Motion Control of Differential Wheeled Robots with Joint Limit Constraints J. Gonzalez-Gomez, J. G. Victores, A. Valero-Gomez, M. Abderrahim Abstract— The motion of wheeled mobile robots is inherently based on their wheels’ rolling capabilities. The assumption is that each wheel can rotate indefinitely, forward and backwards. This is the starting point for all motion control mechanisms of wheeled robots. In this paper, a new motion capability of differential mobile robots with limited wheel rotation ca- pabilities is presented. The robot will be able to travel any distance and change its direction of movement even if the its wheels can not rotate within more than a certain range of angles. The proposed solution is based on the bio-inspired controller principles used for modular and legged robots, in which oscillations are generated for achieving motion. A total of two oscillators, one per wheel, are enough to generate well- coordinated rhythms on the wheels to control the robot motion. The kinematics of this new type of mobile robot motion is presented, and the relation between the oscillator’s parameters and the trajectory is studied. Experiments with real robots will demonstrate the viability of this new locomotion gait. I. I NTRODUCTION Motion control of a mobile robot assumes that its wheels can rotate indefinitely and in any direction. Based on this principle, controllers are designed to set the speed of the wheels in order to follow a trajectory or reach a target location. This motion principle is inherent to the wheel concept, and the four basic wheel types rely on it: standard wheels, castor wheels, spherical wheels, and Swedish wheels [1]. All of these configurations are controlled by means of their wheel’s angular velocities, assuming that their rotation is not constrained by any internal or external factor. Researchers around the world are designing articulated wheeled robots [2] that include wheels and joints. The combination of wheels and joints allows robots to adapt their morphology to the terrain, increasing their maneuverability or even climbing steps [3]. These robots also have the capability of reconfiguring themselves if a wheel is broken, continuing movement (with a reduced maneuverability), thus increasing their robustness. Fault tolerant control systems is currently a hot topic of research, including its applications in the field of mobile wheeled robots. Within this topic, there are two important research issues: first, how to detect faults from their conse- quences (self-aware agents) [4]; second, how to cope with faults once they are detected [5]. Among this second line of research, it is important to deal with hardware faults, that may require a reconfiguration of the robot to replace the func- tionality of the faulty part. Robustness can be also achieved J. Gonzalez-gomez, J. G. Victores, A. Valero-Gomez and M. Ab- derrahim are members of the Robotics Lab research group within the Department of System Engineering and Automation, Universi- dad Carlos III de Madrid( jggomez, jcgvicto, avgomez, mohamed)@ing.uc3m.es Fig. 1. A mobile robot with limited wheels, which cannot rotate 360 degrees by means of reconfigurable robots, which are capable of adapting themselves to given tasks. In these situations robots are not dealing with faults but with unexpected situations or scenarios. Hofbaur et al. [6] have recently proposed a new wheeled modular re-configurable robot. It consists of interconnected hexagonal cells that allow the user to quickly configure/reconfigure various robot drives and change the robot’s geometry. The drive units that can be attached to each module are either standard wheels or omni-directional wheels. In 2002 Quinn et at. [7] developed the idea of whegs, that combines the advantages of wheels and legs. Wheels are relatively simple, and allow a vehicle to move over terrain quickly. Legs allow robots to climb obstacles that are higher than what a wheeled vehicle would be able to climb over. Whegs have also been used for climbing robots [8]. The X-RHex biologically inspired hexapedal robot [9] is the latest generation of the RHex family. It includes six legs with a half-circle shape, each one connected to a rotatory actuator. Therefore, the legs turn like standard wheels. Even if this design is mechanically simple, the robot is able to walk, run, move on rough terrains, and climb stairs. Shen et al. [10] have designed the Quattroped, a new Leg-wheel hybrid mobile platform. The morphology of the wheels can change dynamically from a full circle into a half- circle leg, similar to the ones used by Rhex. It has great mobility on both flat grounds (by wheels) and rough terrains