Obstacle-circumventing adaptive control of a four-wheeled mobile robot subjected to motion uncertainties

Abstract

To achieve the collision-free trajectory tracking of the four-wheeled mobile robot (FMR), existing methods resolve the tracking control and obstacle avoidance separately. Guaranteeing the synergistic robustness and smooth navigation of mobile robots subjected to motion uncertainties in a dynamic environment using this non-cooperative processing method is difficult. To address this challenge, this paper proposes an obstacle-circumventing adaptive control (OCAC) framework. Specifically, a novel anti-disturbance terminal slide mode control with adaptive gains is formulated, incorporating specified control laws for different stages. This formulation guarantees rapid convergence and simultaneous chattering elimination. By introducing sub-target points, a new sub-target dynamic tracking regression obstacle avoidance strategy is presented to transfer the obstacle avoidance problem into a dynamic tracking one, thereby reducing the burden of local path searching while ensuring system stability during obstacle circumvention. Comparative experiments demonstrate that the proposed OCAC method can strengthen the convergence and obstacle avoidance efficiency of the concerned FMR system.

Graphical abstract

Keywords

four-wheeled mobile robot / obstacle-circumventing adaptive control / adaptive anti-disturbance terminal sliding mode control / sub-target dynamic tracking regression obstacle avoidance

References

[1] Baumann D , Mager F , Wetzker U , Thiele L , Zimmerling M , Trimpe S . Wireless control for smart manufacturing: recent approaches and open challenges. Proceedings of the IEEE, 2021, 109(4): 441–467

[2] Meng J , Wang S T , Li G , Jiang L Q , Zhang X L , Liu C , Xie Y L . Iterative-learning error compensation for autonomous parking of mobile manipulator in harsh industrial environment. Robotics and Computer-integrated Manufacturing, 2021, 68: 102077

[3] Guo S , Jin Y , Bao S , Xi F F . Accuracy analysis of omnidirectional mobile manipulator with mecanum wheels. Advances in Manufacturing, 2016, 4(4): 363–370

[4] Zhang X L , Zhang W X , Zhao Y Q , Wang H , Lin F , Cai Y F . Personalized motion planning and tracking control for autonomous vehicles obstacle avoidance. IEEE Transactions on Vehicular Technology, 2022, 71(5): 4733–4747

[5] Xie Y L , Zhang X L , Meng W , Zheng S Q , Jiang L Q , Meng J , Wang S T . Coupled fractional-order sliding mode control and obstacle avoidance of a four-wheeled steerable mobile robot. ISA Transactions, 2021, 108: 282–294

[6] Jiang L Q , Wang S T , Xie Y L , Xie S Q , Zheng S Q , Meng J , Ding H . Decoupled fractional supertwisting stabilization of interconnected mobile robot under harsh terrain conditions. IEEE Transactions on Industrial Electronics, 2022, 69(8): 8178–8189

[7] Zheng K S , Wu F , Chen X P . Laser-based people detection and obstacle avoidance for a hospital transport robot. Sensors, 2021, 21(3): 961

[8] Yu X , Jiang J . A survey of fault-tolerant controllers based on safety-related issues. Annual Reviews in Control, 2015, 39: 46–57

[9] Singh A S P , Osamu N . Trajectory tracking and integrated chassis control for obstacle avoidance with minimum jerk. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(5): 4625–4641

[10] XiaoZ XHuM HFuC YQinD T. Model predictive trajectory tracking control of unmanned vehicles based on radial basis function neural network optimisation. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2023, 237(2–3): 347–361

[11] Khan A H , Li S , Luo X . Obstacle avoidance and tracking control of redundant robotic manipulator: an RNN-based metaheuristic approach. IEEE Transactions on Industrial Informatics, 2020, 16(7): 4670–4680

[12] Xie Y L , Zhang X L , Zheng S Q , Ahn C K , Wang S T . Asynchronous H_∞ continuous stabilization of mode-dependent switched mobile robot. IEEE Transactions on Systems, Man, and Cybernetics. Systems, 2022, 52(11): 6906–6920

[13] Yogi S C , Tripathi V K , Behera L . Adaptive integral sliding mode control using fully connected recurrent neural network for position and attitude control of quadrotor. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(12): 5595–5609

[14] Ren C , Li X H , Yang X B , Ma S G . Extended state observer-based sliding mode control of an omnidirectional mobile robot with friction compensation. IEEE Transactions on Industrial Electronics, 2019, 66(12): 9480–9489

[15] AzzabiANouriK. Design of a robust tracking controller for a nonholonomic mobile robot based on sliding mode with adaptive gain. International Journal of Advanced Robotic Systems, 2021, 18(1): 1729881420987082

[16] Huang J , Zhang M S , Ri S , Xiong C H , Li Z J , Kang Y . High-order disturbance-observer-based sliding mode control for mobile wheeled inverted pendulum systems. IEEE Transactions on Industrial Electronics, 2020, 67(3): 2030–2041

[17] Dian S Y , Fang H W , Zhao T , Wu Q , Hu Y , Guo R , Li S C . Modeling and trajectory tracking control for magnetic wheeled mobile robots based on improved dual-heuristic dynamic programming. IEEE Transactions on Industrial Informatics, 2021, 17(2): 1470–1482

[18] Chen Z Y , Liu Y , He W , Qiao H , Ji H B . Adaptive-neural-network-based trajectory tracking control for a nonholonomic wheeled mobile robot with velocity constraints. IEEE Transactions on Industrial Electronics, 2021, 68(6): 5057–5067

[19] Zhang X L , Xie Y L , Jiang L Q , Li G , Meng J , Huang Y . Fault-tolerant dynamic control of a four-wheel redundantly-actuated mobile robot. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 157909–157921

[20] Thomas M , Bandyopadhyay B , Vachhani L . Discrete-time sliding mode control design for unicycle robot with bounded inputs. IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, 68(8): 2912–2916

[21] Chen M . Robust tracking control for self-balancing mobile robots using disturbance observer. IEEE/CAA Journal of Automatica Sinica, 2017, 4(3): 458–465

[22] Wang P W , Gao S , Li L , Cheng S , Zhao L . Automatic steering control strategy for unmanned vehicles based on robust backstepping sliding mode control theory. IEEE Access: Practical Innovations, Open Solutions, 2019, 7: 64984–64992

[23] Zhao Y K , Zhang F , Huang P F , Liu X Y . Impulsive super-twisting sliding mode control for space debris capturing via tethered space net robot. IEEE Transactions on Industrial Electronics, 2020, 67(8): 6874–6882

[24] Norsahperi N M H , Danapalasingam K A . An improved optimal integral sliding mode control for uncertain robotic manipulators with reduced tracking error, chattering, and energy consumption. Mechanical Systems and Signal Processing, 2020, 142: 106747

[25] Shi Z , Deng C C , Zhang S , Xie Y , Cui H T , Hao Y . Hyperbolic tangent function-based finite-time sliding mode control for spacecraft rendezvous maneuver without chattering. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 60838–60849

[26] Sepestanaki M A , Barhaghtalab M H , Mobayen S , Jalilvand A , Fekih A , Skruch P . Chattering-free terminal sliding mode control based on adaptive barrier function for chaotic systems with unknown uncertainties. IEEE Access: Practical Innovations, Open Solutions, 2022, 10: 103469–103484

[27] Alinaghi Hosseinabadi P , Ordys A , Soltani Sharif Abadi A , Mekhilef S , Pota H R . State and disturbance observers-based chattering-free fixed-time sliding mode control for a class of high-order nonlinear systems. Advanced Control for Applications: Engineering and Industrial Systems, 2021, 3(3): e81

[28] Zhang W , Cheng H T , Hao L , Li X C , Liu M F , Gao X F . An obstacle avoidance algorithm for robot manipulators based on decision-making force. Robotics and Computer-integrated Manufacturing, 2021, 71: 102114

[29] Huang Y J , Ding H T , Zhang Y B , Wang H , Cao D P , Xu N , Hu C . A motion planning and tracking framework for autonomous vehicles based on artificial potential field elaborated resistance network approach. IEEE Transactions on Industrial Electronics, 2020, 67(2): 1376–1386

[30] Babinec A , Duchoň F , Dekan M , Mikulová Z , Jurišica L . Vector field histogram* with look-ahead tree extension dependent on time variable environment. Transactions of the Institute of Measurement and Control, 2018, 40(4): 1250–1264

[31] Lee D H , Lee S S , Ahn C K , Shi P , Lim C C . Finite distribution estimation-based dynamic window approach to reliable obstacle avoidance of mobile robot. IEEE Transactions on Industrial Electronics, 2021, 68(10): 9998–10006

[32] Guo K L , Su H , Yang C G . A small opening workspace control strategy for redundant manipulator based on RCM method. IEEE Transactions on Control Systems Technology, 2022, 30(6): 2717–2725

[33] Upadhyay S , Ratnoo A . Continuous-curvature path planning with obstacle avoidance using four parameter logistic curves. IEEE Robotics and Automation Letters, 2016, 1(2): 609–616

[34] LatombeJ C. Robot motion planning. New York: Springer Science & Business Media, 2012

[35] Lu Q , Zhang D , Ye W J , Fan J Y , Liu S , Su C Y . Targeting posture control with dynamic obstacle avoidance of constrained uncertain wheeled mobile robots including unknown skidding and slipping. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11): 6650–6659

[36] Zhou X B , Yu X , Zhang Y M , Luo Y Y , Peng X Y . Trajectory planning and tracking strategy applied to an unmanned ground vehicle in the presence of obstacles. IEEE Transactions on Automation Science and Engineering, 2021, 18(4): 1575–1589

[37] Chen H , Zhang X . Path planning for intelligent vehicle collision avoidance of dynamic pedestrian using Att-LSTM, MSFM and MPC at un-signalized crosswalk. IEEE Transactions on Industrial Electronics, 2022, 69(4): 4285–4295

[38] Zhang Z J , Yang S , Chen S Y , Luo Y M , Yang H , Liu Y . A vector-based constrained obstacle avoidance scheme for wheeled mobile redundant robot manipulator. IEEE Transactions on Cognitive and Developmental Systems, 2021, 13(3): 465–474

[39] He S D , Dai S L , Luo F . Asymptotic trajectory tracking control with guaranteed transient behavior for MSV with uncertain dynamics and external disturbances. IEEE Transactions on Industrial Electronics, 2019, 66(5): 3712–3720

[40] Yang C G , Huang D Y , He W , Cheng L . Neural control of robot manipulators with trajectory tracking constraints and input saturation. IEEE Transactions on Neural Networks and Learning Systems, 2021, 32(9): 4231–4242

[41] Liu C X , Wen G L , Zhao Z J , Sedaghati R . Neural-network-based sliding-mode control of an uncertain robot using dynamic model approximated switching gain. IEEE Transactions on Cybernetics, 2021, 51(5): 2339–2346

[42] Bagheri F , Komurcugil H , Kukrer O , Guler N , Bayhan S . Multi-input multi-output-based sliding-mode controller for single-phase quasi-Z-source inverters. IEEE Transactions on Industrial Electronics, 2020, 67(8): 6439–6449

[43] Peng H J , Li F , Liu J G , Ju Z J . A symplectic instantaneous optimal control for robot trajectory tracking with differential-algebraic equation models. IEEE Transactions on Industrial Electronics, 2020, 67(5): 3819–3829

[44] Rayguru M M , Mohan R E , Parween R , Yi L , Le A V , Roy S . An output feedback based robust saturated controller design for pavement sweeping self-reconfigurable robot. IEEE/ASME Transactions on Mechatronics, 2021, 26(3): 1236–1247

[45] YadavR DSankaranarayananV NRoyS. Adaptive sliding mode control for autonomous vehicle platoon under unknown friction forces. In: Proceedings of the 20th International Conference on Advanced Robotics. Ljubljana: IEEE, 2021: 879–884

[46] Wang D L , Wei W , Yeboah Y , Li Y J , Gao Y . A robust model predictive control strategy for trajectory tracking of omni-directional mobile robots. Journal of Intelligent & Robotic Systems, 2020, 98(2): 439–453

[47] Zhang C Y , Chu D F , Liu S D , Deng Z J , Wu C Z , Su X C . Trajectory planning and tracking for autonomous vehicle based on state lattice and model predictive control. IEEE Intelligent Transportation Systems Magazine, 2019, 11(2): 29–40

[48] Liang X W , Wang H S , Liu Y H , You B , Liu Z , Chen W D . Calibration-free image-based trajectory tracking control of mobile robots with an overhead camera. IEEE Transactions on Automation Science and Engineering, 2020, 17(2): 933–946

[49] Ben Jabeur C , Seddik H . Design of a PID optimized neural networks and PD fuzzy logic controllers for a two-wheeled mobile robot. Asian Journal of Control, 2021, 23(1): 23–41

[50] Xiong R , Li L J , Zhang C X , Ma K , Yi X S , Zeng H S . Path tracking of a four-wheel independently driven skid steer robotic vehicle through a cascaded NTSM-PID control method. IEEE Transactions on Instrumentation and Measurement, 2022, 71: 1–11

[51] Lin H , Yin Y F , Shen X N , Alcaide A M , Liu J X , Leon J I , Vazquez S , Franquelo L G , Wu L G . Fuzzy logic system-based sliding-mode control for three-level NPC converters. IEEE Transactions on Transportation Electrification, 2022, 8(3): 3307–3319

[52] Mei K , Ding S H , Zheng W X . Fuzzy adaptive SOSM based control of a type of nonlinear systems. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(3): 1342–1346

[53] Lan Y P , Li J , Zhang F G , Zong M . Fuzzy sliding mode control of magnetic levitation system of controllable excitation linear synchronous motor. IEEE Transactions on Industry Applications, 2020, 56(5): 5585–5592

[54] Lu Y Y , Zhang W . A piecewise smooth control-Lyapunov function framework for switching stabilization. Automatica, 2017, 76: 258–265

[55] Mozayan S M , Saad M , Vahedi H , Fortin-Blanchette H , Soltani M . Sliding mode control of PMSG wind turbine based on enhanced exponential reaching law. IEEE Transactions on Industrial Electronics, 2016, 63(10): 6148–6159

[56] Orozco-Magdaleno E C , Gómez-Bravo F , Castillo-Castañeda E , Carbone G . Evaluation of locomotion performances for a mecanum-wheeled hybrid hexapod robot. IEEE/ASME Transactions on Mechatronics, 2021, 26(3): 1657–1667

[57] Ulrich I , Borenstein J . VFH+: reliable obstacle avoidance for fast mobile robots. In: Proceedings of 1998 IEEE International Conference on Robotics and Automation. Leuven: IEEE, 1998, 2: 1572–1577

Nomenclature

Abbreviations
ADTSMCAG	Anti-disturbance terminal slide mode control with adaptive gain
APF	Artificial potential field
CSMC	Common slide mode control
ESO	Extended state observer
FMR	Four-wheeled mobile robot
FTC	Fault-tolerant controller
MPC	Model predictive control
OCAC	Obstacle-circumventing adaptive control
PID	Proportional−integral−derivative
RBF	Radial basis function
RCM	Remote center of movement
SDTROA	Sub-target dynamic tracking regression obstacle avoidance
SMC	Slide mode control
TAPF	Traditional artificial potential field
VFH	Vector field histogram
VFH+	Vector field histogram+
Variables
a, b	Normal numbers
A_{s\dot{s}}^i	Fuzzy set of system input
B_{h_1,}^i,B_{h_2}^i	Fuzzy sets of system output
c	Sampling interval
Ci,j	Obstacle determination value of the active cell
COST(i)	Optimal objective function
d	Initial increment of the sub-target point area related to the obstacle
dero	Corrosion radius of the obstacle unit after considering the safety distance
d_{i,j}^{\text{ob}}\left(\mathit{q}\right)	Distance from the current position of FMR to the center of the obstacle unit
dr+s	Radius of the obstacle unit after expansion
ds	Radius of the radar scanning area
D(x)	Sub-target point area
g, λ	Positive parameters satisfying g > 2 and even
G_{i,j}^{\text{ob}}\left(\mathit{q}\right)	Obstacle avoidance constraints
h1, h2, h3	Preset control gains satisfying: h_1>\gamma {\chi }_1\cdot \mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(S\right)/{\left|S\right|}^q, h2 > 0, and h3 > 0
h_{i,j}^{\prime }	Sub polar coordinate obstacle density function
Hk	Polar coordinate obstacle density function
H_{\text{func}}^{\text{B}}	Polar coordinate obstacle density function after binarization processing
H_{\text{funclasttime}}^{\text{B}}	Polar coordinate obstacle density corresponding to the last moment
i	Selected target point label
k	Sector area number corresponding to the obstacle angle
kbound	Boundary range
ktar	Fan-shaped valley
Lf, Lr	Distances from front and rear wheels to the robot center, respectively
m0, m1, m2	Positive parameters
mi, j	Size of the obstacle vector at cell (i, j)
q1, q2	Positive parameters
q, qrob, qr	Robot state, new reference trajectory state, and reference trajectory state, respectively
s	Sliding surface value
smax	Set maximum width
S_{p_{\text{sub}}}\left(t\right)	Sub-target point area
S_{p_{\text{sub}1}},S_{p_{\text{sub}2}}	Upper and lower bounds of the sub-target point area
\dot{S}	Adaptive sliding mode surface derivative
S\left(t_n\right), \overline{S}\left(t_n\right)	Adaptive sliding mode surface and sub adaptive sliding mode surface, respectively
t	System convergence time
t1, t2	Time of phases 1 and 2, respectively
tn	Control framework running time
treach	Time for the system to reach the sliding surface
T	Extending reference position
Tmax	Maximum convergence time
{\nu }_{B_{h_1}^i}, {\nu }_{B_{h_2}^i}	Membership degrees of the conclusion
V	Lyapunov function
Vl, Vlr	Linear velocity and reference linear velocity, respectively
x, y, θ	Robot positions
\dot{x},\dot{y},\dot{\theta }	Robot position derivatives
xe, ye, θe	Robot position errors
xi	Selected target point
x_{i,j}^{\text{ob}},y_{i,j}^{\text{ob}}	Coordinates of the obstacle unit
xo	Current location of FMR
xr, yr, θr	Reference robot positions
{\dot{x}}_{\text{r}},{\dot{y}}_{\text{r}},{\dot{\theta }}_{\text{r}}	Reference robot position derivatives
xT, yT	Position T
X1, X2	Variables of the equations of state
α, β, ϖ	Positive parameters
α′	Set angle resolution
β1, β2	Predefined error coefficients satisfying: β1 ∈ (1, ∞) and β2 ∈ (0, 1)
{\beta }_{i,j}^{\prime }	Angle from the center of the specific obstacle unit to the FMR
\gamma, {\gamma }^{\prime }	Bounded lumped uncertainties and external disturbances, respectively
{\gamma }_{i,j}	Preset angle
{\varpi }_{A_{s\dot{s}}^i}	Membership degrees of the premise
δf, δr	Virtual front and rear wheel angles, respectively
{\theta }^{\prime }	Forward direction of FMR
θobr	Updated reference trajectory output
θP	Tangent direction angle of the reference position
χ1, χ2, χ3, χ4	Preset control gains
\kappa	Positive parameter
\varsigma	Obstacle detection angle
ζ	Ultrasonic radiation angle
τ	Yaw correction parameter
τh, τl	Set boundaries of binarization judgment
Γ	Dynamic adjustment factor
υ	Obstacle-size correction parameter
ψ(t)	Angle between the heading of the FMR
∆t	System parameter perturbations
Ξ, Ω	Intermediate control variables

Acknowledgements

The work was supported in part by the National Natural Science Foundation of China (Grant Nos. 52275488 and 52105019), in part by the Key R&D Program of Hubei Province, China (Grant No. 2022BAA064), and in part by Dongguan Social Development Project, China (Grant No. 20211800904902).

Conflict of Interest

The authors declare that they have no conflict of interest.

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