finding (optimal) solution to the given problem by choosing proper representation. Phenotypic space is later revealed through decoding of individuals. In this paper, genotypic space will contain encoded information about moving of the robots in consecutive time-steps. There are two main possibilities of representation of the robots' movement: 1. occupancy grid representation, with environment divided in to finite number of elements and corresponding nodes in intersections. The movement of the robot would be indirectly encoded through intersections of the mesh. And 2. to encode movement of the robot directly as real-valued parameters of lengths and angles of robotic arms. Although both of the approaches were considered, it is decided to adopt direct real-valued encoding approach. The reason is in increased flexibility of the robot being able to continuously move through the space, as opposing the occupancy grid where the arm of the robot can move only discretely from one grid intersection to another.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

The above expression presents one candidates' form, whereat first part of the string corresponds to lengths of arm of robot 1 and second part of the string corresponds to angles of the same robot. In such manner it is possible to reveal movement of the robot via corresponding pairs ([x.sub.i], [y.sub.i]). The length of the chromosome is important parameter. It is environment dependant, and it should be incorporated into the algorithm through some sort of heuristic knowledge. For example, the environment presented in Fig. 2 is solvable with two strings of length l=4, because it is necessary only to determine two consecutive positions in the environment. It might be interesting to limit the amount of change for which the robot can move within one time step to achieve more realistic behaviors.

4. SELECTION

Selection of the candidates for the next generation is not based on the performance of particular candidate per se. It has rather to be evaluated according to collaboration with candidates from another population. In this paper; two independent populations of individuals competing to collaborate with individuals from other population are assumed.

[FIGURE 3 OMITTED]

Naturally, one population will represent the work of first robot, and another population the work of second robot.

It is important to mention that complete evaluation of these two populations can be done in parallel, on separate processors (Sims, 1994). The only point where these two populations interact with each other is the fitness evaluation.

The objective function has take in account following parameters: distance from the first robots' gripper to the object [d.sub.1], distance from the second robots' gripper to the object [d.sub.2,] distance from the object to the goal [d.sub.3] number of collisions C. The objective function is thus of the following form:

min {[THETA]= [THETA]([d.sub.1],[d.sub.2],[d.sub.3] C)|<[d.sub.1],[d.sub.2],[d.sub.3]> [member of] R, C [member of] Z} (2)

Relative distance from one robots' gripper to the other ones must be constant after grasping the object. Otherwise, the object could be damaged. In the study presented here, the object is considered a point in the work space, and corresponding distance equals 0.

5. CONCLUSIONS

The paper presents possibilities of application of coevolutionary principles to an operation of a dual arm robot. Several critical points such as: representation, selection, fitness function, robot kinematics were discussed and solutions proposed. Representation chosen enables to easily add more degrees of freedom to the robot. This should be beneficial in the case of obstacles present in the work space or in the case of expanding the problem to 3D. At the same time, it would be able to evolve optimized architecture of the robot in terms of degrees of freedom of a robot for a specific environment. Future work will include more detail development of the proposed model with computer simulations of robots work.

6. ACKNOWLEDGEMENTS

The authors kindly acknowledge Croatian Ministry of Sciences Education and Sport for the support through grant No. 120-1201948-1941 Autonomous multiagent automated assembly and Croatian Institute of Technology for the grant TP-E-46.

7. REFERENCES

Cai, Z.; Peng, Z. (2002). Cooperative coevolutionary adaptive genetic algorithm in path planning of cooperative multi-mobile robot systems. Journal of intelligent and robotic systems. Vol 33, pp 61-67.

Eiben, A.E.; Smith J.E. (2007). Introduction to evolutionary computing. Springer, 978-3-540-40184-1, Berlin, Heidelberg, New York

Fei, Y.; Fuqiang, D. & Xifang, Z. (2004). Collision-free motion planning of dual-arm reconfigurable robots. Robotics and computer-integrated manufacturing, Vol.20. pp. 351-357

Kasac, J.; Novakovic, B. (2001). Neural network application to optimal control of nonlinear systems. Computer aided optimal design of structures, Vol. 10.

Mermigikis, I.; Petrou, L. (2006). Exploring coevolutionary relations by alternations in fitness function: Experiments with simulated robots, Journal of intelligent robotic systems, Vol. 47, pp. 257-284.

Sims, K. (1994). Evolving 3D morphology and behaviour by competition. Artificial life IV Proceedings, MIT Press, pp.28-39.

Uchibe, E.; Asada, M.; & Hosoda, K. (1998). Cooperative behavior acquisition in multimobile robots environment by reinforcement learning based on state vector estimation. In Proc. of IEEE International Conference on Robotics and Automation.