Grounding an Internal Body Model of a Hexapod Walker Control of Curve Walking in a Biologically Inspired Robot Malte Schilling 1,2 , Jan Paskarbeit 2 , Josef Schmitz 2 , Axel Schneider 2 , and Holk Cruse 2 Abstract— While internal models are a prerequisite for higher-level function, they have to be grounded in lower- level function serving sensorimotor control. In this paper we introduce an internal body model for the control of a hexapod walker. The internal model deals with a highly complex robotic structure of 22 degrees of freedom and coordinates the single joint movements to achieve an overall stable and adaptive walking behavior. It is implemented as a hierarchical recurrent neural network consisting of different levels of abstraction which are tightly intertwined. We demonstrate the feasibility of the concept by applying the model to a simulated robot and show how the different levels of the body model interact and how this allows to scale the model even further. While the internal model is used in this context explicitly for motor control, it is also a predictive model and can be applied for sensor fusion. We discuss how in this way such an internal model offers the flexibility to be utilized in motor control and to be used for planning ahead by a cognitive expansion of the movement controller. I. INTRODUCTION Cognitive function have been found to be based on lower-level and motor control related function [13]. Plan- ning ahead—following [16] as the defining characteristic of cognition—in this sense recruits [1] internal models originally co-evolved in the context of action [26] in a form of internal simulation [11]. While this provides a grounding for internal models, i.e., they are directly anchored in the sensorimotor system, the internal models are in addition required to be flexible. Only a flexible model allows to be applied in a new context. In this way, for example, a predictive model can be exploited as an internal simulator to anticipate consequences of possible actions and to select only an appropriate one when facing a never experienced and possibly harmful situation. An internal model of the body [4] can be assumed as a cen- tral representation and has been found active in quite diverse tasks besides motor control [28], perception of movements [14], planning [9] and, in the case of humans, even language [19]. The body model appears to serve different functions. First, in motor control it has to solve the inverse kinematic problem to coordinate whole body movements. Second, as there are multiple noisy, but redundant sensory information in *This work has been supported by the Center of Excellence Cognitive Interaction Technology (EXC 277), by the EC-IST EMICAB project # FP7– 270182 and by a DAAD postdoctoral fellowship. 1 M. Schilling is with the International Computer Science Institute Berkeley (CA), 1947 Center Street, Suite 600, 94704 Berkeley (CA), USA malteschilling at googlemail.com 2 M. Schilling, J. Paskarbeit, J. Schmitz, A. Schneider, and H. Cruse are with the Center of Excellence Cognitive Interaction Technology, University of Bielefeld, Germany s 0 s 1 s 2 f 1 r 1 f 0 a) b) body coxa femur tibia γ β α ↺ coxa z x y leg target vector Fig. 1. The body model for the six-legged walker is divided into two layers. The lower layer contains six networks, each representing one leg (a). The upper layer (b) represents the body and the six legs, which are only represented by vectors pointing towards the tip of each leg. On this level the leg is described with reference to the respective body segment. Both layers are connected via the shared representation of the target position of the leg and are implemented as recurrent neural networks. α, β, and γ denote the three joint angles. biological systems, it is important to integrate the redundant information and to fuse the sensory data. Third, predictive models are already important in motor control to account for the delay of sensory feedback. But in addition they are a prerequisite for the ability to plan ahead. In this paper, we present a recurrent neural network approach for an internal model of the body which addresses all three tasks mentioned. We want to focus here on the inverse function and show how this type of model can be applied to the control of a simulated six-legged walking robot. As this robot has a high number of degrees of freedom, the overall complexity will be distributed onto two levels of representation. We will explain how these levels are interconnected. The work presented demonstrates the feasibility of the approach for very complex manipulator structures and how an internal model of the body can be grounded that can be also used for prediction and sensor fusion. II. MMC BODY MODEL The task of the body model is to control the walking of a six-legged robot. Each leg consists of three joints. The central body of the robot consists of three segments that are coupled via two universal joints. Therefore, the robot has 22 degrees of freedoms in total. During walking not all the legs are on the ground at the same time. But even with only three legs on the ground—as during tripod walking— there are still at least 13 degrees of freedom which have to be controlled and which are directly coupled. Therefore, it is helpful to distribute the complexity onto different levels of representation (Fig. 1). In our approach we divide the complexity onto two levels. On the lower level, each leg is represented. The kinematics of the leg are described through