d Practical Stabilization of a Skid - steering Mobile Robot - A Kinematic - based Approach and calculate the resultant reactive force as III . CONTROL DEVELOPMENT

This paper presents kinematic control problem of In this paper we propose to treat SSMR a as system skid-steering mobile robot using practical smooth and timesubjected to non ideal nonintegrable constraint. Next, we varying stabilizer. The stability result is proved using Lyapunov formulate kinematic control law based on tunable oscillator analysis and takes into account both input signal saturation and uncertainty of kinematics. In order to ensure stable motion of [4] and transverse functions [5] which is robust to uncertain the robot the condition of permissible velocities is formulated bounded kinematic parameter. Taking into account the part of according to dynamic model and wheel-surface interaction. dynamics we give a condition of stable motion with respect Theoretical considerations are illustrated by simulation results. to position of instantaneous center of rotation. Here we consider control problem assuming that linear and angular velocity can be treated as control input and Considering ground wheeled vehicles one can distinguish neglect the task of enforcing this velocities by actuators. Such two main categories, i.e. vehicles for which non-slip and approach is used for dividing control tasks onto two levels, i.e pure-rolling conditions may be assumed [3] and vehicles for kinematic and dynamic and can be relatively easy used in real which skid phenomena is used for proper operation. Although applications. skidding effect between wheels and surface may be observed The paper is organized as follows. In Section II kinematic for all vehicles, only for the second group known as skidand dynamic model of SSMR is presented and condition of steering vehicles it is necessary to change their heading. stable motion is formulated. In the next section the control law Skid-steering structure is commonly used in robotics that is using tunable oscillator is developed with respect to limited due to its simplicity and mechanical robustness. In particular kinematic uncertainty and formal proof of stability is given. skid-steering mobile robots (SSMRs) are quite similar to In order to limit robot velocity scaling algorithm is proposed. robots equipped with two-wheeled differential driving system In Section IV simulation results are presented. Concluding (i.e. unicycle-like robots). However, there is an important remarks are given in Section V. difference between them, namely for SSMR ground-wheels interaction and skidding effect play an important role within II. MODEL OF SSMR ROBOT high range of velocities and accelerations (in contrast for other vehicles skidding is usually noticeable only for higher A. Kinematics linear and angular velocities). Since ground reaction forces Consider a Four Wheel Drive (4-WD) SSMR placed on the are very difficult to calculate and measure the model of plane (Fig. 1) with inertial frame X.Yg and define a local SSMR dynamics is not accurate. Moreover, in spite of that f a ^ ~~~~frame xy,V attached to itS center of mass (COM). Let q= fact that skidding is necessary to change robot's orientation, [X Y Q] x S denotes generalized coordinates describing extensive skidding causes the motion to be unstable hence robot's position, X and Y, in the inertial frame and orientation, it is necessary to limit velocity of the vehicle.~, it is ecessay mi veocity le 0, of the local frame with respect to the inertial one. Control problem for SSMR is quite challenging mainly 0ofth lalsme withe reset to theiertial oe. Next, assume that the robot moves with velocity vector q. because of two facts. Firstly, SSMR is an underactuacted sysIn the local frame one can describe robot motion using vector tem and secondly, its mathematical model is highly uncertain. A[vx v0 Te R3, where vx, v and w denotes longituIn the robotics literature not much has been written about a v y controlling of SSMR using formal mathematical approach and stability analysis. In some papers (see [2] and [8]) for control From Fig. 1 one can easily find the following tangent map purposes authors assumed an ideal nonholonomic constraint rB=J (q) qji (1) which cannot be enforced in practice. Additionally, linear techniques presented in [2] do not allow to solve stabilization A FR70) 01 saJcba arxwt 0 problem because of Brockett's obstruction [1] and to control whr J1o i orientation directly (only position tracking is considered). $O (2). 1-4244-971 3-41061$20.OO ©2006 IEEE 519 Authorized licensed use limited to: INDIAN INSTITUTE OF TECHNOLOGY MADRAS. Downloaded on May 6, 2009 at 23:46 from IEEE Xplore. Restrictions apply. ICM 2006 * IEEE 3rd International Conference on Mechatronics Y i It should be noted that determination of F (q) is quite diffiIC = cult since it results from complicated wheel-ground interaction phenomena. In this paper in order to describe reactive lateral 3 forces Fri (i = 1, 2, 3, 4) (see Fig. 2) we use the following Y L _ ------>Nvsy< b}