Image Based Visual Servoing for Omnidirectional Wheeled Mobile Robots in Voltage Mode
Abstract
This paper presents a new image based visual servoing (IBVS) control scheme for omnidirectional wheeled mobile robots with four swedish wheels. The contribution is the proposal of a scheme that consider the overall dynamic of the system; this means, we put together mechanical and electrical dynamics. The actuators are direct current (DC) motors, which imply that the system input signals are armature voltage applied to DC motors. In our control scheme the PD control law and eye-to-hand camera configuration are used to compute the armature voltages and to measure system states, respectively. Stability proof is performed via Lypunov direct method and LaSalle’s invariance principle. Simulation and experimental results were performed in order to validate the theoretical proposal and to show the good performance of the posture errors.
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Introduction
Wheeled mobile robots (WMR) are robotic systems with free motion in a plane, and they have capacity to reach every position on the same plane. WMR issues are about how to move them, because they may have or not may have limited trajectories to perform. In our case, we are going to study the omnidirectional mobile robots (OMR)[1] whose trajectories are not limited. In a more particular way, it is emphasized in OMR with four swedish wheels [2]. The methodology proposed in [3], was chosen to obtain the dynamic model, together with the direct current (DC) motor equations presented in [4].
In order to acquire WMR posture by means of computer vision, it is possible to implement global vision systems (GVS). The GVS fits in the intelligent space concept [5], [6]. An intelligent space is comprised by sensors (e.g. cameras, microphones, ultrasound or laser range finder), computer, actuators and communication devices. The sensors are used to identificate and track the objects in the space and/or to receive orders from operators. The computer acquires information from sensors, performs image processing, computes control law and communicates with actuators. The intelligent space interacts with objects through robotic platforms (e.g. WMR) that provide services like carrying or delivering loads. GVS are used in robotics soccer competitions to acquire the posture of every robot on the playground [7], [8]. So, GVS are a good option to obtain the posture measurement of WMR.
The contribution of our paper is the proposal of a new control scheme to OMR posture control in voltage mode, requiring only vision system measurements. Furthermore, in our control scheme, the DC motors do not require encoders or drivers with current loop or velocity loop. Document is structured as follow. Section 2 presents the problem statement and the dynamic model in image space too. Control law and stability proof is presented in Section 3. Simulation and experimental results are showed in Section 4. Finally, Section 5 shows our conclusions.
Conclusion
We have presented a new IBVS scheme for OMR with four swedish wheels. The PD control law was implemented with errors in image space. Stability was proven via Lyapunov direct method, and globally asymptotically stability of the closed loop system was established by using the LaSalle’s invariance principle. Positive PD gains of the controller are sufficient to guarantee asymptotic stability in accordance with the stability proof. Simulations show satisfactory results because the states achieved the desired states. Experimental results show a steady state error in the orientation variable, the position reaches to desired position. Steady state error is due to non-modeled static friction in the DC motors axes. As long as, the states are brought closer to desired states, the computed armature voltage by control law decreases. The above implies that the voltage is insufficient to move the remaining angle. A possible solution could be to implement functions like hyperbolic tangent to keep a higher voltage near of desired posture.