Adaptive Control of Dynamic Legged Locomotion Alexander Schmitz *† , Gabriel G´ omez * , Fumiya Iida *‡ and Rolf Pfeifer * * Artificial Intelligence Laboratory, Department of Informatics, University of Zurich, Andreasstrasse 15, CH-8050 Zurich, Switzerland † Department of Philosophy of Science, University of Vienna, Universit¨ atsstrasse 7, 1010 Vienna, Austria ‡ Robot Locomotion Group, CSAIL, MIT, 32 Vassar Street, Cambridge, MA 02139, USA alex@cognitivescience.at, [gomez, pfeifer]@ifi.unizh.ch, iida@csail.mit.edu Abstract— Rapid adaptation of behavior is important partic- ularly for embodied systems that interact dynamically with the environment. This paper demonstrates how dynamic embodied interaction can be exploited to simplify not only the control architecture but also the learning processes of behavior control. A learning architecture of a four-legged running robot is explored as a case study both in simulation and in the real world. We first explain how a simple control architecture can adjust the running speed using only one control parameter by exploiting the passive dynamics of a quadruped robot. In simulations, a 2-layer learning neural network is then compared to a preprogrammed controller. Tests using an ARTMAP neuronal network controller demonstrate that the real-world robot can run and stabilize its position on a treadmill as the speed varies. The multimodal sensory information is also analyzed, which is used for designing a feedback control of forward velocity. I. INTRODUCTION There has been an increasing interest in dynamic locomotion by exploiting passive dynamics. Previously, a series of four- legged robots have demonstrated robust running behavior by using simple control architectures (e.g. [1], [2], [3], [4], [5], [6]). In general, legged locomotion behavior can be achieved by exploiting the particular body dynamics resulting in self-stabilization mechanisms (some of the concepts have been proposed in for example [7], [8], [9]). The intrinsic stability of the compliant leg in the feed-forward locomotion has been extensively explored previously, although most researchers investigated the control scheme with a stance and flight phase. (e.g. [10], [11]). Such self-stabilization mechanisms have advantages for autonomous systems (e.g., energy efficiency, simple control architectures, and better adaptability). Previously it has been shown that a learning architecture can exploit the dynamic system-environment interaction for real-time learning of relatively complex bipedal walking [12], [13]. Most of the machine learning studies of legged locomo- tion in the past focused on the learning of a basic behavioral function (e.g. walking with optimal energy efficiency). In this paper we demonstrate how a dog robot can maintain its forward velocity adaptively while running on a treadmill. Because the robot exploits its body dynamics, the running This work was supported by the Swiss National Science Foundation (Grant No. 200021-109210/1) speed can be adjusted by just one control parameter, which results in a simple learning process. Experiments were carried out in simulation and the real world, in both we first used a preprogrammed controller to adjust the speed and then used a neural network to obtain the sensorimotor relationships. In each case the goal of the robot was to stay as close as possible to a target. In the real world this was the middle of the treadmill, defined by a certain distance to a white wall in front of the treadmill, and in the simulation we introduced a target which moved forward at varying speeds. In other words, in the real world the treadmill moved the robot away from its target position and in the simulation the target itself moved. Seen from the point of the robot this makes no difference: it has to adapt its speed to the one of the target. The structure of this paper is as follows. In section 2 we explain the design and control of our quadruped robot. Section 3 describes experiments done in simulation and section 4 and 5 in the real world. We conclude with a discussion and an outlook to future developments in section 6. II. DESIGN AND CONTROL OF THE ROBOT A. Morphological Design The design of the robot is inspired by the spring-mass model studied in biomechanics. As shown in Fig. 1, the robot has four identical legs, each of which consists of one standard servomotor located at the shoulder/hip, and two limbs connected through a passive elastic joint. We used aluminum for the design of the body frame and the legs. The robot is 20 cm long, 11 cm wide, 15 cm high and weighs 1 kg (refer to Table I for more detailed specifications). The control signal for the motors and the electricity are supplied externally through cables. We used the standard USB communication protocol to send the positions of the servomotors, set the speed of the treadmill, and acquire the sensory input at a rate of 50 Hz. B. Motor Control We apply a parsimonious control strategy, in which the controller is kept as simple as possible. This control method does not require any global sensory feedback: it does not need to distinguish between a stance and a flight phase, nor