Filtered Tube-Based LTV MPC for AWOISV

• FT-LTVMPC is a robust path-tracking controller that integrates online linearization, tube-based MPC, and filtered error feedback to manage large steering angles.
• It maintains lateral and heading tracking accuracy by compensating for linearization errors, model mismatches, and measurement noise in real time.
• Experimental results demonstrate significant reductions in lateral/heading errors and smoother control inputs compared to conventional MPC methods.

Filtered Tube-Based Linear Time-Varying MPC (FT-LTVMPC) denotes a robust path-tracking control strategy introduced for an all-wheel omni-directional independent steering vehicle (AWOISV), a vehicle whose wheels can independently steer up to approximately $\pm 90^\circ$. In that formulation, FT-LTVMPC combines an online-linearized linear time-varying MPC, a tube-MPC-style nominal/error decomposition, and a filtering stage applied to the state error used in the ancillary tube feedback. Its stated purpose is simultaneous tracking of lateral position and an arbitrary desired heading angle relative to the reference path, while remaining robust to linearization error, model mismatch, parameter uncertainty, and measurement fluctuations, and still being computationally light enough for real-time execution (Yang et al., 19 Aug 2025). In the broader tube-MPC literature, closely related formulations include filter-based system level tube-MPC, elastic tube-based MPC with online uncertainty refinement, and horizon-varying tube parameterizations; these do not all use the FT-LTVMPC label, but they clarify the method’s place within robust time-varying and adaptive tube MPC (Sieber et al., 2024).

1. Definition and conceptual scope

FT-LTVMPC is presented as the authors’ robust path-tracking controller for an AWOISV, built specifically to exploit the extra maneuverability of that platform while overcoming the modeling and implementation difficulties that come with large steering angles, arbitrary sideslip, and mode transitions. The paper defines four precise objectives for the controller: to track lateral position relative to a reference path, to track arbitrary reference heading angle relative to the path rather than only tangent alignment, to remain robust to model inaccuracies, parameter uncertainties, and disturbances introduced by linearization and real vehicle effects, and to be real-time implementable on embedded or industrial hardware (Yang et al., 19 Aug 2025).

In that formulation, FT-LTVMPC differs from standard LTV-MPC because the latter uses the same linearized prediction model but no robust tube mechanism, and it differs from nominal tube-based LTV-MPC because the standard tube version directly feeds back the raw state error $e$, whereas FT-LTVMPC replaces it by a filtered error $\hat e$. The control law is written as

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$

where $\bar{\bm u}(k)$ is the nominal MPC control and $\hat{\bm e}(k)$ is obtained by Kalman filtering plus a dynamic hysteresis mechanism. This filtered correction is the “filtered” part of the method (Yang et al., 19 Aug 2025).

Within the surrounding literature, the exact FT-LTVMPC name is not standard. A close conceptual relative is “filter-based system level tube-MPC,” which represents uncertainty through a causal disturbance filter and optimizes horizon-dependent tube responses online (Sieber et al., 2024). Another close relative is elastic tube-based MPC with time-varying ancillary feedback, time-varying tube scaling, and online refinement of uncertainty sets (Ghiasi et al., 24 Dec 2025). This suggests that FT-LTVMPC belongs to a broader family of robust MPC schemes in which the tube, the uncertainty description, or the ancillary feedback is updated online rather than fixed offline.

2. AWOISV modeling foundations

The FT-LTVMPC formulation is inseparable from the AWOISV motion representation used to generate the prediction model. The paper starts from the observation that AWOISV motion is naturally described by the instantaneous center of rotation (ICR). If the ICR is at $(B_0,C_0)$ in the body frame, then the steering angle of wheel $i*$ is

$$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$

Because $(B_0,C_0)$ is unbounded and inconvenient for control, the paper introduces the finite-angle representation $e$0, where $e$1 is the theoretical steering radius angle and $e$2 is the theoretical sideslip angle. The mapping is

$e$3

with domain

$e$4

This representation is the control input space used by FT-LTVMPC (Yang et al., 19 Aug 2025).

Using the ICR location relative to wheel geometry, the paper distinguishes straight driving modes and steering modes. Straight driving corresponds to $e$5, with longitudinal, diagonal, and lateral subcases parameterized by $e$6. Steering modes correspond to $e$7 and include longitudinal steering mode (LoSM), lateral steering mode (LaSM), and pivot steering mode (PSM). The paper notes that LoSDM, DSDM, and LoSM can transition continuously among one another, and similarly LaSDM, LaSM, and PSM can transition continuously, while other inter-group transitions generally require stopping. For controller design, operation is mainly restricted to LoSM (Yang et al., 19 Aug 2025).

The dynamic model uses the generalized $e$8-$e$9-$\hat e$0 state, with

$\hat e$1

and control inputs $\hat e$2 and $\hat e$3. The paper writes the body-force balance, yaw dynamics, and tire forces using an improved Fiala model, then expresses the reduced AWOISV dynamics as

$\hat e$4

The important modeling point is that these equations do not assume small steering angle or near-zero sideslip, unlike a conventional bicycle model (Yang et al., 19 Aug 2025).

3. Linear time-varying prediction model and tube structure

FT-LTVMPC operates in Frenet coordinates with state

$\hat e$5

The nonlinear prediction model includes

$\hat e$6

and

$\hat e$7

with $\hat e$8 and $\hat e$9 obtained from the reduced generalized AWOISV dynamics. The paper then linearizes online around $\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$0,

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$1

where

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$2

With first-order Euler discretization,

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$3

This is the paper’s LTV prediction model (Yang et al., 19 Aug 2025).

The nominal system is

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$4

and the error is

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$5

With ancillary feedback

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$6

the paper writes the error dynamics as

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$7

The method then assumes a robust positively invariant set for the filtered error,

$\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$8

and tightens the nominal constraints by Pontryagin difference: $\bm u(k)=\bar{\bm u}(k)+\bm K_e\hat{\bm e}(k),$9 This is the tube-MPC part of the FT-LTVMPC construction (Yang et al., 19 Aug 2025).

The resulting finite-horizon optimization is

$\bar{\bm u}(k)$0

subject to the LTV dynamics, tightened state and input constraints, a terminal set constraint, the LoSM/ICR feasibility condition

$\bar{\bm u}(k)$1

and wheel-rate constraints

$\bar{\bm u}(k)$2

The actual applied control is

$\bar{\bm u}(k)$3

The wheel steering angles are then reconstructed from $\bar{\bm u}(k)$4 using

$\bar{\bm u}(k)$5

All of these equations are part of the exact FT-LTVMPC formulation in the AWOISV paper (Yang et al., 19 Aug 2025).

4. Filtering mechanism and relation to broader filtered-tube MPC research

The filtering mechanism is applied to the state error used in the ancillary tube feedback, not to the reference path or the nominal optimizer’s output. The observation equation is

$\bar{\bm u}(k)$6

and the Kalman predictor-corrector recursion is

$\bar{\bm u}(k)$7

$\bar{\bm u}(k)$8

$\bar{\bm u}(k)$9

$\hat{\bm e}(k)$0

After Kalman filtering, each component is passed through a dynamic hysteresis rule,

$\hat{\bm e}(k)$1

The paper states that this reduces sensitivity to measurement noise and small fluctuations, preventing control chattering and excessive wheel-angle vibration (Yang et al., 19 Aug 2025).

The boundedness argument is also given explicitly. Assuming

$\hat{\bm e}(k)$2

the filtered error satisfies

$\hat{\bm e}(k)$3

If

$\hat{\bm e}(k)$4

then $\hat{\bm e}(k)$5 is bounded, and the paper uses this as the rationale for the invariant set $\hat{\bm e}(k)$6 (Yang et al., 19 Aug 2025).

In neighboring literature, “filter-based system level tube-MPC” adopts a more explicit filter interpretation. There, the lumped uncertainty $\hat{\bm e}(k)$7 is overapproximated by

$\hat{\bm e}(k)$8

and the error and tube controller are parameterized as causal finite-horizon responses

$\hat{\bm e}(k)$9

with block-lower-triangular structure and explicit receding-horizon guarantees (Sieber et al., 2024). By contrast, the AWOISV FT-LTVMPC paper uses “filtered” in the narrower sense of filtering the ancillary feedback error (Yang et al., 19 Aug 2025).

A second neighboring direction is elastic tube MPC with data-consistent and prior-consistent refinement of disturbance/model sets. In that setting, the tube scaling $(B_0,C_0)$0, the ancillary feedback $(B_0,C_0)$1, and the closed-loop model set are updated online, yielding a $(B_0,C_0)$2-contractive time-varying tube (Ghiasi et al., 24 Dec 2025). This suggests that FT-LTVMPC can be understood more generally as part of a family of tube MPC methods that reduce conservatism through online adaptation, filtered uncertainty descriptions, or horizon-varying ancillary laws.

5. Stability, feasibility, and implementation structure

The FT-LTVMPC paper includes the standard terminal ingredients of robust tube MPC, but presents them in an engineering-oriented rather than theorem-heavy way. The terminal matrix satisfies

$(B_0,C_0)$3

with

$(B_0,C_0)$4

and a terminal set constraint

$(B_0,C_0)$5

The manuscript states that the terminal cost ensures asymptotic stability, and it uses the tube set $(B_0,C_0)$6 together with tightened constraints to support robust constraint satisfaction. It does not, however, present a formal theorem of recursive feasibility, a complete proof of robust asymptotic stability, or an explicit minimal-RPI construction (Yang et al., 19 Aug 2025).

The controller architecture is divided into four modules: a preprocess module for Frenet conversion and path geometry, a $(B_0,C_0)$7-$(B_0,C_0)$8 solving module containing FT-LTVMPC, a wheel-angle calculation module mapping $(B_0,C_0)$9 to $i*$0, and a forward velocity control module for traction or torque allocation. FT-LTVMPC is therefore a high-level steering or motion controller rather than a low-level wheel-actuation controller (Yang et al., 19 Aug 2025).

The implementation parameters reported are: $i*$1 The weight matrices are

$i*$2

The ancillary gain used in experiments is

$i*$3

The empirical state and input limits include

$i*$4

together with

$i*$5

The paper does not specify the exact numerical solver, but it reports that all linearized methods except NMPC solve in under $i*$6 ms, with hardware-in-the-loop solving times around $i*$7 ms and a maximum below $i*$8 ms (Yang et al., 19 Aug 2025).

A broader theoretical context is provided by related arXiv work. Heterogeneously parameterized tube MPC for LPV systems gives theorem-level recursive feasibility and stability for horizon-varying tube/controller parameterizations (Hanema et al., 2019). Filter-based system level tube-MPC gives receding-horizon recursive feasibility and ISS for online-optimized filtered tube responses (Sieber et al., 2024). Elastic zonotopic tube MPC establishes recursive feasibility and exponential stability of the error dynamics under adaptive tube-gain updates (Ghiasi et al., 24 Dec 2025). These papers clarify what a fully formal FT-LTVMPC theory would typically require, even when the exact AWOISV paper emphasizes implementation and experimental validation rather than full theorem development.

6. Empirical performance and place in the literature

The AWOISV FT-LTVMPC paper reports three main validation cases. In a sinusoidal-path case with reference curvature radius varying between $i*$9 m and target relative heading varying between $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$0, the method is tested at $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$1, $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$2, $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$3, and $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$4 m/s. The reported result is that FT-LTVMPC accurately tracks the sinusoidal relative heading profile, and even at $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$5 m/s the lateral error stays within about $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$6 m while the heading error stays within about $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$7 (Yang et al., 19 Aug 2025).

In a controller comparison at $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$8 m/s, the reported baselines are C-MPC, NMPC, LTVMPC, T-LTVMPC, and FT-LTVMPC. The paper states that C-MPC performs worst, especially for heading tracking, because it cannot realize arbitrary relative heading; NMPC slightly outperforms nominal LTVMPC in lateral tracking but is computationally heavier; and T-LTVMPC and FT-LTVMPC perform best overall, showing the benefit of robust compensation. It also states that all methods except NMPC remain under $$\delta_{i*}=\arctan\!\left(\frac{x_{i*}-B_0}{C_0-y_{i*}}\right).$$9 ms (Yang et al., 19 Aug 2025).

The strongest practical evidence comes from hardware-in-the-loop experiments on a composite path combining LoSM, LoSDM, and DSDM, with speed varying from $(B_0,C_0)$0 to $(B_0,C_0)$1 m/s. Using median tracking error, T-LTVMPC reduces lateral and heading errors by $(B_0,C_0)$2 and $(B_0,C_0)$3 versus LTVMPC, while FT-LTVMPC reduces them by $(B_0,C_0)$4 and $(B_0,C_0)$5, respectively. The paper also reports smoother yaw-rate behavior for the tube-based methods and lower yaw-rate vibration frequency for FT-LTVMPC than for T-LTVMPC. For control smoothness, it gives the average sliding standard deviation of wheel steering angles as

$(B_0,C_0)$6

and concludes that FT-LTVMPC improves control-input smoothness by $(B_0,C_0)$7 relative to T-LTVMPC (Yang et al., 19 Aug 2025).

The broader literature helps situate these results.

Related direction	Main shared feature	Main distinction
Filter-based system level tube-MPC (Sieber et al., 2024)	Filtered uncertainty propagation and online tube/controller synthesis	Uses system-level responses and an auxiliary disturbance filter
Elastic zonotopic tube MPC (Ghiasi et al., 24 Dec 2025)	Time-varying tube scaling and online uncertainty refinement	Uses constrained matrix zonotopes and $(B_0,C_0)$8-contractive adaptive tubes
Heterogeneous tube MPC for LPV systems (Hanema et al., 2019)	Horizon-varying tube and controller parameterizations	No explicit filtering mechanism

This suggests that FT-LTVMPC is best understood not as an isolated acronym, but as a concrete AWOISV-specific realization of a broader research direction: robust MPC with time-varying tube geometry or ancillary feedback, online adaptation of uncertainty handling, and implementation mechanisms that reduce conservatism without sacrificing real-time feasibility.