International Journal of Engineering Insights: (2025) Vol. 3, Nro.1, Regular Paper

https://doi.org/10.61961/injei.v3i1.84

A Comprehensive Review of Four-Wheel Independent

Drive and Steering Systems: Integrating Double Ackermann

Kinematics, Advanced Trajectory Tracking, and Active Safety

Mar´ıa del Carmen Claudio · Cristian P. Chuchico · Fernando A. Chicaiza

Received: 15 Apr 2025 / Accepted: 22 Aug 2025 / Published: 15 Nov 2025

Abstract: The transition from conventional front-wheel

steering to over-actuated four-wheel independent steer-

ing and driving architectures has fundamentally rede-

ﬁned the limits of robotic mobility in constrained envi-

ronments. Among these conﬁgurations, the double Ack-

ermann geometry has emerged as the optimal solution

to minimize lateral slip and enable advanced non-holonomic

maneuvers, such as pure lateral crabbing and zero-radius

turning. However, the redundant degrees of freedom in-

troduce severe complexities in multibody dynamic mod-

eling and optimal torque allocation. This paper presents

a comprehensive review of the scientiﬁc literature pub-

lished between 2016 and 2026 regarding the model-

ing, trajectory tracking, and safety integration of these

highly agile platforms. We deconstruct the mathemat-

ical foundations used in contemporary research, high-

lighting the application of Newton-Euler laws for high-

ﬁdelity 3-DOF and 7-DOF dynamic modeling and the

utilization of Bolzman-Hamel theory to manage non-

holonomic constraints through local quasi-velocities. Fur-

thermore, we analyze the evolution of high-level control

architectures, emphasizing the consolidation of linear

time-varying model predictive control for handling hard

actuator constraints, and the recent breakthroughs in

deep reinforcement learning, speciﬁcally utilizing group

intelligent experience replay to overcome sample inef-

ﬁciency in continuous action spaces. The review also

synthesizes critical low-level safety mechanisms, includ-

ing load transfer ratio monitoring for active rollover

prevention and fault-tolerant control for steer-by-wire

Mar´ıa del Carmen Claudio

Inmersoft Technologies

Quito, Ecuador

E-mail: mclaudio@inmersoft.com

Cristian P. Chuchico

Escuela de Doctorado, Programa de Doctorado en Ingenier´ıa

Electr´onica, Universidad de Zaragoza, Zaragoza, Espa˜na.

E-mail: 980122@unizar.es

Fernando A. Chicaiza

Centro de Investigaci´on MIST, Facultad de Ingenier´ıas, Uni-

versidad Indoam´erica, Ambato, Ecuador

E-mail: fachicaiza@indoamerica.edu.ec

systems. By correlating these theoretical advancements

with ﬁeld applications in precision agriculture, under-

ground mining, and planetary exploration, this review

provides a consolidated roadmap for addressing the re-

maining challenges in domain adaptation and real-time

edge computing for the next generation of autonomous

terrestrial systems.

Keywords Double ackermann · 4WS robots ·

Ackermann robots

1 Introduction

The last decade has consolidated a disruptive transi-

tion in the morphology of robotic locomotion, shift-

ing from conventional diﬀerential and simple Acker-

mann steering schemes toward over-actuated architec-

tures of the four-wheel independent steering and inde-

pendent driving type [1]. Historically, front-wheel steer-

ing systems have been constrained by a fundamental

kinematic limitation: the instantaneous center of ro-

tation must reside collinearly on the rear axle. This

severely restricts agility in conﬁned spaces and gen-

erates a strongly coupled dependency between lateral

velocity and yaw rate at high speeds. To overcome this

barrier, the double Ackermann geometry has emerged

as an optimal solution. This conﬁguration allows all

four wheels to converge toward a dynamic instanta-

neous center of rotation that can be positioned arbi-

trarily in the two-dimensional plane, minimizing lateral

side-slip and optimizing traction eﬃciency [2,3]. Fur-

thermore, the capability to maintain precise trajectory

tracking and minimize dynamic vibrations through this

over-actuated geometry is no longer merely a locomo-

tion objective, but rather a critical prerequisite for the

reliable operation of advanced onboard payloads. As

autonomous vehicles increasingly function as complex

sensory and manipulation hubs, the kinetostatic stabil-

ity of the mobile base directly dictates the eﬃcacy of

high-level cognitive tasks. For instance, the deployment

of cutting-edge environmental perception architectures

14 International Journal of Engineering Insights, (2025) 3:1

strictly demands a highly predictable kinematic plat-

form to mitigate motion-induced sensor artifacts and

spatial misalignment during complex maneuvers [4].

Unlike holonomic platforms based on Mecanum or

classic omnidirectional wheels [5], which suﬀer from low

load capacity and high susceptibility to terrain irregu-

larities, the four-wheel independent steering and driv-

ing architecture preserves the robustness of traditional

tire-road contact while expanding the control space. By

providing redundant degrees of freedom through four

independent steering angles and four independent driv-

ing torques, the system explicitly decouples the control

of the chassis position from its orientation. This en-

ables advanced non-holonomic locomotion modes, such

as pure lateral displacement known as crabbing and ro-

tation about the geometric center known as turn-in-

place. These capabilities are critical in scenarios requir-

ing high precision in constrained environments, such as

high-density precision agriculture [6] and lunar explo-

ration [7].

Although the superior maneuverability is evident,

the over-actuation introduces a highly redundant con-

trol topology. The optimal distribution of contact forces

at the tire-road interface becomes a multi-objective op-

timization problem. At high speeds, the nonlinearity

of lateral friction, typically modeled using the Pacejka

Magic Formula, causes traditional front-wheel steering

systems to quickly reach a critical oversteer velocity. In

contrast, the active control of rear steering in four-wheel

steering platforms allows the modulation of the center

of gravity side-slip angle toward zero, guaranteeing a

signiﬁcantly wider stability margin even on low-friction

roads [8]. Achieving this degree of control, however, re-

quires transitioning from idealized kinematic models to

high-ﬁdelity multibody dynamic models that can han-

dle non-linear constraints in real time.

This review article provides a critical and exhaustive

analysis of the scientiﬁc literature published between

2016 and 2026, focusing strictly on mobile robots uti-

lizing the four-wheel independent steering and driving

architecture with double Ackermann geometry. Unlike

previous reviews that address autonomous navigation

generically, this paper deconstructs the contemporary

convergence between advanced dynamic modeling, par-

ticularly the Gibbs-Appell formulation, and upper-level

control architectures. The scope encompasses strategies

ranging from linear time-varying model predictive con-

trol to cutting-edge implementations in deep reinforce-

ment learning, such as group intelligent experience re-

play and twin delayed deep deterministic policy gradi-

ent frameworks [9,10]. The primary objective is to es-

tablish a rigorous taxonomy of uncertainty mitigation

and trajectory planning strategies, oﬀering a consoli-

dated theoretical foundation for the next generation of

highly agile robotic locomotion systems.

2 Advanced Mathematical Foundations

The synthesis of robust controllers for four-wheel inde-

pendent steering and driving platforms requires a math-

ematical representation that captures both the intrin-

sic geometric constraints of the undercarriage and the

inertial forces of a multibody system. This section an-

alyzes contemporary approaches to kinematic and dy-

namic formulation, highlighting the methodologies re-

quired for handling non-holonomic constraints.

2.1 Double Ackermann Geometry and Kinematic

Constraints

The fundamental principle of the four-wheel steering

kinematic model, when assuming parallel steering for

the front and rear axles, relies on the simpliﬁcation of

the planar motion into a single-track or bicycle equiv-

alent model. In this speciﬁc operational conﬁguration,

both the inner and outer wheels on the front axle are

actuated to an identical steering angle, and a similar

uniﬁed parallel actuation is applied to the rear axle

wheels. For a vehicle with a total wheelbase l, which

is divided into the distance from the center of gravity

to the front axle a and to the rear axle b, the kinematic

relationships must satisfy the zero lateral slip condi-

tion at the center of each axle. As illustrated in Figure

1, the global velocity vector V of the center of grav-

ity, the side-slip angle beta, and the yaw rate gamma

strictly dictate the required steering inputs to maintain

a common instantaneous center of rotation.

Mathematically, by relating the lateral and longitu-

dinal velocity components mapped from the center of

gravity to the front and rear axles, the geometric con-

straint for pure rolling without lateral slip is expressed

as:

tan δ

V sin β + aγ

V cos β

, tan δ

V sin β − bγ

V cos β

(1)

where the subscripts f and r represent the uniﬁed

front and rear steering angles, respectively. This formu-

lation directly links the vehicle’s desired yaw rate and

center of gravity side-slip angle to the physical actua-

tor commands without requiring independent inner and

outer wheel angle computations. Contemporary litera-

ture evidences that utilizing this parallel steering as-

sumption signiﬁcantly reduces the computational com-

plexity of the control allocation layer. This approach

15 International Journal of Engineering Insights, (2025) 3:1

Fig. 1 Foundational kinematic architectures

allows for the direct algebraic mapping of the virtual

control eﬀorts to the steering mechanisms while still

enabling advanced non-holonomic maneuvers, such as

zero side-slip cornering and pure lateral displacement,

provided that the vehicle operates within the linear tire

friction region [2,11].

2.2 Jacobian Matrix Formulation for Logistic Trains

In intralogistics applications, these over-actuated robots

frequently operate as traction units in logistic trains or

continuous supply systems. The kinematic modeling of

such articulated structures becomes intractable using

purely trigonometric approaches. Recent studies have

demonstrated the eﬃcacy of utilizing Jacobian matrix-

based formulations for these interconnected multibody

systems [3]. The direct mathematical relationship to the

double Ackermann geometry lies in the formulation of

the non-holonomic constraint matrix. For a standard

trailer with a ﬁxed rear axle, the constraint matrix in-

herently causes a trajectory cut-in eﬀect known as oﬀ-

tracking. However, when the trailers are equipped with

double Ackermann steering, the zero lateral slip con-

straints must be satisﬁed for both the front and rear

steered axles simultaneously to maintain a common in-

stantaneous center of rotation. Consequently, the ele-

ments of the Jacobian transformation matrix, which

mathematically represents the null space of the con-

straint matrix, become explicit trigonometric functions

of the four independent steering angles [10]. The general

kinematic equation at the diﬀerential level is deﬁned as:

˙q = J(q, δ)v, (2)

where the term on the left is the time derivative of

the generalized coordinate vector, the vector on the

right contains the pseudo-velocities of the actuators,

and the central matrix represents the Jacobian trans-

formation matrix parameterized by the double Acker-

mann steering variables. This explicit inclusion of the

double Ackermann geometry mathematically binds the

velocity vector of the articulated unit to the trajectory

curvature of the preceding tractor. This high tracking

ﬁdelity is paramount to completely mitigate the phe-

nomenon of lateral oﬀ-tracking error ampliﬁcation in

narrow warehouse aisles [12].

2.3 Dynamic Modeling via Newton-Euler and

Bolzman-Hamel Theories

Representing the vehicle through a simpliﬁed purely ge-

ometric or kinematic model based on Jacobian matrices

and Ackermann distance relationships loses validity un-

der high lateral accelerations and abrupt variations in

terrain adhesion. To capture the true transient behavior

of four-wheel independent steering platforms, the litera-

ture relies on multibody dynamic models. The historical

and contemporary derivation of the equations of motion

for both rotational and translational dynamics is pre-

dominantly achieved through the direct application of

Newton-Euler laws. By explicitly balancing the external

tire contact forces and the inertial moments acting on

the center of gravity, researchers formulate robust an-

alytical models [13,2]. This methodology is extensively

applied to derive standard two-degree-of-freedom dy-

namic bicycle models for fundamental lateral control,

as well as more complex three-degree-of-freedom mod-

els. The three-degree-of-freedom formulation explicitly

16 International Journal of Engineering Insights, (2025) 3:1

captures the nonlinear coupling between longitudinal

velocity, lateral velocity, and yaw rate, which is math-

ematically expressed as:

m( ˙v

− v

γ) =

m( ˙v

+ v

γ) =

˙γ =

(3)

where m is the vehicle mass, Iz is the yaw moment of

inertia, v

and v

are the longitudinal and lateral veloc-

ities, gamma is the yaw rate, and the right-side terms

represent the sum of forces and moments generated by

the four independent tires.

Furthermore, dealing with the non-holonomic con-

straints inherent to the moving reference frame presents

analytical challenges when designing advanced model-

based controllers. To manage the complex velocity trans-

formations without relying on computationally heavy

constraint multipliers, speciﬁc studies in the reviewed

literature employ the Bolzman-Hamel theory [14]. This

theoretical framework is utilized to formulate the lin-

ear equations of motion directly related to the quasi-

velocities within the local coordinate system attached

to the vehicle. By projecting the dynamics onto these

quasi-velocities, the Bolzman-Hamel equations provide

a mathematically rigorous yet streamlined representa-

tion of the system [14]. This approach signiﬁcantly re-

duces the complexity of the dynamic matrices, facili-

tating the real-time execution of optimal control alloca-

tion algorithms and ensuring that the vehicle maintains

kinetostatic stability even when the linear tire friction

limits are approached.

3 High-Level Path Tracking Strategies

3.1 Geometric and Classical Control Evolution

The control architecture for four-wheel independent steer-

ing and driving platforms has transitioned from purely

geometric algorithms to sophisticated optimization-based

and robust control frameworks capable of handling high-

speed dynamics and external disturbances. The funda-

mental pure pursuit algorithm, while computationally

inexpensive, suﬀers from a critical limitation due to

its ﬁxed look-ahead distance, which causes either cut-

ting corners at high speeds or oscillatory behavior on

straight paths [15]. To address this, contemporary liter-

ature demonstrates the eﬀectiveness of adaptive look-

ahead mechanisms. For instance, fuzzy logic controllers

have been utilized to dynamically adjust the look-ahead

distance based on real-time lateral and heading devi-

ations, signiﬁcantly reducing tracking errors in agri-

cultural machinery operating in unstructured environ-

ments [6,16]. Additionally, improved pure pursuit for-

mulations that incorporate the derivative of the path

curvature and real-time pose feedback have been shown

to minimize steady-state tracking errors and improve

the transient response of four-wheel independent steer-

ing robots [17]. While these geometric methods are ad-

equate for low-speed kinematic tracking, longitudinal

speed tracking is frequently decoupled and managed

via expert proportional-integral-derivative controllers

to simplify the overall control topology [18,2].

3.2 Optimal and Robust Control

As operational speeds increase and environmental inter-

actions become highly nonlinear, geometric controllers

fail to guarantee stability. Robust optimal control strate-

gies have therefore become essential to mitigate para-

metric uncertainties, such as varying payload masses

and tire cornering stiﬀness. H-inﬁnity robust adaptive

controllers have been successfully integrated into way-

point navigation systems for double Ackermann robots

operating in orchard environments. This approach pro-

vides a mathematically guaranteed level of disturbance

attenuation against sensor noise and terrain irregulari-

ties, ensuring that the lateral deviation remains bounded

even under severe external perturbations [19]. By solv-

ing the associated Riccati equations, the H-inﬁnity con-

troller synthesizes a feedback gain matrix that mini-

mizes the worst-case energy gain from the disturbance

inputs to the regulated tracking errors.

3.3 Model Predictive Control and Adaptive Horizons

Despite the robustness of H-inﬁnity methods, their in-

ability to explicitly handle hard actuator constraints

makes them suboptimal for highly constrained systems.

Consequently, model predictive control has emerged as

the benchmark for high-performance path tracking in

over-actuated vehicles. Model predictive control formu-

lates the tracking problem as a constrained multi-objective

optimization over a ﬁnite receding horizon, allowing

it to systematically manage steering angle limits and

torque saturation. To alleviate the computational bur-

den of solving nonlinear programs onboard, linear time-

varying model predictive control is widely adopted. This

technique linearizes the nonlinear multibody vehicle model

around the reference trajectory at each sampling in-

stant, transforming the optimization into a computa-

tionally tractable quadratic program [18,2]. The inte-

gration of advanced solvers, such as CasADi, enables

the real-time execution of these predictive algorithms.

17 International Journal of Engineering Insights, (2025) 3:1

Furthermore, recent advancements have introduced adap-

tive mechanisms to the model predictive control frame-

work, such as utilizing a multivariate Gaussian mixture

model combined with ant colony optimization to dy-

namically tune the prediction horizon and weight ma-

trices in response to changing environmental obstacles

[10].

3.4 Nonlinear and Discontinuous Control

In scenarios characterized by sudden losses of tire adhe-

sion or severe modeling mismatches, nonlinear discon-

tinuous control methods are required to enforce trajec-

tory convergence. Sliding mode control is frequently im-

plemented in the upper-level coordination layer to com-

pute the desired corrective yaw moment based on the

lateral position and heading error dynamics [18]. How-

ever, the standard sliding mode control introduces high-

frequency switching, known as chattering, which can

excite unmodeled high-frequency dynamics and cause

severe mechanical wear in steer-by-wire actuators. To

overcome this limitation, higher-order sliding mode tech-

niques, particularly the super-twisting algorithm, have

been integrated into the trajectory tracking loops. The

super-twisting algorithm provides a continuous control

signal by hiding the discontinuous switching function

under an integral, thereby completely eliminating chat-

tering while preserving the exact ﬁnite-time conver-

gence and absolute robustness against bounded matched

uncertainties inherent to traditional sliding mode con-

trol.

4 Deep Reinforcement Learning in Motion

Control

While model predictive control and sliding mode con-

trol oﬀer robust mathematical guarantees, their reliance

on accurate plant models makes them susceptible to un-

modeled dynamics in extreme oﬀ-road or high-slip con-

ditions [20]. Deep reinforcement learning has emerged

as a powerful model-free alternative, capable of learning

optimal control policies directly from complex, high-

dimensional state spaces through continuous environ-

mental interaction. For four-wheel independent steering

and driving vehicles, deep reinforcement learning archi-

tectures are typically implemented within a compound

control framework, serving either as an end-to-end tra-

jectory tracker or as an auxiliary compensator that dy-

namically adjusts the parameters of a baseline classical

controller.

4.1 Sample Eﬃciency and Experience Replay

Mechanisms

The fundamental challenge in applying deep reinforce-

ment learning to over-actuated platforms lies in the

sheer dimensionality of the action space, which encom-

passes four independent steering angles and four inde-

pendent driving torques. This high dimensionality ex-

acerbates the issue of reward sparsity and sample skew-

ness during the exploration phase. Traditional experi-

ence replay buﬀers randomly sample past transitions,

which is highly ineﬃcient when successful trajectory

tracking events are rare. While hindsight experience re-

play mitigated this by substituting achieved goals for

desired goals to maximize learning from failed episodes,

it does not adequately address the skewed distribution

of vehicle states in complex nonlinear maneuvers.

To resolve this, recent literature proposes the group

intelligent experience replay mechanism [9]. The group

intelligent experience replay algorithm applies non dom-

inated sorting to the samples in the experience buﬀer,

categorizing transitions based on tracking error met-

rics and temporal diﬀerence errors. By facilitating both

within-group and between-group collaboration during

the sampling process, this mechanism ensures a bal-

anced distribution of training data. It eﬀectively har-

monizes the exploration and exploitation phases, pre-

venting the policy from converging to suboptimal local

minima and signiﬁcantly accelerating the learning rate

for complex double Ackermann kinematic maneuvers.

4.2 Composite Actor-Critic Architectures and

Information Bottlenecks

Standard deep deterministic policy gradient algorithms

frequently suﬀer from an overestimation bias in the Q-

function, leading to brittle control policies that fail un-

der real-world physical constraints. Therefore, the twin

delayed deep deterministic policy gradient architecture,

which utilizes two separate critic networks and delays

the actor network updates, has become the preferred

baseline for continuous control in four-wheel indepen-

dent steering systems. However, feeding raw, high di-

mensional sensory data directly into these networks in-

troduces severe feature redundancy. Variables such as

sequential pose errors, tire slip angles, and varying ter-

rain friction coeﬃcients often contain overlapping in-

formation that degrades the generalization capability

of the neural network.

To address the generalization problem in the com-

plex nonlinear dynamics of these vehicles, researchers

have integrated the principle of the information bottle-

neck into the actor-critic framework. Speciﬁcally, the

18 International Journal of Engineering Insights, (2025) 3:1

two-stream information bottleneck method is employed

to ﬁlter the state representations before they reach the

decision layers [9]. By mathematically constraining the

mutual information between the raw state input and

the extracted latent representation, while simultane-

ously maximizing the mutual information between the

latent representation and the target action, the infor-

mation bottleneck eﬀectively strips away redundant en-

vironmental noise. This extraction of compact, high-

ﬁdelity features allows the deep reinforcement learn-

ing agent to synthesize highly generalized steering and

torque allocation commands, maintaining precise tra-

jectory tracking even when the vehicle is subjected to

previously unseen external disturbances.

5 Obstacle Avoidance and Motion Planning

The integration of obstacle avoidance mechanisms in

four-wheel independent steering and driving platforms

necessitates a delicate balance between immediate reac-

tive behaviors and foresighted trajectory optimization

[21]. The redundant degrees of freedom inherent in the

double Ackermann geometry allow these vehicles to ex-

ecute complex evasive maneuvers, such as lateral crab-

bing or zero-radius turns, which are physically impos-

sible for conventional kinematic models. Consequently,

motion planning architectures have evolved to explicitly

leverage these capabilities, splitting the computational

load between local reactive navigation stacks and global

optimization-based evasion frameworks.

5.1 Reactive Navigation and Behavior Trees

In highly unpredictable environments, such as plane-

tary surfaces or underground mines, relying solely on

global path replanning is computationally prohibitive

and practically unsafe due to the latency in sensor-

to-actuator loops. To address this, contemporary re-

search has widely adopted the Robot Operating Sys-

tem 2 and its advanced navigation framework, Nav2, to

handle local reactive planning [7]. The transition from

ﬁnite state machines to behavior trees in these navi-

gation stacks provides a modular and highly respon-

sive decision-making structure. Behavior trees allow the

robot to evaluate sensory inputs in real time and asyn-

chronously preempt current tasks to execute emergency

maneuvers.

Recent implementations for lunar rovers demonstrate

the eﬃcacy of this approach by utilizing specialized ma-

neuver servers within the ROS 2 ecosystem [7]. When a

local costmap detects an imminent collision that cannot

be bypassed via standard forward steering, the behav-

ior tree triggers a mode-switching protocol. Depending

on the spatial constraints and the surrounding regolith

topology, the navigation stack dynamically reconﬁgures

the four independent steering actuators to transition

from standard double Ackermann steering to a crabbing

mode for lateral evasion, or to a turn-in-place mode

to completely reverse the heading. This reactive layer

ensures survivability in unstructured terrain, although

it primarily addresses immediate geometrical conﬂicts

rather than holistic dynamic eﬃciency.

5.2 Optimization-Based Evasion in Predictive

Horizons

While reactive navigation provides an essential safety

net, high-speed maneuvers require obstacle avoidance

strategies that account for the vehicle’s multibody dy-

namics, tire friction limits, and actuator saturation. In

these scenarios, reactive algorithms often fail to prevent

loss of lateral stability or unrecoverable side-slip. There-

fore, the state-of-the-art methodology formulates ob-

stacle avoidance as an optimal control problem within

a receding horizon framework, predominantly utilizing

model predictive control.

In this architecture, static and dynamic obstacles

are mathematically modeled as non-linear inequality

constraints within the cost function of the model predic-

tive controller. To maintain the computational tractabil-

ity of the optimization problem, obstacles are typically

represented by elliptical exclusion zones that expand

based on the relative velocity and uncertainty covari-

ance of the detected object. As the vehicle approaches

an obstacle, the predictive solver evaluates the cost of

deviating from the global reference path against the

safety margins of the exclusion zones, computing the

optimal independent steering angles and driving torques

required to navigate the spatial bottleneck safely [10].

The real-time resolution of these highly constrained,

non-convex optimization problems is facilitated by ad-

vanced algorithmic diﬀerentiation frameworks and non-

linear programming solvers, such as CasADi. Further-

more, recent literature highlights the integration of meta-

heuristic algorithms to dynamically tune the prediction

horizon and weighting matrices of the model predictive

controller. For example, utilizing a multivariate Gaus-

sian mixture model combined with ant colony optimiza-

tion allows the system to adaptively adjust its evasion

aggressiveness [10]. In open spaces, the controller prior-

itizes energy-eﬃcient path tracking, but upon detecting

a dynamic obstacle, it autonomously shortens the pre-

diction horizon and increases the penalty on constraint

violations, ensuring a rapid and kineto-statically safe

19 International Journal of Engineering Insights, (2025) 3:1

evasive trajectory without violating the fundamental

double Ackermann geometric relationships.

6 Low-Level Control and Safety Integration

The successful execution of high-level trajectory com-

mands in four-wheel independent steering and driving

platforms relies heavily on the eﬃciency and reliabil-

ity of the low-level control architecture. While upper-

level controllers, such as the model predictive controller,

compute the virtual generalized forces and the desired

yaw moment required to track a path, the low-level

layer is tasked with mapping these virtual demands

onto the physical actuators. Due to the inherent over-

actuation of the double Ackermann geometry, the sys-

tem possesses inﬁnite combinations of individual wheel

torques and steering angles that can satisfy a given

net force and moment requirement. Consequently, the

low-level control is formulated as a constrained multi-

objective optimization problem known as control allo-

cation.

The primary objective of the torque allocation algo-

rithm is to maintain tire forces well within the linear re-

gion of the friction circle while simultaneously minimiz-

ing the overall energy consumption of the drive motors.

Traditional pseudo-inverse mapping methods are com-

putationally fast but often fail to account for actuator

saturation and dynamic variations in the tire-road fric-

tion coeﬃcient. To address this, contemporary research

has successfully implemented meta-heuristic algorithms

for real-time optimal torque distribution. Speciﬁcally,

the mutant particle swarm optimization algorithm has

been utilized to solve the non-convex allocation prob-

lem. By introducing a mutation operator into the stan-

dard particle swarm optimization framework, the algo-

rithm avoids premature convergence to local minima.

This ensures an optimal distribution of driving and

braking torques among the four wheels, which not only

improves the overall energy eﬃciency but also maxi-

mizes the traction margin of each tire, thereby enhanc-

ing longitudinal and lateral stability during high-speed

cornering [2].

As these autonomous platforms execute tight turn-

ing maneuvers enabled by the double Ackermann ge-

ometry, the resulting high lateral accelerations intro-

duce severe safety risks, particularly for vehicles with

a high center of gravity such as autonomous electric

road sweepers and high-clearance agricultural sprayers.

The prevention of un-tripped rollovers is mathemati-

cally quantiﬁed using the load transfer ratio. The load

transfer ratio is deﬁned as the normalized diﬀerence be-

tween the vertical reaction forces on the right and left

tires. A value of zero indicates a perfectly balanced load,

while a value approaching positive or negative one signi-

ﬁes imminent wheel lift-oﬀ. Advanced low-level safety

integration involves continuously monitoring the pre-

dicted load transfer ratio. If the calculated index ex-

ceeds a predeﬁned dynamic stability threshold, a rollover

prevention intervention is triggered. This active safety

layer seamlessly overrides the nominal path tracking

commands by either distributing diﬀerential braking to

rapidly reduce longitudinal velocity or actively reduc-

ing the front and rear steering angles to safely increase

the radius of the instantaneous center of rotation [22,

8].

Furthermore, the physical decoupling of the steer-

ing wheel from the actuators in steer-by-wire systems

necessitates robust fault-tolerant control strategies. In

the event of a critical hardware or software failure,

such as a steering actuator locking at a ﬁxed angle

or a drive motor losing power, the structural redun-

dancy of the four-wheel independent steering and driv-

ing architecture allows for dynamic system reconﬁgura-

tion. Fault-tolerant control algorithms detect the spe-

ciﬁc actuator anomaly and instantaneously update the

kinematic Jacobian matrix and the dynamic stability

domain bounds. The allocation layer then mathemati-

cally redistributes the required corrective yaw moment

to the remaining functional wheels. By generating dif-

ferential thrust and adapting the steering angles of the

healthy actuators, the vehicle can actively compensate

for the asymmetrical drag or locked geometry, ensuring

the robot remains within the extension dynamic stabil-

ity domain and can safely navigate to a maintenance

point without catastrophic loss of control [18].

7 Field Applications and Sectoral Performance

The theoretical maturity of four-wheel independent steer-

ing and driving architectures, combined with the double

Ackermann geometry, has catalyzed their deployment

across industrial sectors characterized by highly restric-

tive and unstructured operational environments. In pre-

cision agriculture, autonomous navigation in high-density

orchards and autonomous furrow tracking require ex-

ceptional maneuverability to minimize soil compaction

and avoid mechanical damage to crops during headland

turns. Recent literature demonstrates that integrating

fuzzy logic and H-inﬁnity robust adaptive controllers

allows high-clearance agricultural machinery to main-

tain sub-centimeter trajectory tracking precision, ac-

tively compensating for severe nonlinearities introduced

by varying soil moisture and external environmental

disturbances [6,19]. Furthermore, the reduced turning

radius and the convergence toward a common instan-

taneous center of rotation inherent in this kinematic

20 International Journal of Engineering Insights, (2025) 3:1

conﬁguration resolve the critical issue of maneuvering

space in greenhouses, thereby optimizing the cultivable

area without compromising lateral stability.

In the underground coal mining sector, trackless

auxiliary transport robots face the immense challenge of

navigating through narrow, irregular tunnels with un-

predictable friction proﬁles. For these heavy-duty appli-

cations, advanced dynamic modeling based on Gibbs-

Appell formulations and coordinated trajectory track-

ing control are vital to prevent lateral collisions against

gallery walls [13]. The ability of the over-actuated sys-

tem to independently modulate the front and rear steer-

ing angles enables these vehicles to perform continuous

heading corrections with minimal lateral chassis devi-

ation, ensuring safe, stable, and high-capacity under-

ground load transport.

Concurrently, modern manufacturing intralogistics

demands multi-unit transport systems, commonly re-

ferred to as milk-run logistic trains, capable of operat-

ing at high speeds in increasingly narrow storage aisles.

The application of Jacobian matrices to model the kine-

matics of multiple coupled trailers featuring double Ack-

ermann steering ensures strict tracking ﬁdelity relative

to the tractor unit [3]. This kinematic precision com-

pletely mitigates the trajectory error ampliﬁcation phe-

nomenon, known as oﬀ-tracking, in each successive unit

of the train, which is a fundamental safety factor for the

total automation of high-density warehouses.

Finally, in the demanding ﬁeld of space exploration,

next-generation lunar and planetary rovers maximize

the actuator redundancy of four-wheel independent sys-

tems to operate over extreme topologies and sinkage-

prone regolith. By implementing reactive navigation ar-

chitectures and maneuver servers based on the Robot

Operating System 2, these rovers can dynamically switch

between traditional locomotion modes and complex non-

holonomic base maneuvers, such as pure lateral crab-

bing and turning on their own central axis [7]. These

advanced capabilities not only facilitate reactive obsta-

cle evasion in dead-end scenarios but also permit precise

chassis orientation adjustments required for optimal so-

lar energy collection and static stabilization on steep

inclines. The technical convergence of all these ﬁeld ap-

plications demonstrates that the addressed architecture

transcends mere geometric agility, establishing itself as

the de facto standard for solving extreme mobility chal-

lenges on a global scale.

8 Challenges and Future Directions

Despite the signiﬁcant advancements in the control and

modeling of four-wheel independent steering and driv-

ing systems with double Ackermann geometry, several

open challenges remain for the next decade. A primary

bottleneck is the simulation-to-reality gap in navigation

over unstructured terrains. Although deep reinforce-

ment learning architectures show exceptional results in

simulated environments, their physical deployment in

extreme conditions requires more robust transfer learn-

ing techniques. Domain adaptation remains fundamen-

tal to handle the stochastic nature of tire-soil inter-

action, especially in the presence of dense mud or lu-

nar regolith where traditional tire models fail to predict

traction accurately [9,7].

Furthermore, a stark trade-oﬀ persists between com-

putational eﬃciency and mathematical model ﬁdelity.

High-ﬁdelity nonlinear dynamic formulations, particu-

larly those derived from Newton-Euler laws or Bolzman-

Hamel equations for quasi-velocities, provide superior

analytical accuracy for over-actuated vehicles but de-

mand onboard processing power that is often prohibitive

for real-time applications in agricultural platforms or

space rovers [7]. Future research must therefore focus on

the development of edge artiﬁcial intelligence accelera-

tion algorithms and hardware-in-the-loop optimization

for model predictive control solvers. This is essential

to enable the execution of complex optimization matri-

ces in the kilohertz range, ensuring the stability of the

vehicle during high-speed maneuvers on low-adhesion

surfaces.

Finally, the integration of swarm intelligence and

multi-agent coordination for over-actuated logistic trains

represents an emerging scientiﬁc frontier. The decen-

tralized coordination of multiple independent traction

units requires solving coupled kinematic constraints based

on complex Jacobian matrices to ensure path-following

ﬁdelity. The standardization of low-latency communica-

tion protocols within the robot operating system ecosys-

tem will be pivotal to guarantee collision-free, scalable,

and energy-eﬃcient formation tracking at the industrial

level [3,2].

9 Conclusions

This review has systematically and critically analyzed

the state of the art of mobile robots with four-wheel

independent steering and driving operating under the

double Ackermann geometry during the decade from

2016 to 2026. The transition from classical geometric

steering control schemes toward highly over-actuated

multibody dynamic systems has completely redeﬁned

the theoretical limits of robotic maneuverability and

lateral stability. A key ﬁnding of this synthesis is the

robust integration of Newton-Euler laws for 3-DOF and

7-DOF dynamic modeling, alongside the application of

21 International Journal of Engineering Insights, (2025) 3:1

Bolzman-Hamel theory to manage non-holonomic con-

straints via local quasi-velocities. These mathematical

frameworks have proven essential for capturing the non-

linear coupling of the vehicle’s chassis while maintaining

computational eﬃciency for real-time control.

The literature indicates that linear time-varying model

predictive control has consolidated as the superior math-

ematical framework for managing hard actuator con-

straints and system nonlinearities. Simultaneously, deep

reinforcement learning, driven by advanced data sort-

ing mechanisms such as group intelligent experience

replay, is rapidly closing the sample eﬃciency gap re-

quired for decision-making in uncertain and unstruc-

tured terrains. The integration of low-level safety lay-

ers, speciﬁcally those focused on the continuous moni-

toring of the load transfer ratio and optimal torque allo-

cation through metaheuristic optimization, has proven

to be the enabling factor for the scientiﬁc viability of

these platforms. By preventing kinetostatic catastro-

phes such as untripped rollover and ensuring recovery

through fault-tolerant control in steer-by-wire systems,

these technologies allow for safe deployment in critically

demanding sectors ranging from precision agriculture

to planetary exploration. As research advances toward

fully autonomous ecosystems, the theoretical conver-

gence of robust optimal control for disturbance rejec-

tion and high-ﬁdelity dynamic modeling will undoubt-

edly dictate the design paradigms for the next genera-

tion of high-mobility terrestrial robotic systems.

Conﬂict of interest

The authors declare that they have no conﬂict of inter-

est.

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