Motion planning and tracking control of a four-wheel independently driven steered mobile robot with multiple maneuvering modes

doi:10.1007/s11465-020-0626-y

Front. Mech. Eng.

2021, Vol. 16

Issue (3) : 504-527 https://doi.org/10.1007/s11465-020-0626-y

RESEARCH ARTICLE

Motion planning and tracking control of a four-wheel independently driven steered mobile robot with multiple maneuvering modes

Xiaolong ZHANG¹, Yu HUANG¹, Shuting WANG¹, Wei MENG², Gen LI¹, Yuanlong XIE¹(

)

¹. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
². School of Information Engineering, Wuhan University of Technology, Wuhan 430070, China

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Abstract

Safe and effective autonomous navigation in dynamic environments is challenging for four-wheel independently driven steered mobile robots (FWIDSMRs) due to the flexible allocation of multiple maneuver modes. To address this problem, this study proposes a novel multiple mode-based navigation system, which can achieve efficient motion planning and accurate tracking control. To reduce the calculation burden and obtain a comprehensive optimized global path, a kinodynamic interior–exterior cell exploration planning method, which leverages the hybrid space of available modes with an incorporated exploration guiding algorithm, is designed. By utilizing the sampled subgoals and the constructed global path, local planning is then performed to avoid unexpected obstacles and potential collisions. With the desired profile curvature and preselected mode, a fuzzy adaptive receding horizon control is proposed such that the online updating of the predictive horizon is realized to enhance the trajectory-following precision. The tracking controller design is achieved using the quadratic programming (QP) technique, and the primal–dual neural network optimization technique is used to solve the QP problem. Experimental results on a real-time FWIDSMR validate that the proposed method shows superior features over some existing methods in terms of efficiency and accuracy.

Keywords mobile robot multiple maneuvering mode motion planning tracking control receding horizon control

Corresponding Author(s): Yuanlong XIE

Just Accepted Date: 26 March 2021 Online First Date: 28 April 2021 Issue Date: 24 September 2021

Cite this article:

Xiaolong ZHANG,Yu HUANG,Shuting WANG, et al. Motion planning and tracking control of a four-wheel independently driven steered mobile robot with multiple maneuvering modes[J]. Front. Mech. Eng., 2021, 16(3): 504-527.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0626-y
https://academic.hep.com.cn/fme/EN/Y2021/V16/I3/504

Fig.1 Overall hardware structure of the developed FWIDSMR system.

Fig.2 Proposed motion planning and trajectory tracking control system.

Fig.3 Multimodes of the developed four-wheel independently driven steered mobile robot.

Fig.4 Constructed semantic topological map.

Fig.5 Pseudocode of the exploration guiding algorithm.

Fig.6 Tree of motions for motion planning.

Fig.7 Global planning alternates between multilayer spaces.

Fig.8 Proposed HS-KIECEP algorithm for the developed FWIDSMR.

Fig.9 State–space sampling scheme for the local trajectory planning.

Fig.10 Block diagram of the primal–dual neural network dynamical system.

Fig.11 Output membership functions and fuzzy-rule base. ZE: Zero; S: Small; M: Medium, B: Big; VB: Very big.

Fig.12 Hardware specification of the four-wheel independently driven steered mobile robot control system.

Fig.13 Trajectory planning results under the compared methods. (a) Exploration by EGA; planning by (b) PRM, (c) RRT*, (d) KIECEP, (e) TEB, and (f) HS-KIECEP. EGA: Exploration guiding algorithm; PRM: Probabilistic roadmap; RRT*: Rapidly exploring random tree; KIECEP: Kinodynamic interior–exterior cell exploration planning; TEB: Timed-elastic-band; HS-KIECEP: Hybrid-space KIECEP.

Tab.1 Navigation tasks for motion planning

Tab.2 Average runtime of the motion planning methods

Fig.14 (a) Path length rate and (b) travel time rate under the compared methods.

Fig.15 Navigation in a dynamic environment. (a) Experimental scenario; (b) traveled trajectories.

Fig.16 Reference trajectories, steering angle

ϕ f

, and curvature

k c

using the Ackerman mode.

Fig.17 Tracking errors using the Ackerman mode.

Fig.18 Control inputs using the Ackerman mode.

Fig.19 Reference trajectories, steering angle

ϕ f

, and curvature

k c

using the variable-Ackerman mode.

Fig.20 Tracking errors using the variable-Ackerman mode.

Fig.21 Control inputs using the variable-Ackerman mode.

Fig.22 Reference trajectories, steering angle

ϕ f

, and curvature

k c

using the diagonal-move steer mode.

Fig.23 Tracking errors using the diagonal-move steer mode.

Fig.24 Control inputs using the diagonal-move steer mode.

Mode	L2 mean of the tracking error
Mode	$N = 10$	$N = 20$	$N = 30$	FARHC
m₂	0.0959	0.0731	0.0850	0.0361
m₃	0.0545	0.0393	0.0468	0.0195
m₄	0.0508	0.0334	0.0418	0.0158

Tab.3 L2 mean of the tracking errors with fixed-horizon RHC and the proposed FARHC

Fig.25 Reference trajectories and tracking errors in tracking control experiment case 2.

Fig.26 Control inputs in tracking control experiment case 2.

Error	Index	Performance value
Error	Index	Mode m₂	Mode m₃	Mode m₄	Multimodes
$e x$	ITAE	116.9978	22.9452	24.2386	17.8768
	ISE	0.9001	0.0110	0.0119	0.0085
	STD	0.1080	0.0121	0.0126	0.0106
$e y$	ITAE	938.9947	147.3170	22.3548	21.2334
	ISE	23.0266	0.4755	0.0179	0.0164
	STD	0.5414	0.0776	0.0154	0.0147
$e θ$	ITAE	498.2151	181.8418	2010.0105	173.9620
	ISE	7.7542	2.6286	59.7695	7.4087
	STD	0.3140	0.1870	0.8598	0.3062

Tab.4 Performance indexes of the tracking error under different single-mode and multimode switching control

$a 1$	First adjusting argument
$a 2$	Second adjusting argument
$C$	Configuration space
$C o n f$	A set of configurations derived from the motion
$D obs τ$	Distance to the nearest obstacle
$e x$	Tracking error in the $x$ direction, m
$e y$	Tracking error in the $y$ direction, m
$e θ$	Tracking error in the $θ$ direction, rad
$f i$	Factors used to evaluate a cell
$i m$	Impact of the motion tree
$I t$	Iteration instant
$J$	Cost function
$k c$	Curvature
$k g$	Gain coefficient
$k r$	Relationship coefficient between $ϕ f$ and $ϕ r$
$k maxc$	Maximum curvature
$l$	Path length
$l max ?$	Maximum path length
$l max ? l p$	Maximum length for local planning
$l min ? l p$	Minimum length for local planning
$l f o r e c a s t l p$	Forecast length for local planning
$l τ$	Path length of the trajectory $τ$
$L$	Robot length, m
$L f$	Distance between the virtual center and virtual front wheel, m
$L r$	Distance between the virtual center and virtual rear wheel, m
$m i$	Elements of the set $M$
$M$	Set of modes
$\| M \|$	Cardinal numbers of mode space
$M i n c$	Minimum set
$M i n cint$	Interior cells
$M i n cext$	Exterior cells
$n$	Step number
$N$	Prediction horizon
$N u$	Control horizon
$Ν select$	Iteration number
$N e i g$	Neighbors of a cell
$o area,$	Object of areas
$o tool$	Object of tools
$o item$	Object of items
$o init$	Initial objects
$o goal$	Goal objects
$P Θ$	Piecewise-linear projection operator
$r m$	Minimum turning radius
$S$	Hybrid state space
$S c o r e cell$	Criterion to evaluate a cell
$S c o r e traj$	Criterion to evaluate a motion trajectory
$S goal$	Goal region
$T$	Motion tree
$t$	Duration time
$t d$	Control sampling time
$T a$	Point-in-time a
$T b$	Point-in-time b
$u ˜ 1$	Replanned driving velocity
$u 1$	Driving velocity, m/s
$u 2$	Steering velocity, rad/s
$U$	Control space
$v e l$	Current velocity for local planning
$w c i$	Weighting coefficients
$w p i$	Predefined weighting parameters
$x$	Position of the robot in x direction, m
$y$	Position of the robot in y direction, m
$z i$	The $i th$ element of $Z$
$α$	Predefined greedy coefficient
$β 1$	Initial distance
$β 2$	Forecasting time
$γ$	Fixed step size
$γ c$	Positive parameter to scale the convergence rate
$τ$	Evaluated trajectory candidate
$θ$	Orientation of the robot, rad
$θ s$	Start configuration
$θ f$	Final configuration
$ϕ f$	Front wheel steering angle, rad
$ϕ r$	Real wheel steering angle, rad
$Ψ$	Projection function
$Ω$	Mapping function from continuous space to discrete space
$Γ$	Mapping function from the cell to configuration space
$ζ$	Cell
$Θ$	Motion function
$Λ$	Coverage of the cell
$ϑ$	Total neurons
$Δ C o v$	Coverage increment
$?$	Set of integers
$? k$	Set of k-dimension integers
$? +$	Positive scalar
$? k$	k-dimension vectors
$b$	Constraint coefficient
$Β$	Control coefficient
$c$	Robot configuration
$d$	Mapping matrix
$D$	System matrix
$E$	Partition coefficient
$g$	State function
$g ¯$	Augmented state function
$G$	Network function
$G i$	The $i th$ row of $G$
$h$	Control function
$h ¯$	Augmented control function
$I ¯$	Augmented identity diagonal matrix
$K m$	PDNN coefficient matrix
$M e$	Mode selection matrix of the error state dynamics
$p ori$	Original point
$p loc$	Location of the robot
$p v$	PDNN vector
$q$	State of the robot
$q ¯$	Augmented state vector
$q e$	State vector of the error state dynamics
$Q$	State adjusting matrix
$R$	Control adjusting matrix
$s i n i t$	Initial state
$u$	Control input
$u e$	Control vector of the error state dynamics
$u ¯$	Augmented control vector
$Δ u e$	Control input increment
$Δ u ¯$	Augmented increment control vector
$Δ u ¯ ∗$	Optimal control sequence
$Δ u ¯ max ?$	Maximum value of $Δ u ¯$
$Δ u ¯ min ?$	Minimum value of $Δ u ¯$
$v$	Motion
$v 0$	Initial motion
$W$	Weighting matrix
$Z$	Signal matrix
$μ d$	Dual decision vector
$μ d +$	Upper bound of $μ d$
$μ d −$	Lower bound of $μ d$
$μ p$	Primal–dual decision vector
$μ p +$	Upper bound of $μ p$
$μ p −$	Lower bound of $μ p$ ,
$ζ a$	Cells after the time $T a$
$ζ b$	Cells after the time $T b$
$ϕ$	Internal constraints set of $q e$
$ψ$	Internal constraints set of $u e$
$Θ$	Domain of the dual vector

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