Choice of robot morphology can prohibit modular control and disrupt evolution
چکیده
In evolutionary robotics, controllers are often represented as networks. Modularity is a desirable trait of such networks because modular networks are resistant to catastrophic forgetting and tend to have less connections than nonmodular ones. However, these advantages can only be realized if the control task is solvable by a modular network, and for any given practical task the control task depends on the choice of the robot’s morphology. Here we provide an example of a task solvable by robots with two different morphologies. We consider the most extreme kind of modularity – disconnectedness – and show that with the first morphology the task can be solved by a disconnected controller with few connections. On the other hand, the second morphology makes the task provably impossible for disconnected controllers and requires about three times more connections. For this morphology, most controllers that partially solve the task constitute local optima, forming an extremely deceptive fitness landscape. We show empirically that in this case a connection cost-based evolutionary algorithm for evolving modular controllers is greatly slowed down compared to the first morphology’s case. Finally, this performance gap increases as the task is scaled up. These results show that the morphology may be a major factor determining the performance of controller optimization. Although in our task the optimal morphology is obvious to a human designer, we hypothesize that as evolutionary robotics is scaled to more sophisticated tasks the optimization of morphology alongside the control might become a requirement for evolving modular controllers. Frequently used symbols: Ti – target orientation of ith segment; Ai – absolute orientation of ith segment; ri – relative orientation of ith segment (defined in eq. (2)); si – reading of the target orientation sensor measuring the orientation of the ith segment (5); fi – motor output for ith segment (6); T ,A, r, s, f – corresponding N -dimensional vectors, where N – is a number of segments; J – sensor attachment matrix (5); K – constantN×N matrix such filled with ones on and below the main diagonal and zeros everywhere else (4). Introduction Evolutionary computation and particularly evolutionary robotics are important research tools in the area of artificial life (Langton (1997); Lipson and Pollack (2000); Rohde (2010)). A lot of research effort concerning evolutionary computation is dedicated to the evolution of networks. Network representation has several advantages. First, it can describe many kinds of systems, including controllers and morphologies of artificial agents (e.g. Sims (1994)). Second, it is relatively straightforward to design genetic operators such as mutation and crossover for networks. Last but not least, a lot of models in biology are network-based, making it easier to draw inspiration from natural evolution. One characteristic property of biological networks that attracts a lot of attention from evolutionary computation community is modularity (e.g. Girvan and Newman (2002)). A network is structurally modular if its nodes can be divided into subsets (modules) that are connected more tightly within themselves than with the rest of the network. In computational (e.g. neural, genetic regulatory) networks structural modularity often leads to weak or absent functional dependence. Consequences of such weak dependence include resistance to catastrophic forgetting both in neuroevolutionary setting (Kashtan and Alon (2005); Espinosa-Soto and Wagner (2010); Clune et al. (2013)) and in learning (Ellefsen et al. (2015)). Such resistance allows for a reduced number of training examples (Cappelle et al. (2016)). In addition, modular networks tend to contain less connections, which further simplifies their optimization (Clune et al. (2013); Bernatskiy and Bongard (2015)). Although some techniques for evolving modular computational networks have been developed (e.g. Kashtan and Alon (2005); Espinosa-Soto and Wagner (2010); Clune et al. (2013); Bernatskiy and Bongard (2015)), they mostly focus on finding nearly-optimal modular solutions that are assumed to be exist. In addition, to harness the full power of the approach an appropriate modular variation of the task is desirable, either among the training examples (Cappelle et al. (2016)) or over the evolutionary time (Kashtan and Alon (2005); Espinosa-Soto and Wagner (2010); Clune et al. (2013)). However, in practice, it cannot be assumed that modular solutions for a given task exist, nor that the task itself is modularly varying. Indeed, in the work presented here, we demonstrate that there is a robotic task and a robot morphology for which even the former assumption does not hold. In evolutionary robotics, controllers are often represented as computational networks. Properties of modular networks make modularity a desirable property of such controllers. However, previous work (Bongard et al. (2015); Cappelle et al. (2016)) suggests that performance of modular network evolution techniques in this setting can vary depending on the choice of the robot’s body. In Bongard et al. (2015) evolution produced more modular controllers if the morphology was under the evolutionary control. It was observed that certain morphologies enable modular control while others do not, but it was not clear which mechanism might be responsible for that. In Cappelle et al. (2016), a morphology is defined to be modular iff activation of less than all of robot’s motors results in a change of less than all of its sensors. Similarly, a control system is modular iff a change in less than all of the sensors induces a change in less than all of the motor neurons. It is shown that the number of environments in which the robot needs to be evaluated can be reduced significantly if both morphology and control are fixed to be modular. Despite these findings, many things remain unclear regarding the relationship between the morphology and modularity. In particular, while it is known that certain morphologies are beneficial for the evolution of modular controllers, it is not known why. Another open question is how much worse can the performance of evolution be if a less appropriate morphology is chosen. Here we fill these gaps by introducing a task and a family of robot morphologies with two extremities. The first is a morphology for which some optimal controllers consist of multiple disconnected modules. For the second morphology of interest it is provably impossible for any optimal controller to be disconnected. Additionally, we show the that the latter morphology induces an extremely deceptive fitness landscape in the space of possi-