Complementary-route based ICR control for steerable wheeled mobile robots

Abstract

Emerging industrial applications involving mobile manipulation in the presence of humans is driving attention towards steerable wheeled mobile robots (SWMR), since these can perform arbitrary $2D$ planar trajectories, providing a reasonable compromise between maneuverability (necessary for human avoiding algorithms) and effectiveness. Instantaneous center of rotation (ICR) based kinematic models and controllers are the most suited for such robots, as they assure the existence of a unique ICR point at all times. However, unsatisfactory behavior do exist in numerous applications requiring frequent changes in the sign of the angular velocity command. This is typically the case for robot heading control: moving the ICR point from one border of the $2D$ ICR space to the other makes it pass by the robot geometric center, where only pure rotations are feasible. This behavior is not desirable and should be avoided. In this paper, we propose a novel complementary route ICR controller, where the ICR can go from one extreme to the other by means of border switching in one sample period. Thanks to this approach, fast response to the velocity commands is achieved with little steering motion. The new algorithm has been tested successfully in simulations and experiments, and is more time efficient with far more satisfactory behavior than the state-of-art direct route based controllers. These results have been also confirmed quantitatively, using a newly developed metric, the command fulfillment index (CFI).

Introduction

Steerable wheeled mobile robots employing traditional wheels are getting more popular in industrial applications, due to their lower cost for a given load carrying capacity as compared to fully omnidirectional (holonomic) mobile robots (FOMR) employing swedish or other non-conventional wheels [1]. Other promising holonomic alternatives employ fully powered castor wheels [2], [3] or differential drive system with offset turret [4], [5]. However, since these are not yet commercially available, they are not used in industrial automation.

Despite being non-holonomic, SWMR robots can perform complex $2D$ planar trajectories, assuming correct initial wheel orientation, followed by steer coordination (to maintain a unique ICR point throughout operation). However, their kinematic structure has several challenging research problems, the most critical of which are: 1. proper steering coordination, to avoid actuator fighting [6], [7], [8], [9], 2. avoidance of kinematic and representational singularities [7], [10], [11], [12], [13], [14], [15], [16], and 3. fulfillment of steer joint performance limits while solving the previous problems [13], [17], [18], [19], [20], [21], [22], [23]. Kinematic modeling and control of SWMR is usually done either in the $2D$ ICR space [13], [16], [20], [21] or in the $3D$ Cartesian space [7], [10], [24], [25]. In [11], [26], [27], both are combined, since the ICR space is best suited for steering coordination (to avoid actuator fighting and wheel slippage) as it ensures the existence of a unique ICR point, while Cartesian space is utilized for robot speed control. Here, we also use ICR-based steer coordination, and the focus of this work is precisely to enhance ICR based controllers, through the design of a complementary route strategy.

In applications requiring that some heading angle is maintained (e.g., vision-based tasks where features must stay in the field of view), or that the translation verse changes, the ICR point is required to move long distances from one extreme of the workspace to the other, usually passing by the robot geometric center, where the feasible robot velocity is limited. In such scenarios, the state-of-art ICR based controllers will lead to unsatisfactory behaviors.

To solve this problem, here we propose a comparison between the direct and complementary ICR routes, the former (state-of-art approach) being the shortest straight line connecting the current and desired ICR points, while the latter (proposed here) connecting the ICR extreme borders via a border ICR point that is chosen to minimize the total ICR distance moved across borders. The $4$ borders here define the maximum values that the ICR point is allowed to take on the $x$ and $y$ axes of the geometrically centered robot frame. Instead of moving directly to the desired ICR, the complementary route will move first to the optimum border point lying on the nearest border line, switch borders, for example: from the $+y$ to the $-y$ border line in one sample period, and finally move to the desired ICR point. A graphical representation of such process is shown in Fig. 1.

In [20], the direct ICR route is stereographic projected onto a unit sphere, where moving between complementary borders can be done at the pole of the unit sphere. However, the authors do not provide any investigations on border switching nor simulations showing the joint-space performance. To the best of the author’s knowledge, the work presented in this paper is the first connecting ICR borders to obtain more efficient SWMR control.

One of the contributions of the method adopted here is to provide a solution that is decoupled from the high level command/perception controller. Here, the trajectory planning does not need any prior knowledge of the robot structure: only the current robot velocity and pose will suffice to close the feedback loop. The error between the provided command and the actual capability of the robot is handled locally thanks to the proposed controller. In order to quantitatively assess the enhanced performance, we introduce the command fulfillment index (CFI) that is based on the robot velocity error vector, and we use it to compare the direct and complementary route controllers.

In this work, the authors extend the kinematic control framework of [26] so that it:

• can handle sign variations in the rotational speed commands, that are frequent in orientation (heading) control applications,

• has better responsiveness (assessed via the CFI),

• demands less steering motion (in terms of both velocity and acceleration).

In the rest of the paper, Section 2 presents the necessary background on the kinematic model and controller. The complementary ICR route based controller is detailed in Section 3. The complementary/direct route decision making algorithm is presented in Section 4. Experiments are depicted in Section 5. Conclusions are finally given in Section 6.