Robust forward\backward control of wheeled mobile robots

Highlights

• Proposing a control algorithm for forward and backward trajectory tracking.

• Designing the controller in the configuration space without using transformations.

• Investigating a slip estimator to attenuate the effects of unknown uncertainties.

• Analyzing the stability of the control algorithm using the Lyapunov method.

• Presenting various case studies and comparative results to show the effectiveness.

Abstract

Obtaining a control algorithm capable of navigating the system both in forward and backward motions is one of the control objectives for tractor-trailer wheeled robots (TTWRs). In this paper, a relatively general structure is presented for both forward and backward control of an n-trailer wheeled mobile robot (NTWMR) in the presence of wheel slip effects. To keep better overall performance and track the reference trajectories in forward and backward motions, the NTWMR is intended to be controlled in the presence of slip effects. A control algorithm accompanied by a slip compensation procedure is proposed for the system simultaneously. First, the mathematical model of the system in the presence of slip effects is obtained. A novel physically motivated algorithm is proposed for the tracking control in the presence of unknown uncertainties (longitudinal and lateral slips) for both forward and backward motions. By estimating the slip effects at any instant, the control inputs are produced to compensate for their destructive effects on tracking control of the NTWMR. Then the stability of the closed-loop system is evaluated using the Lyapunov theory. The potential of the proposed controller was verified through several case studies, including comparative results and experimental validation in various motion control manoeuvers for a vehicle with trailers. The proposed method is the first algorithm that can cover a broad range of TTWR motion tasks (forward and backward trajectory tracking, slip attenuation, and global stability), which are required to be developed in NTWMRs.

Introduction

Control of wheeled mobile robots (WMRs) attracted much attention these years in engineering due to the existence of nonholonomic constraints, which are limitations on system generalized velocities [1], [2]. Due to the Brockett necessary condition for asymptotic feedback stabilization, a nonholonomic system cannot attain exact stability via a static state feedback control algorithm and requires specific tools and algorithms [3]. Most of the previous works in this field have been proposed for wheeled systems without trailers, and fewer papers have studied cars with passive trailers. Among mobile robots, tractor-trailer systems have many industrial and engineering applications in transportation and also in agricultural systems [4], [5]. An n-Trailer WMR (NTWMR) has n $+$ 3 generalized coordinates and two velocity inputs, where n is the number of trailers connected to the tractor. Therefore, the tractor-trailer wheeled robots (TTWRs) are under-actuated systems. These systems have two kinematic inputs, including rotational velocities of the tractor wheels. A TTWR can be maneuvered from point to point in the system workspace. The proposed control algorithms are mainly used for forward control of TTWRs and there exist little works on backward control of TTWRs, [6]. In this paper a new control algorithm is proposed that can be used for both forward and backward trajectory tracking of NTWMRs.

In most of the works, motion constraints are assumed not to be violated to simplify the problem. However, in real applications, unknown features exist, such as slipping wheels that violate the ideal constraints. Therefore, robustifying the control algorithms against these disturbances and uncertainties is necessary for real engineering systems.

With the fast evolution of mobile robotics, control algorithms are required to exhibit a more accurate performance and resist disturbances and uncertainties. Resolving the effects of uncertainties and disturbances is one of the most robotics challenges in robotics [7]. These systems suffer from the effects of unknown and unpredictable phenomena that disrupt the behavior of control algorithms. Therefore, achieving proper control performance in these conditions requires further studies and further developments. A variety of control methods have been designed to compensate for uncertainties and perturbations in robotic systems. Sliding mode control [8], [9], adaptive control [10], [11], backstepping control [2], [12], and neural networks [11] are some of the control algorithms proposed for WMRs.

In [8] a sliding mode controller is proposed for a tractor-trailer wheeled robot assuming a prior knowledge of system disturbances. A dual closed-loop sliding mode controller is presented for a wheeled mobile manipulator in [13]. To guarantee that the sliding surface is attractive, usually large control coefficients are used. Therefore, fluctuations in the control inputs are amplified, and the undesirable so-called chatting effect occurs. This phenomenon causes destructive effects on actuators or instability of the algorithm.

On the other hand, robust control methods often require boundaries of system uncertainties. These margins are not readily computable due to the unknown nature of the uncertainties. Therefore, pure robust controllers are mostly conservative because of the necessity of using previous information about margins of system uncertainties in worst-case schemes. For this reason, they do not have the proper speed in tracking problems. To resolve the negative properties, adaptive rules can be used to remove the need for prior knowledge of the uncertainties’ boundaries. These methods can eliminate the drawbacks using a trade-off between the performance specifications and robustness. To improve the ability of disturbances and uncertainties attenuation, [14], [15] investigated robust adaptive controllers with the estimation of boundaries of system uncertainties. In [16] an adaptive sliding mode control algorithm has been used for the tracking control of WMRs. In [2] adaptive backstepping method is used to estimate and attenuate the slip disturbances.

Reference [17] reviews linear and nonlinear disturbance/uncertainty estimation techniques and then compares different compensation methods and the ways of mixing disturbance/ uncertainty compensation with a designed linear/nonlinear algorithms.

A radial basis function neural network controller based on disturbance observer is investigated in [18] for a differential drive WMR. In [11] an adaptive neural network-based tracking control algorithm is proposed for a WMR with full state constraints. However, the method is complicated and suffers from a considerable computational cost. In [19] a disturbance observer is presented to estimate the lumped disturbance in a unicycle type wheeled vehicle. In [20] an extended Kalman filter is used to deal with disturbances for the trajectory tracking control of a differential drive WMR. Also [21] proposed a disturbance rejection model predictive controller for a unicycle type wheeled robot. An active disturbance rejection control is also presented in [22] for a 6 wheel skid-steer mobile robot. The presented approaches are mostly applied to WMRs without trailers. In this paper, in addition to the new algorithm proposed for both forward and backward trajectory tracking of NTWMRs (as the main contribution), a least-square compensation as an alternative approach along with the control algorithm is used to compensate for uncertainty effects in tractor-trailer wheeled robots. Precise guidance in real systems such as agricultural vehicles with trailers is somewhat difficult due to uneven and indeterminate ground conditions, which cause both lateral and longitudinal slips. Therefore, the presence of such kinematic uncertainties leads to unsatisfactory results in real systems. The chosen uncertainty estimation tool is algebraic and therefore preferable due to the simplicity of the method, convenience in employing the approach, and requiring less computational cost which results in fast and efficient uncertainty elimination in tractor-trailer systems.

Theoretically, there is no restriction on the number of trailers. However, in reality, this number is restricted. Since a multi-body TTWR has a sequential connected structure, any measurement or modeling error affects the control performance. In practice, disturbances and uncertainties may be sources for system control errors. Therefore, general analytical solutions in the existence of modeling uncertainties are proposed using robust and adaptive controllers [23].

Backward motion control of TTWRs is also a challenging problem because the open-loop system of the TTWRs in backward motion is unstable. This is as a result of the well-known jack-knife effect [24]. In the references [25], [26] an idea is proposed to prevent the jack-knife phenomenon and the trailer crash with the vehicle for the forward and backward movements, to ensure greater accuracy in tracking control. In [6] a Lyapunov-based method is proposed to control the backward orientation control of an NTWMR. While the proposed approaches cannot simultaneously control the forward and backward motions, only the orientations are regulated.

In applications for tracking and regulation control of tractor-trailer systems, the aim is to control the last trailer’s position and orientation within an acceptable range of errors usually. Therefore, all other connected trailers should transfer appropriate designed control inputs to steer the last trailer toward the desired configuration [23]. The interesting kinematic design used in passive trailer systems can be deduced that the motion of each trailer can be converted to the next trailer’s motion as a kinematic chain. So the most critical point here for a passive trailer system is to design a feedback control with a slip estimation module as a frequent source of uncertainty.

The proposed algorithm is the first control algorithm (to the authors’ best knowledge) that can be used simultaneously for the forward and backward motions of TTWRs in the presence of wheel slips. Most of the controllers proposed for wheeled robots use transformations such as chained form and power form, and so on, [27]. In contrast, the proposed method is designed in the robot configuration coordinates space. This makes it possible to control the system both in the forward and backward motions. An estimation mechanism is also used to attenuate slip effects, which is focused, in this paper. The proposed method is one of the first researches that can cover a broad range of TTWR applications and motion tasks (forward and backward trajectory tracking, slip attenuation, and global stability), which are required to be developed in NTWMRs. Therefore the main contributions of this paper are listed as follows:

• Proposing a novel physically motivated control algorithm that can cover a broad range of TTWR applications and motion tasks, including forward and backward trajectory tracking, slip attenuation, and global stability (Main Contribution).

• Designing the control algorithm in the robot configuration space without using conventional transformations such as chained form, power form, etc., makes it possible to control the system both in the forward and backward motions.

• Investigating a slip compensation mechanism to attenuate the destructive effects of unknown uncertainties on tracking control of n-trailer systems at any instant of time.

• Analyzing the stability of the proposed control algorithm using the Lyapunov method.

• Presenting various case studies, including comparative results and experimental validation, to show the robustness and effectiveness of the proposed method, which are compared and summarized in Table 1.

In the following, first, the kinematic model of a WMR with NTWMR is presented in the presence of slip effects. Then, a control law is proposed for tracking control of the system. Next, a slip estimation module is added to the control algorithm for online estimation, and wheel slips compensation. The stability of the closed-loop system is also analyzed using the Lyapunov theory. Finally, the obtained comparison and experimental results are presented. The results show that the robot wheel slip effects are compensated in both forward and backward motion control maneuvers using the provided control algorithm.