Sage Journals: Discover world-class research

Abstract

This article presents sliding mode–based robust tracking control for a redundant wheeled drive system, which is designed for energy saving and fail safe motion. Wheeled mobile robots are widely used in different applications such as a wheelchair and an automated guided vehicle because of their loading capability, low mechanical complexity, and simple engineering design. In addition, using wheeled mobile robots is an effective way to enhance the quality of life for elderly and disabled people to promote their independence and to extend their activities. Wheeled mobile robots are generally operated using embedded batteries, which determine the operating time. Therefore, saving energy motion is a significant requirement to extend the operation time. The dynamics of a redundant wheeled drive system is described. Distribution control and sliding mode control for wheeled mobile robots are proposed, and its stability is guaranteed based on the Lyapunov stability theory. Finally, the robustness and effectiveness of the proposed method are demonstrated experimentally, providing superior results to conventional state feedback control and robust tracking in the real environment with less energy.

Keywords

Sliding mode control wheeled mobile robot robust control energy saving control redundant drive system

Introduction

Wheeled mobile robots (WMRs) can be used in many different fields; civil and military applications such as search and exploration, guidance, rescue, hazard detection, surveillance and transportation tasks.^1,2 Recently, many control strategies have been considered to research the tracking control problem of WMRs.^3–10 Xin et al.⁴ proposed robust adaptive tracking control of WMRs. Chen et al.⁶ proposed adaptive tracking control for a class of nonlinear stochastic system. Yang et al.⁸ proposed a robust tracking control based on extended state observer. An adaptive tracking controller for a nonholonomic mobile robot with unknown parameters has been proposed.¹⁰ Many control schemes are potentially useful for tracking control of WMRs such as dynamic surface control and disturbance observer based on fuzzy control.^11–14 However, the effectiveness of all controllers is shown only by simulation and the energy saving is not analyzed theoretically nor experimentally.

As a robust control approach, the sliding mode control (SMC) of WMRs is recently receiving increasing attention. The advantages of using SMC are fast response, good transient and robustness against system uncertainty and external disturbance.^15–21 Jorge et al.¹⁵ proposed SMC that exploits a property named differential flatness of the kinematics of nonholonomic systems. Shim et al.¹⁶ proposed SMC in which unicycle-like robots converge to a reference trajectory with bounded errors of position and velocity. Aguilar et al.¹⁷ used a path-following feedback controller with sliding mode which is robust to localization and curvature estimation errors for a car-like robot. Other control approaches such as adaptive control based on neural network for WMRs are proposed in recent years.^3,22,23 However, energy saving is not considered in those control strategies.

Furthermore, WMRs are widely used in ports, agriculture, and other different engineering fields because of their loading capability, relative low mechanical complexity, and simple engineering design. In addition, using WMRs is an effective way to enhance the quality of life for elderly and disabled people to promote their independence and extend their activities.^24,25 In fact, energy consumption is considered as one of the important problems currently faced in the field of robotics, in particular, WMRs. In the last few decades, many scientific researches have been conducted for energy saving in mobile robots.^26–32 There exist hardware approaches by reducing weights of components and changing actuators, improving the efficiency of motor power supply. Robust and optimal energy control has become prevailing approaches that are implemented in robot drivers to save consumed energy.³⁰ Ueno et al.³¹ proposed a differential drive steer system with energy saving for an omni-directional mobile robot. However, improvement of energy consumption is not analyzed theoretically nor experimentally. Mohamed et al.³³ established a new wheeled device with a redundant drive system to continue its motion safely even when one of motors breaks down for some reasons. However, robustness of the control system for the practical use is not considered.

The main contribution of this study is therefore to enhance tracking performance and conservation of energy in motor drivers of the WMRs using SMC with suitable sliding surfaces. In addition, the proposed design of WMR provides secure motion for disabled and aged people who use wheeled mobility to support their self-movement. According to the distribution controller presented in our previous article, comparative study with pole placement control (PPC) was conducted. Computer simulations are performed to verify the effectiveness of the proposed method, and there is no significant difference between the SMC and PPC approaches. In experiments, SMC provides a viable and effective method with strong robustness better than PPC. Experimental results show that the SMC approach improves the robustness performance of tracking in the real environment with less energy than PPC.

This article is organized as follows. Section “Modeling of redundant drive system” presents dynamics system structure. Distribution controller and application of SMC are included in section “Controller design and stability analysis.” Section “Simulation results” presents the simulation results. Section “Experiments” presents the experimental results. Section “Energy evaluation” presents the energy consumption. Section “Conclusion” provides concluding remarks and future work.

Modeling of redundant drive system

Dynamics system structure

This article considers a redundant wheeled drive system shown in Figures 1 and 2.³⁴ The system has two drive wheels with three motors and two planetary gears, which have high transmission efficiency and durability for high power. As shown in Figure 1, motors 1 and 2 are connected to right and left wheels through each planetary gear. Motor 3 is connected to both right and left planetary gears, and it supplies power for both wheels. Planetary gears consist of a planetary carrier and an outer gear that revolve around a sun gear. The sun gear connects to motor 3, the outer gear connects to motors 1 and 2, and the planetary carrier connects to each wheel. In this study, we do not consider any actuator constraint.

Figure 1.

Redundant wheeled drive system.

Figure 2.

Experimental device (rear side).

Dynamics model

Motion of the WMR is schematically shown in Figure 3. The proposed model includes a planetary gear property. A WMR is a plate body which has two identical driving rear wheels that are controlled by three independent actuators and two caster front wheels that are used for motion stability. In this study, it is assumed that the slipping of wheels can be ignored. The dynamics of the mobile robot is given by

M_{w} \overset{\cdot}{ν} = D_{R} + D_{L}

(1)

I \overset{\cdot\cdot}{ϕ} = (D_{R} - D_{L}) L

(2)

where $M_{w}$ , I, $\overset{\cdot}{ν}$ , and $\overset{\cdot\cdot}{ϕ}$ are the mass, moment of inertia, translational acceleration, and angular acceleration of the robot, respectively, and $D_{R}$ , $D_{L}$ , and L represent the driving force applied to the right and left wheels, and the distance from WMR’s center point to the driving wheel, respectively.

Figure 3.

Two-wheeled mobile robot.

The relationship between the linear velocity of the WMR $ν$ , angular velocity of the WMR $\overset{\cdot}{ϕ}$ , and angular velocity of two driving wheels is given by

[\begin{matrix} ν \\ \overset{\cdot}{ϕ} \end{matrix}] = [\begin{matrix} R_{w} / 2 & R_{w} / 2 \\ - R_{w} / 2 L & R_{w} / 2 L \end{matrix}] [\begin{matrix} {\overset{\cdot}{θ}}_{L} \\ {\overset{\cdot}{θ}}_{R} \end{matrix}]

(3)

where ${\overset{\cdot}{θ}}_{R}$ and ${\overset{\cdot}{θ}}_{L}$ represent the angular velocity of the right and left wheels, respectively, and $R_{w}$ is the radius of wheels. In Mohamed et al.,³³ we have the equation of motion of the WMR as

M \overset{\cdot\cdot}{θ} + C \overset{\cdot}{θ} = G τ + h

(4)

where M is the 3 × 3 inertia matrix, C is the 3 × 3 viscous friction matrix, and G is the 3 × 3 control input matrix, as follows

M = [\begin{matrix} m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \\ m_{31} & m_{32} & m_{33} \end{matrix}], τ = [\begin{matrix} τ_{1} \\ τ_{2} \\ τ_{3} \end{matrix}]

(5)

\overset{\cdot}{θ} = [\begin{matrix} {\overset{\cdot}{θ}}_{1} \\ {\overset{\cdot}{θ}}_{2} \\ {\overset{\cdot}{θ}}_{3} \end{matrix}], \overset{\cdot\cdot}{θ} = [\begin{matrix} {\overset{\cdot\cdot}{θ}}_{1} \\ {\overset{\cdot\cdot}{θ}}_{2} \\ {\overset{\cdot\cdot}{θ}}_{3} \end{matrix}]

(6)

\begin{matrix} m_{11} = \frac{J_{1}}{R_{R}} + \frac{R_{R} R_{w}^{2}}{4} {M_{w} + \frac{I}{L^{2}}} + J_{L} R_{R} \\ m_{12} = \frac{R_{R} R_{w}^{2}}{4} {M_{w} - \frac{I}{L^{2}}} \\ m_{13} = \frac{M_{w} R_{1} R_{w}^{2}}{2} + J_{L} R \\ m_{21} = \frac{R_{R} R_{w}^{2}}{4} {M_{w} - \frac{I}{L^{2}}} \\ m_{22} = \frac{J_{2}}{R_{R}} + \frac{R_{R} R_{w}^{2}}{4} {M_{w} + \frac{I}{L^{2}}} + J_{R} R_{R} \\ m_{23} = \frac{M_{w} R_{1} R_{w}^{2}}{2} + J_{R} R_{1} \\ m_{31} = \frac{M_{w} R_{R} R_{w}^{2}}{2} + J_{L} R_{R} \\ m_{32} = \frac{M_{w} R_{R} R_{w}^{2}}{2} + J_{R} R_{R} \\ m_{33} = M_{w} R_{1} R_{w}^{2} + J_{L} R_{1} + J_{R} R_{1} + \frac{J_{3}}{R_{1}} \end{matrix}

(7)

G = [\begin{matrix} 1 / R_{R} & 0 & 0 \\ 0 & 1 / R_{R} & 0 \\ 0 & 0 & 1 / R_{1} \end{matrix}]

(8)

R_{1} = \frac{1}{1 + R}, R_{R} = \frac{R}{1 + R}

(9)

C = [\begin{matrix} \frac{C_{1}}{R_{R}} + C_{L} R_{R} & 0 & C_{L} R_{1} \\ 0 & \frac{C_{2}}{R_{R}} + C_{R} R_{R} & C_{R} R_{1} \\ C_{L} R_{R} & C_{R} R_{R} & \frac{C_{3}}{R_{1}} + C_{L} R_{1} + C_{L} R_{1} \end{matrix}]

(10)

where $J_{i}$ and $C_{i}$ , $i = 1, 2, 3$ , represent the moment of inertia, and the viscous friction coefficient of the ith motor in Figures 1 and 2, respectively. $J_{R}$ and $J_{L}$ represent the moment of inertia for the right and left wheels, respectively. $C_{R}$ and $C_{L}$ are the viscous friction coefficients for them. $M_{w}$ and R are the mass of a WMR and the ratio of internal gear radius to the sun gear, respectively. $h = [h_{1}, h_{2}, h_{3}]^{T}$ is the unknown disturbance vector.

Controller design and stability analysis

Distribution controller

In this study, we assume a WMR like personal mobility such as an electrical wheelchair. The reference translational speed $ν_{ref}$ and turning speed ${\overset{\cdot}{ϕ}}_{ref}$ of the vehicle are given by an operator. The reference rotational speed ${\overset{\cdot}{θ}}_{iref}$ , $i = 1, 2, 3$ , of each motor is obtained by the distribution controller.³³ From the reference translational velocity $ν_{ref}$ and turning speed ${\overset{\cdot}{ϕ}}_{ref}$ , reference wheel velocities ${\overset{\cdot}{θ}}_{Lref}$ and ${\overset{\cdot}{θ}}_{Rref}$ are obtained from equation (3). We introduced a fixed ratio d of angular velocities of wheels to the velocity of motor 3 as follows

R_{1} {\overset{\cdot}{θ}}_{3 ref} = \frac{ν_{ref}}{R_{w}} . \frac{1}{d}

(11)

By substituting equation (3) into equation (11), we obtain angular velocity ${\overset{\cdot}{θ}}_{3 ref}$ of motor 3

{\overset{\cdot}{θ}}_{3 ref} = \frac{1}{2 d R_{1}} ({\overset{\cdot}{θ}}_{Lref} + {\overset{\cdot}{θ}}_{Rref})

(12)

From Mohamed et al.,³⁴ we have the equation of motion of the angular velocities ${\overset{\cdot}{θ}}_{1 ref}$ and ${\overset{\cdot}{θ}}_{2 ref}$ of motors 1 and 2 as follows

[\begin{matrix} {\overset{\cdot}{θ}}_{1 ref} \\ {\overset{\cdot}{θ}}_{2 ref} \end{matrix}] = \frac{1}{R_{R}} [\begin{matrix} 1 - 1 / (2 d) & - 1 / (2 d) \\ - 1 / (2 d) & 1 - 1 / (2 d) \end{matrix}] [\begin{matrix} {\overset{\cdot}{θ}}_{Lref} \\ {\overset{\cdot}{θ}}_{Rref} \end{matrix}]

(13)

When $d = 1$ , only motor 3 is used for the linear motion, while only motors 1 and 2 are used for the linear motion when $d = \infty$ (the case of typical drive condition by two motors). For any other value of d, three motors are used for the linear motion.

Application of SMC

The tracking control problem can be achieved by keeping the system trajectory on the sliding surface. The sliding surface for the ith motor is chosen as follows³⁵

s_{i} = {\overset{\cdot}{e}}_{i} + λ e_{i}, i = 1, 2, 3

(14)

e_{i} = θ_{i} - θ_{iref}

(15)

where $e = [e_{1}, e_{2}, e_{3}]^{T}$ is a vector of tracking error and $λ$ is a positive constant.

Substituting equation (15) into equation (14) leads to

s_{i} = {\overset{\cdot}{θ}}_{i} - {\overset{\cdot}{θ}}_{ir}

(16)

where ${\overset{\cdot}{θ}}_{ir} = {\overset{\cdot}{θ}}_{iref} - λ (θ_{i} - θ_{iref})$ . We apply the following sliding mode controller

\begin{matrix} τ = G^{- 1} {M {\overset{\cdot\cdot}{θ}}_{r} + C {\overset{\cdot}{θ}}_{r} - K sign (s)} \\ = G^{- 1} {(M {\overset{\cdot\cdot}{θ}}_{ref} + C {\overset{\cdot}{θ}}_{ref}) - M λ (\overset{\cdot}{θ} - {\overset{\cdot}{θ}}_{ref}) \\ - C λ (θ - θ_{ref}) - K sign (s)} \end{matrix}

(17)

where K = diag{k₁,…,k₃} and $k_{i} \geq | h_{i} |$ . $s = [s_{1}, s_{2}, s_{3}]^{T}$ , and sign(s) = [sign({s₁},…, sign(s₃)]^T is as follows

sign (s_{i}) = {\begin{matrix} 1 & if s_{i} > 0 \\ 0 & if s_{i} = 0 \\ - 1 & if s_{i} < 0 \end{matrix}

(18)

The sign(.) in equation (17) is a switching function which causes discontinuity in control signal and produces chattering that should be avoided practically. This chattering can be eliminated by smoothing the control discontinuity in a thin boundary layer, neighboring the sliding surface.³⁵ The sign(.) function is replaced by saturation function, sat(.) as follows

sat (s_{i}) = {\begin{matrix} sign (s_{i}) & if | s_{i} | > β_{i} \\ \frac{s_{i}}{β_{i}} & if | s_{i} | ⩽ β_{i} \end{matrix}

(19)

where $β_{i} > 0$ .

In order to prove the stability of the proposed system, we consider the Lyapunov function candidate as follows

V (t) = \frac{1}{2} s^{T} Ms

(20)

Differentiating equation (20) with respect to time

\overset{\cdot}{V} (t) = s^{T} M \overset{\cdot}{s}

(21)

By applying equations (4) and (16) to equation (21), we have

\overset{\cdot}{V} (t) = s^{T} (G τ - C \dot{θ_{r}} - M {\overset{\cdot\cdot}{θ}}_{r} + h) - s^{T} Cs

(22)

Considering the control law in equation (17), we have

\overset{\cdot}{V} < 0

(23)

which guarantees the stability.

Simulation results

To verify the effectiveness, the proposed controller is compared with a typical PPC by computer simulation. This study considers only smooth trajectories. We used an S-shaped velocity profile as a reference translation velocity of the WMR.³⁴ Parameters of the experimental system are as follows: M_w = 46.0 kg, I = 0.625 kg m², R_w = 0.165 m, L =0.275 m, J₁ = J₂ = 0.149 × 10⁻¹kg m², J₃ = 0.181 ×10⁻² kg m², J_L = J_R = 0.034 kg m²,C₁ = C₂ =0.268 ×10⁻¹ N m s/rad, C₃ = 0.102 × 10⁻¹ N m s/rad, C_L =0.713 ×10⁻² N m s/rad, C_R = 0.584 ×10⁻² N m s/rad, d = 3, and R = 3.

The feedback gains of PPC used in the simulation are shown in Table 1,³⁴ which are obtained by poles at −2, −2, −3 [1/s]. The SMC parameters are tuned to achieve the best results and are obtained as follows (units are omitted): K = diag{0.05, 0.05, 0.05}, λ = diag{12, 12, 12}, and $β = 0.2$ . Figures 4 and 5 show the simulation results of the translational velocity of the WMR and velocity for each motor by SMC and PPC, respectively. Figures 6 and 7 show the simulation results of the control input for each motor corresponding to Figures 4 and 5, respectively. Tracking error resulting from both control approaches in the simulation is shown in Figures 8 and 9. It can be seen that the both approaches achieve similar tracking errors and good tracking performance is obtained. The mean of tracking errors is shown in Table 2.

Table 1.

Feedback gains of PPC.³⁴

$k_{pij}$	Value (N m/rad)	$k_{dij}$	Value (N m s/rad)
$k_{p 11}$	1.40 × 10⁻¹	$k_{d 11}$	1.07 × 10⁻¹
$k_{p 12}$	3.97 × 10⁻³	$k_{d 12}$	1.6 × 10⁻³
$k_{p 13}$	1.87 × 10⁻²	$k_{d 13}$	2.14 × 10⁻²
$k_{p 21}$	3.97 × 10⁻³	$k_{d 21}$	1.6 × 10⁻³
$k_{p 22}$	1.40 × 10⁻¹	$k_{d 22}$	1.08 × 10⁻¹
$k_{p 23}$	1.86 × 10⁻²	$k_{d 23}$	2.16 × 10⁻²
$k_{p 31}$	1.87 × 10⁻²	$k_{d 31}$	2.14 × 10⁻²
$k_{p 32}$	1.86 × 10⁻²	$k_{d 32}$	2.16 × 10⁻²
$k_{p 33}$	3.61 × 10⁻²	$k_{d 33}$	1.80 × 10⁻²

Figure 4.

Simulation results with SMC (d = 3).

Figure 5.

Simulation results with PPC (d = 3).

Figure 6.

Simulation results with SMC (d = 3); control input of all motors. Same profile is obtained for $τ_{1}$ and $τ_{2}$ .

Figure 7.

Simulation results with PPC (d = 3); control input of all motors. Same profile is obtained for $τ_{1}$ and $τ_{2}$ .

Figure 8.

Simulation result with SMC depicted in Figure 4.

Figure 9.

Simulation result with PPC depicted in Figure 5.

Table 2.

Average of root mean square error (RMSE).

RMSE	SMC	PPC	Unit
Velocity of WMR	6.7 × 10⁻³	3.4 × 10⁻²	m/s
Velocity of motor 1	4.3 × 10⁻²	1.7 × 10⁻¹	rad/s
Velocity of motor 2	4.32 × 10⁻²	1.7 × 10⁻¹	rad/s
Velocity of motor 3	6.5 × 10⁻²	3.01 × 10⁻¹	rad/s

Experiments

In this work, we design an experimental test bed as shown in Figure 2. The proposed controller was experimentally verified and compared with PPC. The control law in equation (17) is implemented using C# language on a laptop PC (OS: Windows 8.1, CPU: 2.3 GHz) with sampling time of 50 ms. In addition, two optical encoders whose resolution is 0.352°/count are attached to motors 1 and 2, and an optical encoder whose resolution is 0.18°/count is attached to motor 3 to measure angular velocities of motors. A pulse counter board with two channels of 24-bit up/down counters and a DA board with 16-bit resolution are used. Motor drivers are also used in a current control mode, by which electric current is supplied proportional to the voltage commanded from the laptop PC to each motor. The control parameter values of PPC and SMC in the experiment are the same with those in simulation. Figures 10 –12 show the experimental results of the translational velocity of the WMR and velocity of each motor with SMC and PPC, respectively.

Figure 10.

Experimental result with SMC.

Figure 11.

Experimental result with SMC (sat(.)).

Figure 12.

Experimental result with PPC.

The tracking performance of a redundant wheeled drive system is improved using SMC as shown in Figures 10 –12. Figures 13 –15 show experimental results of the control input of each motor corresponding to Figures 10 –12, respectively. The chattering in the control input as shown in Figure 10 can be eliminated by replacing the sign(.) function by saturation function, sat(.), as shown in Figure 14. Tracking error resulting from both control approaches in the experiment is shown in Figures 16 –18. It can be seen that the SMC approach achieves smaller tracking errors than PPC. To verify the repeatability of SMC approach, the same experiments that were performed in Figures 10 –15 were repeated five times and the mean value of the tracking error magnitude was compared with PPC approach as shown in Figure 19. It can be seen that the SMC approach reduced the mean value of the tracking error magnitude, and it provides robust tracking control in the real environment.

Figure 13.

Experimental result with SMC; control input of all motors.

Figure 14.

Experimental result with SMC (sat(.)); control input of all motors.

Figure 15.

Experimental result with PPC; control input of all motors.

Figure 16.

Experimental result with SMC depicted in Figure 10.

Figure 17.

Experimental result with SMC (sat(.)) depicted in Figure 11.

Figure 18.

Experimental result with PPC depicted in Figure 12.

Figure 19.

Experimental result. Mean tracking error magnitude.

The circular motion was obtained by the SMC of the WMR on a circle with a radius of 2 m, and the same S-curve velocity profile with the linear motion for tangential velocity,³⁴ as shown in Figures 20 and 21. This trajectory is considered for energy comparison in the next section.

Figure 20.

Experimental result for circular motion with SMC.

Figure 21.

Experimental result for linear and angular velocity for circular motion depicted in Figure 20.

Energy evaluation

Mobile robots are operated using embedded batteries, and hence, energy saving is studied to increase the operation time. Energy required for the motors is obtained by the following equation³³

E = \sum_{i = 1}^{3} \int_{0}^{t} | τ_{i} {\overset{\cdot}{θ}}_{i} | dt

(24)

where E is the total energy consumption. Figures 22 and 23 show simulation results of total energy consumed in all motors for various values of d using SMC and PPC for linear and circular motion, respectively. We can see that in the simulation, SMC and PPC approaches have the almost same energy consumption. In addition, in both cases, $d = 3$ provides best efficiency, and compared to $d = 20$ (similar to general two-wheel drive case), around 20% energy reduction is achieved.

Figure 22.

Simulation result total energy consumption for linear motion.

Figure 23.

Simulation result total energy consumption for circular motion.

The practicability was verified by conducting five times experiments with the same condition. Figures 24 –26 show the total energy consumed in all motors for various values of d for linear motion using SMC and PPC, respectively. The minimum mean energy required was 50.08 J using SMC ( $d = 1.5$ in Figure 24), with sat(.) was 38 J ( $d = 2$ in Figure 25), and 63.43 J by PPC ( $d = 2$ in Figure 26). The total energy consumption for circular motion is shown in Figures 27 and 28 using SMC and PPC, respectively. The minimum mean energy required was 50.92 J using SMC ( $d = 1.5$ in Figure 27) and 59.37 J by PPC ( $d = 2$ in Figure 28). The SMC approach requires less energy in the real environment while achieving the better tracking performance as shown in Figure 19.

Figure 24.

Experimental result with SMC; total energy consumption for linear motion.

Figure 25.

Experimental result with SMC (sat(.)); total energy consumption for linear motion.

Figure 26.

Experimental result with PPC; total energy consumption for linear motion.

Figure 27.

Experimental result with SMC; total energy consumption for circular motion.

Figure 28.

Experimental result with PPC; total energy consumption for circular motion.

From the viewpoint of the tracking performance and consumed energy in simulation and experiment, the SMC approach is more effective only in the real case with disturbance. Equation (17) consists of three parts, first part is feed forward control which gives better tracking, the second part is position and velocity feedback control that is similar as PPC, and the last part guarantees the robustness. These control terms have good effect for tracking performance without increasing energy consumption.

Conclusion

In this article, we consider robust tracking and energy saving control for a redundant wheeled drive system using SMC. According to the distribution controller presented in our previous paper (design of a redundant wheeled drive system for energy saving and fail safe motion), comparative study with PPC was conducted. Computer simulations are performed to verify the effectiveness of the proposed method, and there is no significant difference between the SMC and PPC approaches. The effectiveness and reliability of the proposed method are evaluated by multiple times experiments in real environment with disturbance. Experimental results show that the SMC provides robust tracking performance with less energy. Future work will consider to find optimal value of a fixed ratio d. Experiments on rough terrain and public road with large distance will also be studied.

Footnotes

Academic Editor: Bin Xu

Author note

Author Shuaiby Mohamed is also an IEEE member.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

References

Chan

RPM

Stol

Halkyard

CR.

Review of modelling and control of two-wheeled robots. Annu Rev Control 2013; 37: 89–103.

Tzafestas

SG.

Introduction to mobile robot control. London: Elsevier, 2013.

Sun

Pei

Pan

. Robust wavelet network control for a class of autonomous vehicles to track environmental contour line. Neurocomputing 2011; 74: 2886–2892.

Xin

Wang

She

. Robust adaptive tracking control of wheeled mobile robot. Robot Auton Syst 2016; 78: 36–48.

Chen

CLP

Wen

Liu

. Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems. IEEE T Cybern 2016; 46: 1591–1601.

Chen

CLP

Liu

Wen

GX.

Fuzzy neural network-based adaptive control for a class of uncertain nonlinear stochastic systems. IEEE T Cybern 2014; 44: 583–593.

Shi

Yang

. Composite neural dynamic surface control of a class of uncertain nonlinear systems in strict-feedback form. IEEE T Cybern 2014; 44: 2626–2634.

Yang

Fan

Xia

. Robust tracking control for wheeled mobile robot based on extended state observer. Adv Robotics 2015; 30: 68–78.

Wen

Liu

Chen

CLP

. Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems. IET Control Theory A 2015; 9: 1927–1934.

10.

Fukao

Nakagawa

Adachi

Adaptive tracking control of a nonholonomic mobile robot. IEEE T Robotic Autom 2000; 16: 609–615.

11.

Pan

Dynamic surface control via singular perturbation analysis. Automatica 2015; 57: 29–33.

12.

Disturbance observer-based dynamic surface control of transport aircraft with continuous heavy cargo airdrop. IEEE T Syst Man Cy A 2017; 47: 161–170.

13.

Pan

Composite learning from adaptive dynamic surface control. IEEE T Automat Control 2016; 61: 2603–2609.

14.

Sun

Pan

. Disturbance observer based composite learning fuzzy control of nonlinear systems with unknown dead zone. IEEE T Syst Man Cy A 2016; PP: 1–9.

15.

Jorge

Chacal

Sira-Ramirez

. On the sliding mode control of wheeled mobile robots. In: Proceedings of the 1994 IEEE international conference on systems, man, and cybernetics: humans, information and technology, San Antonio, TX, 2–5 October 1994, pp.1938–1943. New York: IEEE.

16.

Shim

Kim

Koh

. Variable structure control of nonholonomic wheeled mobile robot. In: Proceedings of the 1995 IEEE international conference on robotics and automation, Nagoya Congress Center, Nagoya, Japan, 21–27 May 1995, vol. 2, pp.1694–1699. New York: IEEE.

17.

Aguilar

Hamel

Soueres

. Robust path following control for wheeled robots via sliding mode techniques. In: Proceedings of the 1997 IEEE/RSJ international conference on intelligent robots and systems (IROS’97), Grenoble, 11 September 1997, vol. 3, pp.1389–1395. New York: IEEE.

18.

Yang

Kim

JH.

Sliding mode control for trajectory tracking of nonholonomic wheeled mobile robots. IEEE T Robotic Autom 1999; 15: 578–587.

19.

Filipescu

Stancu

Filipescu

. Realtime sliding-mode adaptive control of a mobile platform wheeled mobile robot. IFAC P Vol 2008; 41: 4393–4399.

20.

Wang

Tsai

CC.

Adaptive robust control of nonholonomic wheeled mobile robots. IFAC P Vol 2005; 38: 475–480.

21.

Hamel

Meizel

Robust control laws for wheeled mobile robots. Int J Syst Sci 1996; 27: 695–704.

22.

Sun

Pei

Pan

. Robust adaptive neural network control for environmental boundary tracking by mobile robots. Int J Robust Nonlin 2011; 23: 123–136.

23.

Zhang

Sun

Pan

Neural network observer-based finite-time formation control of mobile robots. Math Probl Eng 2014; 2014: 267307 (9 pp.).

24.

Horiuchi

Muraki

Horiuchi

. Energy cost of pushing a wheelchair on various gradients in young men. Int J Ind Ergonom 2014; 44: 442–447.

25.

Satoh

Sakaue

An omnidirectional stereo vision-based smart wheelchair. EURASIP J Image Vide 2007; 2007: 087646.

26.

Dogru

Marques

. Energy efficient coverage path planning for autonomous mobile robots on 3D terrain. In: Proceedings of the 2015 IEEE international conference on autonomous robot systems and competitions (ICARSC), Vila Real, 8–10 April 2015, pp.118–123. New York: IEEE.

27.

Mei

. Deployment of mobile robots with energy and timing constraints. IEEE T Robot 2006; 22: 507–522.

28.

Mei

. Energy-efficient motion planning for mobile robots. In: Proceedings of the 2004 IEEE international conference on robotics and automation (ICRA), New Orleans, LA, 26 April–1 May 2004, vol. 5, pp.4344–4349. New York: IEEE.

29.

Mei

. A case study of mobile robot’s energy consumption and conservation techniques. In: Proceedings of the 12th international conference on advanced robotics (ICAR’05), Seattle, WA, 18–20 July 2005, pp.492–497. New York: IEEE.

30.

Barili

Ceresa

Parisi

. Energy-saving motion control for an autonomous mobile robot. In: Proceedings of the IEEE international symposium on industrial electronics (ISIE ’95), Athens, 10–14 July 1995, vol. 2, pp.674–676. New York: IEEE.

31.

Ueno

Ohno

Terashima

. Novel differential drive steering system with energy saving and normal tire using spur gear for an omnidirectional mobile robot. In: Proceedings of the 2010 IEEE international conference on robotics and automation (ICRA), Egan Convention Center, Anchorage, AK, 3–8 May 2010, pp.3763–3768. New York: IEEE.

32.

Kato

Sano

Uchiyama

. Design and control of a redundant wheeled drive system. In: Proceedings of the 2013 SICE annual conference, Nagoya, Japan, 14–17 September 2013, pp.2004–2006. New York: IEEE.

33.

Mohamed

Yamada

Sano

. Design of a redundant wheeled drive system for energy saving and fail safe motion. Adv Mech Eng 2016; 8: 1–15.

34.

Mohamed

Yamada

Sano

. Simulation study on velocity distribution for energy saving of a redundant wheeled drive system. In: Proceedings of the 2015 IEEE/SICE international symposium on system integration, Nagoya, Japan, 11–13 December 2015, pp.116–120. New York: IEEE.

35.

Slotine

JJE

. Applied nonlinear control, vol. 199. Englewood Cliffs, NJ: Prentice Hall, 1991.

Robust control of a redundant wheeled drive system for energy saving and fail safe motion

Abstract

Keywords

Introduction

Modeling of redundant drive system

Dynamics system structure

Dynamics model

Controller design and stability analysis

Distribution controller

Application of SMC

Simulation results

Experiments

Energy evaluation

Conclusion

Footnotes

Author note

Declaration of conflicting interests

Funding

References