Traction-Adaptive Super-Twisting Sliding Mode Control for Mecanum Robotaxi Tracking under Wheel-Speed Constraints: Modeling, Estimation, and Benchmarking

The rapid development of autonomous transportation, on-demand mobility services, and smart-city infrastructure has heightened interest in mobile robotic platforms capable of operating safely and precisely in constrained urban environments. While most public attention has focused on car-like autonomous vehicles, low-speed service platforms with omnidirectional mobility are also highly relevant for last-mile transportation, curbside pickup assistance, indoor-outdoor logistics, and precision docking tasks in dense service areas. In these applications, the ability to translate laterally without reconfiguring the steering is a major advantage. For this reason, Mecanum-wheeled mobile robots have attracted growing interest as candidate platforms for compact robotaxi-style or service-mobility systems operating in narrow, cluttered spaces [1-7].

Despite this maneuverability advantage, Mecanum platforms remain challenging to control accurately in practice. Their omnidirectional motion relies on roller-ground interaction, and the resulting body motion is sensitive to load transfer, changes in floor or road conditions, micro-slip, actuator nonlinearities, and mismatches between nominal wheel kinematics and effective platform motion [8-14]. These effects are especially important in realistic service situations, such as curb approach, docking near painted or polished surfaces, payload changes, and localized low-friction regions. Consequently, a controller designed only from nominal kinematics may provide acceptable tracking in mild conditions but may lose repeatability, robustness, or terminal precision when traction conditions vary during motion.

The literature on wheeled and omnidirectional mobile robots offers several useful directions, but each addressed only part of this practical problem. Classical works established the structural and kinematic foundations of wheeled mobile robots and provided the modeling tools needed to describe holonomic and omnidirectional motion [8-12]. More recent comparative studies have emphasized that Mecanum and omniwheel systems exhibit performance limitations strongly influenced by wheel geometry, contact quality, and implementation details [13, 14]. These studies underscore the need for control laws that remain effective when actual motion deviates from the nominal wheel-speed-to-body-velocity mapping.

A large class of practical mobile-robot controllers still relies on Proportional-Integral-Derivative (PID)-family designs for their simplicity, low implementation burden, and direct tunability [15]. For Mecanum systems, PID and fuzzy-PID variants remain attractive in embedded applications and can achieve good performance when operating conditions remain close to nominal. However, their robustness may degrade when traction changes quickly or when actuator feasibility becomes the dominant factor near aggressive maneuvers or terminal docking. In parallel, more advanced methods such as neural tracking control, sensor-fusion-aided path following, and predictive control have been developed to improve trajectory tracking under uncertainty or sensing imperfections. For example, neural control has been used to improve Mecanum tracking performance [16], and sensor-fusion-based path following has been shown to improve state estimation under nonuniform measurements and practical nonlinearities such as saturation and wheel sliding [17]. Observer-based predictive control has also recently been used to combine disturbance estimation with explicit handling of physical constraints in Mecanum robots, while sliding-mode-observer-based model predictive tracking has further highlighted the value of estimation-enhanced robust control in this class of systems [18]. These studies are valuable, but they generally emphasize estimation, optimization, or tracking accuracy rather than a benchmark-oriented study of traction adaptation under strict wheel-speed feasibility constraints. In contrast, the present work combines online traction estimation, adaptive super-twisting control, and wheel-speed-feasible command projection within a common benchmark framework against a practically relevant PID baseline. Robust nonlinear control is another important line of work. Sliding mode control (SMC) is well known for its invariance to matched uncertainties and disturbances [19-21]. Higher-order variants, especially the super-twisting algorithm, are attractive because they preserve strong robustness while reducing the chattering associated with first-order switching laws [22-24]. Adaptive-gain super-twisting methods further extend this idea by allowing the control gains to change online when the uncertainty level is unknown or time-varying [25, 26]. For mobile robots, observer-based and sliding-mode-based methods have shown strong disturbance rejection and robustness to modeling errors [27-28]. Recent studies also continue to explore sliding-mode-based control design for Mecanum omnidirectional robots, including optimal-control-oriented SMC formulations that evaluate trajectory error, execution time, and energy-related performance [29]. Nevertheless, for Mecanum-wheeled systems, relatively few studies examine the combined problem of traction variability represented directly in the body-velocity channels, online traction estimation for slip-aware control adaptation, actuator-feasible implementation under wheel-speed bounds, and standardized comparison against a practically meaningful baseline across multiple service scenarios.

This gap is important because omnidirectional service robots operate in a regime where robustness and precision must be evaluated together rather than separately. A controller may show strong disturbance rejection in unconstrained simulations yet still lose docking accuracy when wheel-speed limits become active. Conversely, a simple baseline controller may achieve good terminal accuracy under mild conditions but offer weaker resilience to traction variations during route-following motion. Therefore, from an application perspective, the relevant question is not whether one controller is universally superior, but rather how different controller structures trade off robustness, traction awareness, control aggressiveness, and terminal accuracy under the same physical constraints.

Motivated by this issue, this paper investigates a two-loop control architecture for a four-Mecanum-wheeled mobile robot designed for low-to-moderate-speed robotaxi-style operation in smart-city service environments. The outer loop generates pose-to-velocity references, while the inner loop is implemented in two alternative forms for fair comparison: a baseline PID body-velocity controller and a traction-adaptive super-twisting sliding mode controll (ASTSMC) with online traction estimation. In the proposed formulation, traction variation is modeled as channel-wise multiplicative uncertainty in the feasible body-velocity input, and the estimated traction level is used to adapt the super-twisting gains. To preserve implement ability, all controller-generated commands are mapped through wheel-speed constraints and projected back to feasible body motion.

The main contributions of this work are as follows. First, a slip-aware ASTSMC framework is formulated for a Mecanum platform, with explicit enforcement of wheel-speed feasibility and online traction estimation. Second, a benchmark-oriented evaluation protocol is constructed so that both the proposed ASTSMC and the PID baseline operate under the same outer-loop reference generator, actuator limits, and scenario definitions. Third, five representative service scenarios are considered, including curb docking, repeated curvature tracking, spatially varying friction, payload-related traction change, and terminal slip shock. This enables quantification of not only tracking error but also terminal docking performance, traction-estimation quality, saturation statistics, and control activity. The resulting comparison reveals a practically important robustness-precision tradeoff: ASTSMC improves robustness and traction awareness during traction-varying service motion, whereas the tuned PID baseline can remain preferable for the tightest terminal docking tasks when the motion becomes strongly constraint-dominated.

The remainder of the paper is organized as follows. Section 2 presents the mathematical model, the wheel-speed feasibility mapping, the slip-affected body-velocity representation, and the traction estimator. Section 3 details the outer-loop reference generation and the proposed ASTSMC inner-loop design. Section 4 discusses boundedness, feasibility, and a Lyapunov-based interpretation of the proposed controller. Section 5 introduces the benchmark suite and evaluation protocol. Section 6 presents the simulation results. Section 7 discusses their practical implications. Section 8 concludes the paper and outlines future work.

3.1 Outer loop: Pose-to-velocity reference generation

The outer loop converts pose errors into a body-frame velocity reference. Let $q_d=\left[x_d, y_d, \theta_d\right]^{\top}$ be the desired pose and $\dot{\theta}_d$ the desired yaw rate. Define the inertial-frame position error

$e_p \triangleq\left[\begin{array}{l}x_d-x \\ y_d-y\end{array}\right]$                    (12)

and transform it to the body frame using the rotation matrix $R(\theta)$ [9]:

$e_b \triangleq R^{\top}(\theta) e_p, R(\theta)=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]$                (13)

Let $e_\theta \triangleq \operatorname{wrap}\left(\theta_d-\theta\right)$ denote the wrapped heading error. The velocity reference is generated by feedforward plus proportional feedback:

$\begin{aligned} & v_{x, \mathrm{ref}}=v_{d, x}^b+k_x e_{b, x}, \\ & v_{y, \mathrm{ref}}=v_{d, y}^b+k_y e_{b, y}, \\ & \omega_{\mathrm{ref}}=\dot{\theta}_d+k_\theta e_\theta\end{aligned}$                (14)

where, $\left[v_{d, x}^b, v_{d, y}^b\right]^{\top}=R^{\top}(\theta) \dot{p}_d$ is the feedforward velocity expressed in $\{B\}$ and $\dot{p}_d=\left[\dot{x}_d \dot{y}_d\right]^{\top}$.

Docking speed shaping and comfort limiting.

For curbside docking, distance-based shaping is applied to reduce speed near the goal, improving passenger comfort and safety:

$\sigma_d \triangleq \min \left(1, \frac{\left\|e_p\right\|}{r_d}\right),\left[\begin{array}{l}v_{x, \mathrm{ref}} \\ v_{y, \mathrm{ref}}\end{array}\right] \leftarrow \sigma_d\left[\begin{array}{l}v_{x, \mathrm{ref}} \\ v_{y, \mathrm{ref}}\end{array}\right]$             (15)

A similar shaping can be applied to $\omega_{\text {ref }}$ using a yaw-radius $r_\theta>0$. Additionally, to avoid abrupt changes in commanded velocity, a discrete-time slew limiter can be applied:

$\begin{aligned} v_{\text {ref }}[k]= & v_{\text {ref }}[k-1] +\operatorname{sat}_{\Delta v_{\text {max }}}\left(v_{\text {ref }}^{\text {raw }}[k]-v_{\text {ref }}[k-1]\right)\end{aligned}$              (16)

where, $v_{\text {ref}}^{\text {raw}}$ is given by Eqs. (14) and (15), and $\operatorname{sat}_{\Delta v_{\text {max}}}(\cdot)$ acts elementwise with componentwise rate limits.

3.2 Inner loop: Slip-aware adaptive super-twisting sliding mode control

The inner loop regulates body velocity $v$ to track $v_{\text {ref}}$ under the slip-affected model Eq. (10). SMC is well known for robustness to matched uncertainties and disturbances [19-21]. Define the velocity tracking error (sliding variable) as

$s \triangleq v-v_{\mathrm{ref}}$               (17)

To reduce chattering in practice, a boundary-layer saturation is employed:

$\sigma \triangleq \operatorname{sat}\left(\frac{S}{\phi}\right), \phi=\left[\begin{array}{ccc}\phi_x & \phi_y & \phi_\omega\end{array}\right]^{\top}, \phi_x, \phi_y, \phi_\omega>0$                (18)

where the division is elementwise. The saturation operator is also applied elementwise, with

$\operatorname{sat}(\xi)= \begin{cases}\xi, & |\xi| \leq 1 \\ \operatorname{sgn}(\xi), & |\xi|>1\end{cases}$

Super-twisting structure.

Second-order sliding mode methods, including super-twisting, achieve finite-time convergence of $s$ and $\dot{s}$ without requiring $\dot{s}$ measurement, under standard boundedness assumptions [23, 24]. Let

$z=\left[\begin{array}{l}z_x \\ z_y \\ z_\omega\end{array}\right] \in \mathbb{R}^3$

denote the super-twisting internal state, updated by

$\dot{z}=-K_2 \sigma, K_2=\operatorname{diag}\left(k_{2, x}, k_{2, y}, k_{2, \omega}\right)$                  (19)

Using the estimated traction matrix

$\hat{\Lambda}=\operatorname{diag}\left(\hat{\lambda}_x, \hat{\lambda}_y, \hat{\lambda}_\omega\right)$

The commanded body input is formed as a traction-compensated reference term plus a super-twisting correction:

$\begin{gathered}u=\hat{\Lambda}^{-1} v_{\text {ref }}-K_1\left(|s|^{1 / 2} \odot \sigma\right)+z, \\ K_1 \triangleq \operatorname{diag}\left(k_{1, x}, k_{1, y}, k_{1, \omega}\right)\end{gathered}$              (20)

where, $\odot$ denotes elementwise multiplication, and

$|s|^{1 / 2}=\left[\begin{array}{l}\left|s_x\right|^{1 / 2} \\ \left|s_y\right|^{1 / 2} \\ \left|s_\omega\right|^{1 / 2}\end{array}\right]$

is applied elementwise.

In this implementation, traction compensation is applied only to the reference (equivalent) term through $\hat{\Lambda}^{-1} v_{\mathrm{ref}}$, while the super-twisting correction remains unscaled. This choice avoids excessive amplification of the discontinuous correction when the estimated traction becomes small.

Traction-adaptive gains. Because traction variations in Eq. (10) effectively modify the available control authority in each channel, adaptive-gain super-twisting is used to strengthen the corrective action when the estimated traction decreases [25, 26]. For each channel $i \in\{x, y, \omega\}$, define the scheduling variable

$\rho_i \triangleq \frac{1}{\hat{\lambda}_i+\delta_i}, \delta_i=\delta>0$              (21)

The gains are then scheduled as

$\begin{gathered}k_{1, i}[k]=\operatorname{clip}\left(k_{10, i} \rho_i[k]^{\alpha_i}, k_{1, i}^{\min }, k_{1, i}^{\max }\right), \\ k_{2, i}[k]=\operatorname{clip}\left(k_{20, i} \rho_i[k]^{\beta_i}, k_{2, i}^{\min }, k_{2, i}^{\max }\right), i \in\{x, y, \omega\}\end{gathered}$              (22)

where, $k_{10, i}>0$ and $k_{20, i}>0$ are nominal base gains, $\alpha_i>0$ and $\beta_i>0$ are channel-wise scheduling exponents, and

$\operatorname{clip}\left(x, x_{\min}, x_{\max}\right)=\min \left(\max \left(x, x_{\min}\right), x_{\max}\right)$.

The role of these parameters is as follows. The gain $k_{1, i}$ primarily scales the instantaneous nonlinear correction in channel $i$, whereas $k_{2, i}$ governs the buildup rate of the internal state $z_i$, which supports disturbance rejection and sustained corrective action. When $\hat{\lambda}_i$ decreases, the scheduling variable $\rho_i$ increases; therefore, both $k_{1, i}$ and $k_{2, i}$ increase, which compensates for the loss of effective control authority in that channel. The lower bounds prevent the gains from becoming too small under nominal conditions, while the upper bounds prevent excessive aggressiveness, actuator stress, and highfrequency control activity in low-traction conditions.

Table 2. Outer-loop reference generation and inner-loop controller parameters

The nominal gains $k_{10, i}$ and $k_{20, i}$ are selected from stable near-nominal tracking trials so that the inner loop remains faster than the outer loop and the wheel-speed projection is mostly inactive away from severe traction loss. The clipping bounds are then chosen to preserve robustness while limiting excessive wheel speed demand. Channel-wise exponents $\alpha_i$ and $\beta_i$ allow different adaptation sensitivities in the translational and yaw channels, consistent with the parameter choices reported in Table 2. Discrete-time implementation and wheel feasibility.

With sampling time $\Delta t$, Eq. (19) is implemented as

$z\lceil k+1\rceil=z\lceil k\rceil-\Delta t K_2\lceil k\rceil \sigma\lceil k\rceil$            (23)

and $u[k]$ is computed from Eq. (20). The commanded body input is then converted to wheel speeds using Eq. (5), constrained by Eqs. (7) and (8), and projected back to a feasible body command using Eqs. (6) and (9) before being applied to the slip model Eq. (10). This ensures that the implemented closed loop respects actuator limitations while preserving the practical robustness advantages of super-twisting sliding-mode control, provided sufficient control authority remains available under the wheel-speed constraint [24].

This section defines the evaluation methodology used to validate and compare the proposed ASTSMC against a PID baseline for a Mecanum mobile robot platform motivated by robotaxi-style operation. To ensure a fair comparison, both controllers use the same robot parameters, outer-loop pose-to-velocity reference generator, sampling time, initial conditions, actuator limits, wheel-speed constraints, and benchmark scenarios.

5.1 Controllers under comparison

Two inner-loop body-velocity controllers are evaluated while keeping the same outer-loop reference generator and the same wheel-speed feasibility layer for both cases:

(i) a baseline PID inner-loop body-velocity controller, widely used in mobile robotics because of its simplicity and tunability; (ii) the proposed ASTSMC, which combines super-twisting action with online traction estimation to improve robustness under slip and traction variation.

Thus, the comparison is designed so that any observed difference arises primarily from the inner-loop control structure rather than from unequal reference generation, scenario definition, or actuator handling.

5.2 Benchmark scenarios

Five scenarios are considered:

• CurbDocking: precise pose docking to a target curb location (low-speed accuracy emphasis).
• RoundedSquareLoop: continuous tracking with repeated curvature changes (transient response emphasis).
• FrictionMap: spatially varying traction/slip parameters to emulate heterogeneous road conditions.
• PayloadEvent: sudden payload changes leading to inertial/traction mismatch.

The push disturbance, traction-estimator parameters, and scenario-to-traction-mode mapping are summarized in Table 3.

• DockingSlipShock: short-duration traction loss during the final docking phase.

Table 3. Disturbance settings, traction estimator parameters, and scenario-to-traction-mode mapping

5.3 Wheel-speed constraints

Wheel angular velocities are constrained by the limit

$\left|\omega_i\right| \leq \Omega_{\max }, i=1, \ldots, 4$

In all reported benchmarks, this wheel-speed magnitude constraint is enforced at every sampling instant. The optional discrete-time wheel slew limit introduced in Eq. (8) is not activated in the benchmark results reported here unless explicitly stated otherwise. Accordingly, controller-generated body commands are first mapped to wheel speeds, then passed through the wheel-speed feasibility layer, and finally projected back to a feasible body command before being applied to the slip-affected model. This ensures that both controllers are evaluated under the same actuator constraints and that only realizable commands are delivered to the robot model.

5.4 Performance metrics

For each run, the following metrics are reported:

• RMSE $(x, y, \theta)$ over the full trajectory,
• planar tracking error $\operatorname{RMSE}_{x y}=\sqrt{\operatorname{RMSE}_x^2+\operatorname{RMSE}_y^2}$,
• final docking position and heading error for docking scenarios,
• peak wheel speed and saturation statistics to verify constraint compliance,
• traction-estimation RMSE, and
• control activity (TV) as a relative indicator of command aggressiveness.

For the traction estimator, the channel-wise estimation error is evaluated by comparing the true traction coefficients $\lambda_x, \lambda_y, \lambda_\omega$ with their corresponding estimates $\hat{\lambda}_x, \hat{\lambda}_y, \hat{\lambda}_\omega$ over the simulation horizon. When a combined translational traction-estimation metric is reported, it is computed from the longitudinal and lateral channels using a root-mean-square aggregation consistent with the notation used later in the robustness summary presented later in this section.

5.5 Implementation and reproducibility

All simulations are executed in MATLAB. Each benchmark returns time histories of pose, reference pose, body-frame tracking errors, wheel speeds, and traction estimates. A single script executes all scenarios for both controllers and generates the time histories and quantitative metrics used in the comparative analysis. The benchmark design follows the general principle of providing standardized, repeatable tracking tests [9]. Additional robustness runs are performed under measurement noise and discrete-time wheel-speed command delay to assess sensitivity to sensing and implementation non-idealities.

5.6 Benchmark parameters and traction map definition

The benchmark traction profiles are defined as follows (all values are channel-wise in the body frame as $\lambda=\left[\lambda_x, \lambda_y, \lambda_\omega\right]^{\top}$):

• mapA (mild spatial variation): nominal

$\lambda=[0.95,0.80,0.95]^{\top}$;

tile patch if $3<x<5$ and $1<y<3$, then

$\lambda=[0.85,0.65,0.90]^{\top}$.

• mapB (harsher spatial variation): nominal

$\lambda=[0.92,0.75,0.95]^{\top}$;

wet region if $2<x<4$ and $0<y<2$, then

$\lambda=[0.70,0.55,0.85]^{\top}$;

tile region if $4<x<6$ and $2<y<4$, then

$\lambda=[0.80,0.60,0.88]^{\top}$.

• event (payload/traction drop):

$\lambda=[0.95,0.80,0.95]^{\top}$ for $t \leq 18 \mathrm{~s}$

and

$\lambda=[0.75,0.55,0.85]^{\top}$ for $t>18 \mathrm{~s}$.

The benchmark results under the realistic wheel-speed bound $\left|\omega_i\right| \leq 40 \mathrm{rad} / \mathrm{s}$ highlight a clear tradeoff between (i) terminal docking accuracy and (ii) robustness to traction variability with reliable online traction estimation. Table 4 summarizes tracking and docking performance, while Table 5 reports traction-estimation RMSE, wheel-speed saturation statistics, and control activity.

The Lyapunov-based interpretation in Section 4.5 clarifies these observations: when wheel-speed projection is mostly inactive, the super-twisting mechanism effectively rejects traction-induced uncertainty and matched disturbances; when projection becomes active near terminal docking, the closed loop becomes input-limited, and precision is dominated by feasible control authority under $\Omega_{\max}$. Therefore, the observed docking tradeoff is consistent with constrained robust control behavior rather than a contradiction of super-twisting robustnessThe Lyapunov-based interpretation in Section 4.5 clarifies these observations: when wheel-speed projection is mostly inactive, the super-twisting mechanism effectively rejects traction-induced uncertainty and matched disturbances; when projection becomes active near terminal docking, the closed loop becomes input-limited, and precision is dominated by feasible control authority under $\Omega_{\max}$. Therefore, the observed docking tradeoff is consistent with constrained robust control behavior rather than a contradiction of super-twisting robustness.

7.1 Docking scenarios: Accuracy vs. constraint-dominated behavior

In curbside docking maneuvers (CurbDocking and DockingSlipShock), the PID baseline achieves tighter terminal position error compared with ASTSMC (Table 4). This is expected because docking is a low-speed, precision-oriented task in which command feasibility and transient shaping dominate performance. The wheel-speed constraint clips aggressive wheel commands, and any controller that relies on strong corrective action near the end of the maneuver can experience reduced effectiveness when the constraint becomes active. This behavior is evident in the wheel-speed subplots of Figures 3-12, where the commanded motion approaches the actuator limits more frequently during the final approach for the robust controller.

Importantly, even when docking accuracy is less favorable, ASTSMC maintains higher traction-estimation quality (Table 5), supporting the paper's main objective: slip/traction awareness for robotaxi-style operation, where road conditions can change rapidly near curbside regions (painted markings, polished asphalt, and localized wet patches).

7.2 Service-motion scenarios: Robustness under traction variability

In service-motion scenarios that emulate continuous operation (RoundedSquareLoop, FrictionMap, and PayloadEvent), the traction-adaptive design goal of ASTSMC becomes more pronounced. The body-frame error subplots and path-tracking plots (Figures 5-10) show that ASTSMC sustains stable tracking despite traction variations induced by spatial friction changes and event-type disturbances. This is consistent with the purpose of using a sliding-mode-based inner loop: to reduce sensitivity to uncertain traction scaling and disturbance-like effects in the velocity dynamics.

A key contribution is that ASTSMC consistently produces lower RMSE for traction estimation than the PID baseline (Table 5). This is relevant for future autonomy functions because traction estimates can be used for supervisory decisions such as speed reduction near low-friction zones, safer docking, or constraint-aware planning. In addition, the supplementary noise and delay tests in Table 6 preserve the same qualitative trend, indicating that the proposed ASTSMC remains more robust in traction-varying service-motion scenarios, whereas PID remains preferable for the tightest terminal docking tasks under the tested non-idealities.

7.3 Control activity, saturation, and practical implications

Both controllers explicitly enforce the wheel-speed constraint. However, Table 5 indicates that ASTSMC exhibits higher saturation-related statistics and substantially larger control activity (TV) than PID. Large TV values are characteristic of sliding-mode-type laws in discrete-time implementations, even with boundary layers, because switching-like corrective actions increase high-frequency content. While this behavior can improve robustness to matched uncertainties, it may also raise practical concerns for deployment, including increased actuator wear and heating, amplified sensitivity to measurement noise, excitation of unmodeled dynamics (e.g., roller compliance and drivetrain backlash), and reduced passenger comfort through increased jerk.

Several mitigation mechanisms are already incorporated in the proposed implementation: (i) a boundary-layer saturation (18) to soften discontinuities; (ii) adaptive-gain clipping 22(a) and (b) to prevent excessive gains under low traction; (iii) explicit wheel-speed feasibility projection (9), together with outer-loop feasibility scaling, to ensure actuator-realizable commands; and (iv) saturation-aware update of the super-twisting internal state to reduce windup when wheel limits are active. In addition, the two-loop architecture requires the outer-loop reference generator to remain constraint-feasible and the inner loop to be sufficiently faster than the outer loop, especially in omnidirectional maneuvers that combine lateral motion and yaw correction.

TV should therefore be interpreted as a relative indicator of command aggressiveness under fixed sampling, sensing, and actuator conditions. In particular, measurement noise and implementation non-idealities can increase wheel-speed variation even when the qualitative tracking behavior remains similar; hence, TV comparisons are most informative when made under the same experimental conditions. Overall, the results suggest that ASTSMC is well-suited to service-motion robustness under traction variability, while docking maneuvers benefit from additional softening or scheduling. A practical implementation may therefore employ docking-mode gain scheduling (larger boundary layer and reduced gains near the goal) or a hybrid terminal strategy to retain traction awareness without unnecessary high-frequency control action.

7.4 Summary of implications for Mecanum robotaxi control

Overall, the results support the following conclusions. First, the proposed traction-adaptive ASTSMC improves traction estimation and maintains robust tracking under traction variability, matching the intended smart-city operating conditions. Second, the PID baseline can be preferable for final docking precision under strict wheel-speed limits, suggesting that a practical deployment may use either (i) a dedicated docking-mode gain schedule for ASTSMC, or (ii) a hybrid strategy where ASTSMC is used for route/service motion and PID (or softened SMC) is used for the terminal docking phase. These findings strengthen the case for traction-aware robust control as a candidate inner-loop strategy for omnidirectional robot platforms operating on real roads.

During the preparation of this manuscript, ChatGPT (OpenAI) was used solely for language editing and writing support. The author reviewed, revised, and approved the final manuscript and accepts full responsibility for its content.