Passivity-based tracking control of an omnidirectional mobile robot using only one geometrical parameter

Highlights

• A passivity-based output feedback control is proposed based on energy shaping plus damping concept.

• The proposed control design does not require dynamic model information.

• The robot natural damping is effectively exploited.

• The stability proof is given based on the Lyapunov method.

• Experiments are conducted to verify the tracking and robustness performance.

Abstract

This paper presents an output feedback tracking control scheme for a three-wheeled omnidirectional mobile robot, based on passivity property and a modified generalized proportional integral (GPI) observer. The proposed control approach is attractive from an implementation point of view, since only one robot geometrical parameter (i.e., contact radius) is required. Firstly, a nominal dynamic model is given and the passivity property is analyzed. Then the controller is designed based on passivity property and a modified GPI observer. The controller design objective is to preserve the passivity property of the robot system in the closed-loop system, which is conceptually different from the traditional model-based control methodology. Particularly, the designed control system takes full advantage of the robot natural damping. Therefore, only considerably small or non differential feedback is needed. In addition, theoretical analysis is given to show the closed-loop stability behavior. Finally, experiments are conducted to validate the effectiveness of the proposed control system design in both tracking and robustness performance.

Introduction

Omnidirectional mobile robots (OMRs) can be applied in many areas, especially those confined environments, such as medical institutions, factories. OMRs can move in arbitrary motion in an arbitrary orientation without changing the direction of wheels (Song & Byun, 2004), thus they can perform motions with high maneuverability.

In the literature, dynamic control of OMRs has been extensively studied in recent two decades (Barreto S. et al., 2014, Comasolivas et al., 2017, Huang et al., 2015, Liu et al., 2007, Rotondo et al., 2015, Tu, 2010, Watanabe et al., 1998). In Watanabe et al. (1998), a feedback linearization approach, resolved acceleration control (RAC), was applied to an OMR with three lateral orthogonal-wheel assemblies, in which the control performance depends on the accuracy of the dynamic model. Considering actuator dynamics, Liu et al. (2007) designed a nonlinear controller for an OMR using a trajectory linearization control method. In Barreto S. et al. (2014), a model-predictive control based friction compensation scheme was proposed for a three-wheeled OMR using a static friction model. In this work, six parameters of the static friction model were identified. In Tu (2010), a simple linear model was obtained by linearizing a complicated dynamic model of a three-wheeled OMR using kinematics. Then a linear optimal controller was designed based on the simple linear model. In Huang et al. (2015), a smooth switching adaptive sliding-mode controller was proposed for the tracking control with both structured and unstructured uncertainties. In Rotondo et al. (2015), based on LMI-based techniques, a switching quasi-linear-parameter-varying controller was proposed for a four-wheeled OMR. In Comasolivas et al. (2017), a proportional–integral controller was obtained based on quantitative feedback theory for a redundant OMR with four wheels. However, all of the controllers mentioned above are designed based on dynamic model. It is well known that both the dynamic modeling and parameter identification are complex and time-consuming in practice. Therefore, a control system design will be particularly attractive if the tedious dynamic modeling and parameter identification process can be avoided.

Passivity is a fundamental property of rigid robot systems (Ortega & Spong, 1989). The design philosophy is to reshape the robot system’s natural energy and add damping via velocity feedback, for stability purposes. Specially, the robot physical structure (e.g., natural damping) can be exploited. Therefore, the controller design philosophy of passivity-based control is conceptually different from traditional control methods, such as RAC. It is known that RAC is based on the well-known concept of feedback linearization, in which the natural damping of the robot is completely canceled. Passivity-based control has been applied to solve many control problems of robotics, e.g., robot control (Atashzar et al., 2017, Wang and Xie, 2014, Zhang and Cheah, 2015), teleoperation control (Sabattini et al., 2018, Shahbazi et al., 2018), spacecraft control (Hao et al., 2017, Liang, 2015), to name a few. Besides, it is shown in Bickel and Tomizuka (1999) that the passivity-based approach can be used for the stability analysis of the disturbance observer based algorithm, under the condition of a specific design for Q(s) filter of the disturbance observer. On the other hand, generalized proportional integral (GPI) observer is a disturbance observer (Sira-Ramírez, Núñez, & Visairo, 2010), with simple structure and good estimation of the time-varying disturbances. GPI observer has been successfully applied in various applications (He et al., 2018, Ramos et al., 2015, Rodriguez-Angeles and Garcia-Antonio, 2014, Yang et al., 2018), to name a few. Note that, the Q(s) filter is not used in GPI observer.

In this paper, a passivity-based output feedback control (POFC) is designed for trajectory tracking of a three-wheeled OMR, based on a modified GPI observer. Firstly, a robot dynamic model is given and the passivity property of the robot is analyzed. Then the control system is designed, in which a modified GPI observer is employed to estimate model uncertainties and external disturbances. The design objective is to preserve the passivity property of the robot in the closed-loop system, which is conceptually different from traditional control design, such as feedback linearization control approaches. It should be emphasized that the differential feedback gains can be selected considerably small or even zero due to an effective exploitation of the robot natural damping. Only one geometrical parameter is used in implementation of the proposed control approach (i.e., the contact radius of each wheel). Theoretical analysis is presented to show the closed-loop stability behavior. Finally, experiments are conducted to compare the tracking accuracy and robustness of the proposed control design against traditional model-based RAC.

Compared with the previous works, specially (Arteaga-Pérez & Gutiérrez-Giles, 2014), the contributions of this paper are as follows: (1) an output feedback tracking control scheme is proposed based on the energy shaping plus damping concept, by combining the well-known passivity-based approach of Slotine and Li (1987) and a modified GPI observer; (2) the proposed control scheme does not require any dynamic model information, except a geometrical parameter; (3) the proposed control scheme takes full advantage of the robot natural damping. Only considerably small or non differential feedback is needed; (4) the stability proof is based on a well-known energy method, i.e., the Lyapunov method. The stability proof is quite straightforward.

The remainder of this paper is organized as follows. In Section 2, dynamic modeling and analysis of a three-wheeled OMR are presented. The proposed passivity-based output feedback trajectory tracking control scheme as well as stability analysis is presented in Section 3. In Section 4, implementation details, experimental results and discussions are presented. Finally, conclusions are drawn in Section 5.