# Model Predictive Control for Autonomous Navigation of Smart Wheelchairs Using Ultra-wideband Sensors

Théo Le Terrier, Marie Babel, Vincent Drevelle

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Théo Le Terrier, Marie Babel, Vincent Drevelle. Model Predictive Control for Autonomous Navigation of Smart Wheelchairs Using Ultra-wideband Sensors. JCJC 2025 - Colloque Jeunes Chercheurs, Jeunes Chercheuses, Institut Fédératif de Recherche sur les Aides Techniques pour personnes Handicapées (IFRATH), Jun 2025, Aubervilliers, France. pp.33-38. hal-05384328

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# Model Predictive Control for Autonomous Navigation of Smart Wheelchairs Using Ultra-wideband Sensors

Théo Le Terrier

Univ Rennes, INSA Rennes, Inria

CNRS, IRISA - UMR 6074

Rennes, France

theo.le-terrier@irisa.fr

Marie Babel

Univ Rennes, INSA Rennes, Inria

CNRS, IRISA - UMR 6074

Rennes, France

marie.babel@irisa.fr

Vincent Drevelle

Univ Rennes, Inria, CNRS

IRISA - UMR 6074

Rennes, France

vincent.drevelle@irisa.fr

**Abstract**—In this paper, we present a sensor-based control method to stabilize a power wheelchair to a learned reference pose, using low-cost ultra-wideband (UWB) radio modules. It exploits range-domain differences to mitigate the effects of uncalibrated biases and anchor node position inaccuracies, and robust estimation to handle multipath and non-line-of-sight signal propagation. The obtained relative pose estimate is used as a feedback for a stabilizing nonlinear model predictive controller (NMPC). Exploiting the formalism of the NMPC, input control constraints are integrated, accounting for acceptability and user comfort. We have validated our method through experiments with a power wheelchair equipped with UWB sensors, in various adverse conditions, with a final position error of a few centimeters. Compared to a global pose-based method, the proposed approach yields significantly better results in terms of final pose error and stabilization time.

**Keywords**—Sensor-based control, smart wheelchair, ultra-wideband

## I. INTRODUCTION

Power wheelchair (PW) users may experience difficulties performing daily maneuvering tasks, as it requires dedicated driving skills. People with cognitive disorders may not even be authorized to use a PW [1]. Autonomous PW navigation is thus a relevant problem [2], as impaired mobility may lead to social isolation, anxiety and depression [3]. Even considering the empty-PW autonomous navigation, the independence of the user could be increased, as tasks such as docking the PW to a charging station would not rely on an occupational therapist.

Autonomous control of a PW is a challenging problem, e.g., due to disturbances introduced by steering wheels, or different tire inflation for the two differentially driven wheels. It has been addressed for autonomous corridor following and doorways passing [4], using an image-based visual servoing scheme. More recently, autonomous PW navigation has been widely studied using nonlinear model predictive control (NMPC), as it inherently handles constraints such as physical actuator limitation, and is well suited to shape the behavior of the system. In the context of PW autonomous control, the NMPC formalism is also well suited for integrating user comfort as a set of constraints [5].

Solutions toward PW autonomous navigation using NMPC have been proposed, e.g., for path following [5], or trajectory tracking [6]. The safety of the task can be ensured by integrating obstacle collision avoidance into the NMPC formulation. It is handled either as a soft constraint within the objective cost function [7], or both soft and hard constraints [8].

The design of a fully autonomous system would also require stabilization of the PW at a target pose. A typical case would be the transfer of a PW user from the platform to its bed. The PW should be positioned at a specific position and angle next to the bed, according to the needs of the user. Following the transfer, the PW could autonomously proceed to a docking task at a charging station. The stabilization problem has been widely addressed in the field of NMPC, e.g., for nonholonomic robots [9]. To the best of our knowledge, the stabilization problem of a PW using NMPC has only been tackled in [7], in which the target is generated by the user via a brain-machine interface. However, the PW orientation is not considered in this work.

Furthermore, NMPC strategy relies on both an accurate nonlinear model to predict the behavior of the PW, as well as its precise pose estimation. In autonomous PW control, this pose estimation is handled using sensors such as 2-D [7] or 3-D LiDARs [10], and depth cameras [11]. Since PWs are not initially designed to be equipped with such sensors, their integration into the platform usually requires a cumbersome system, which may reduce the acceptability of the proposed solutions. Also, the cost of the final solution is an important criterion [3], hence the importance of using low-cost and discreet sensors. In this paper, we propose a NMPC controller for the stabilization of a PW using a set of low-cost ultra-wideband (UWB) sensors to estimate the PW pose error.

A typical setup for indoor positioning using UWB sensors consists of a set of fixed anchor nodes communicating with mobile nodes (tags). The distance between a tag and an anchor is determined using methods such as two-way ranging [12]. UWB based positioning has been widely studied in the context of ground robots [13], and aerial robotics [14].

Precise indoor positioning based on UWB range measure-
ments is a challenging problem, as the measurements are affected by factors such as intrinsic UWB noise, non-line-of-sight (NLOS) and multipath signal propagation, biases of radio modules, and anchor position accuracy. State-of-the-art approaches are designed to handle the case of NLOS signal propagation in multipath environments [15], [16], but their precision is dependent on the accuracy of the anchor positions and the calibration of each radio module's bias. When relative positioning is considered, differential UWB measurements can be used to mitigate the effects of these factors [17]. This is the approach we propose in this paper.

We aim to stabilize a PW to a previously learned reference pose. That is, the UWB range measurements have been recorded by the user, potentially helped by an occupational therapist, in a rehabilitation center or at the PW user's home. A typical case would be the recording of UWB reference measurements when the PW is located in an ideal transfer pose, next to the bed of the PW user. Following the principle of pose-based visual servoing [18], this goal is achieved in a two-step process. It first provides a robust pose error estimate from range-domain differences. An NMPC controller is then implemented to stabilize this pose error to zero.

By using an approach based on range differences, the time-consuming tasks of accurately mapping the anchor positions and calibrating the radio modules can be avoided, as these error factors cancel out in the differences. This simplifies and reduces the cost of deploying the system.

Although it is outside the scope of this paper, it is important to mention that a low-cost, easy-to-integrate fully autonomous navigation system could be proposed based on our method, by integrating obstacle avoidance using a set of infrared time-of-flight sensors, as in [1].

This paper is organized as follows. After introducing PW kinematics and UWB ranging models, the robust relative pose estimation method is presented. Then, the nonlinear model predictive controller is detailed. Finally, experimental results with a PW equipped with UWB sensors are presented.

## II. PROBLEM STATEMENT

### A. Wheelchair Model

The PW configuration in the world frame $\mathcal{F}_W$ is denoted $\mathbf{q} = (x, y, \theta)^T$ where $(x, y)$ are the coordinates of the PW's center of rotation, and $\theta$ is the heading angle between the frame $\mathcal{F}_W$ and the local frame attached to the PW $\mathcal{F}_R$. A PW can be modeled as a unicycle robot, hence matching nonholonomous constraints. The two control inputs $\mathbf{u}$ related to the PW are its linear (resp. angular) velocity, denoted $v$ (resp. $\omega$). The continuous-time model of the PW is thus given by

$$f(\mathbf{q}(t), \mathbf{u}(t)) = \begin{cases} \dot{x}(t) = v(t) \cos \theta(t) \\ \dot{y}(t) = v(t) \sin \theta(t) \\ \dot{\theta}(t) = \omega(t). \end{cases} \quad (1)$$

### B. UWB Ranging Model

A set of UWB anchors is installed in a room, and distance measurements to UWB tags installed on the PW are performed. A system overview is presented in Fig. 1.

<figure><img src="image_2.png" /><figcaption>Figure 1. System Overview. Each UWB tag (green) measures its distance to each anchor (yellow). Range measurements can be affected by multipath or NLOS propagation.</figcaption></figure>

Let $n_T$ be the number of tags installed on the PW, and $n_A$ the number of anchors. We denote $T_i, i \in \{1, \dots, n_T\}$, the $i^{th}$ tag, and $A_j, j \in \{1, \dots, n_A\}$, the $j^{th}$ anchor. The coordinates of a tag $T_i$, expressed in $\mathcal{F}_R$, are denoted $x_{T_i} = (x_{T_i}, y_{T_i}, z_{T_i})$. The coordinates of $T_i$ in $\mathcal{F}_W$, denoted $x_{T_i} = (x_{T_i}, y_{T_i}, z_{T_i})$, can be expressed as a function of the PW configuration:

$$\mathbf{x}_{T_i}(\mathbf{q}) = \begin{pmatrix} x + {}^r x_{T_i} \cos \theta - {}^r y_{T_i} \sin \theta \\ y + {}^r x_{T_i} \sin \theta + {}^r y_{T_i} \cos \theta \end{pmatrix}. \quad (2)$$

The fixed coordinates of an anchor $A_j$ in $\mathcal{F}_W$ are denoted $\mathbf{x}_{A_j} = (x_{A_j}, y_{A_j}, z_{A_j})$. The measured range between $T_i$ and $A_j$ is denoted $s_{i,j}$ and is defined as

$$s_{i,j} = \| \mathbf{x}_{T_i}(\mathbf{q}) - \mathbf{x}_{A_j} \|_2 + \beta_{i,j}, \quad (3)$$

where $\beta_{i,j}$ is the range measurement error.

## III. ROBUST RELATIVE POSE ESTIMATION FROM UWB RANGE DIFFERENCES

### A. Observation Model

Let us denote $\mathbf{s}^*$, the vector of desired UWB range measurements recorded at the desired reference PW pose $\mathbf{q}^*$. We define $\mathcal{F}_G$ as the fixed frame attached to $\mathbf{q}^*$ (both in position and orientation). The positions of the anchors in the frame $\mathcal{F}_G$ are denoted $\mathcal{G}\mathbf{x}_{A_j}$. Assuming that each anchor position is known in $\mathcal{F}_W$, and that an estimate $\hat{\mathbf{q}}^*$ of $\mathbf{q}^*$ is available, an estimation of $\mathcal{G}\mathbf{x}_{A_j}$ can be obtained.

Our method seeks to estimate the relative pose $\mathcal{G}\mathbf{q}$ of the PW in the frame $\mathcal{F}_G$. Let us denote $\mathbf{s}_{th}(\mathcal{G}\mathbf{q})$, the vector of all theoretical ranges

$$s_{th,i,j}(\mathcal{G}\mathbf{q}) = \| \mathcal{G}\mathbf{x}_{T_i}(\mathcal{G}\mathbf{q}) - \mathcal{G}\mathbf{x}_{A_j} \|_2 \quad (4)$$
between the pairs of anchors/tags, when the PW is located at $\mathcal{G}\hat{\mathbf{q}}$.

The observation model is expressed as the difference between theoretical range measurements at a given relative pose $\mathcal{G}\hat{\mathbf{q}}$, and theoretical range measurements $\mathbf{s}_{th}^*$ at the learned reference pose:

$$ \mathbf{h}(\mathcal{G}\hat{\mathbf{q}}) = \mathbf{s}_{th}(\mathcal{G}\hat{\mathbf{q}}) - \mathbf{s}_{th}^*. \quad (5) $$

## B. Robust Relative Pose Estimator

We aim to provide, at each measurement epoch $k$, an estimate $\mathcal{G}\hat{\mathbf{q}}_k$ of the relative PW pose $\mathcal{G}\hat{\mathbf{q}}_k$ using range measurement differences

$$ \mathbf{y}_k = \mathbf{s}_k - \mathbf{s}^*. \quad (6) $$

The residuals with respect to the observation model are

$$ \mathbf{r}(\mathcal{G}\hat{\mathbf{q}}) = \mathbf{y}_k - \mathbf{h}(\mathcal{G}\hat{\mathbf{q}}). \quad (7) $$

We denote $r_{i,j}(\mathcal{G}\hat{\mathbf{q}})$, the residual of the range measurement between the $i^{th}$ tag and the $j^{th}$ anchor.

The Huber M-estimation method is used to provide the estimate $\mathcal{G}\hat{\mathbf{q}}_k$, from the observation model and observed range differences. The relative pose estimation problem is then cast into an optimization problem of the form

$$ \mathcal{G}\hat{\mathbf{q}}_k = \arg \min_{\mathcal{G}\hat{\mathbf{q}}} \sum_{(i,j)} L_{\delta}(r_{i,j}(\mathcal{G}\hat{\mathbf{q}})) \quad (8) $$

where $L_{\delta}$ is the Huber loss function [19], with an adjustment parameter $\delta$. This robust estimator is particularly effective at rejecting outliers, such as those caused by multipath or NLOS signal measurements. UWB range outliers are generally positive, but due to the differencing, outliers in $\mathbf{y}_k$ can be either positive (outlier in the current measurement $\mathbf{s}_k$) or negative (outlier in the reference range $\mathbf{s}^*$), necessitating a symmetric loss function.

The problem (8) is solved using the iteratively reweighted least squares (IRLS) method with the Gauss-Newton iteration. The Huber loss weight update rule at the $l^{th}$ iteration is given by

$$ w(r_{i,j}(\mathcal{G}\hat{\mathbf{q}}_l)) = \begin{cases} 1 & \text{if } |r_{i,j}(\mathcal{G}\hat{\mathbf{q}}_l)| \le \delta, \\ \frac{\delta}{|r_{i,j}(\mathcal{G}\hat{\mathbf{q}}_l)|} & \text{otherwise} \end{cases} \quad (9) $$

Denoting $\mathbf{W}_l = \text{diag}[w(r_{i,j}(\mathcal{G}\hat{\mathbf{q}}_l))]$ the diagonal weighting matrix at the $l^{th}$ iteration, the iterative solution to the problem (8) is given by

$$ \mathcal{G}\hat{\mathbf{q}}_{l+1} = \mathcal{G}\hat{\mathbf{q}}_l + (\mathbf{H}^{\mathrm{T}}_l \mathbf{W}_l \mathbf{H}_l)^{-1} \mathbf{H}^{\mathrm{T}}_l \mathbf{W}_l \mathbf{r}(\mathcal{G}\hat{\mathbf{q}}_l) \quad (10) $$

where $\mathbf{H}_l$ is the Jacobian of the observation model at the $l^{th}$ iteration:

$$ \mathbf{H}_l = \frac{\partial \mathbf{h}}{\partial \mathcal{G}\hat{\mathbf{q}}} \bigg|_{\mathcal{G}\hat{\mathbf{q}}_l} \quad (11) $$

The relative pose $\mathcal{G}\hat{\mathbf{q}}_k$ computed from range-domain differences is then sent to the NMPC controller to be stabilized to zero.

<figure><img src="image_3.png" /><figcaption>Figure 2. Range-domain differences NMPC control scheme.</figcaption></figure>

# IV. NONLINEAR MODEL PREDICTIVE CONTROL

## A. Control Architecture

The NMPC consists in computing the control input by solving, at each sampling time $k$, a constrained optimal control problem over a finite prediction horizon $N_p$. At each iteration, the relative PW pose estimated from our method is used as an initial state for the NMPC. Starting from this initial state, the behavior of the system is predicted over the horizon $N_p$, with respect to the PW model described in section II-A. This information is used to obtain a control input sequence $\tilde{\mathcal{U}}$ by minimizing an objective cost function $J$. Considering model uncertainties, as well as potential disturbances, only the first input control of $\tilde{\mathcal{U}}$ is applied to the PW. The procedure is then repeated at the next sampling time with an updated PW pose estimate and a shifted prediction horizon. An overview of our control scheme is shown in Fig. 2.

## B. Constraint Handling

The optimal control problem solved at each sampling time is subject to constraints on input control variables and model states. Constraints on input control variables are used for both consistency with the physical actuator limitations of the platform, as well as for designing an acceptable behavior of the system. Also, constraints should be designed with a user-centered approach, hence considering the comfort of the potential user in the PW during the stabilization task.

In our application, input control variables are constrained both in terms of linear and angular velocities,

$$ \mathbf{u}_{\min} \le \mathbf{u} \le \mathbf{u}_{\max} \quad (12) $$

and in terms of linear and angular accelerations,

$$ \Delta \mathbf{u}_{\min} \le \Delta \mathbf{u} \le \Delta \mathbf{u}_{\max} \quad (13) $$

The set of admissible input controls with respect to (12) and (13) is denoted $\mathcal{U}$.

## C. Mathematical Formulation

The constrained optimization problem is expressed as

$$ \min_{\mathbf{u}} J = \sum_{i=1}^{N_p} \|\mathcal{G}\hat{\mathbf{q}}_{i|k}\|_{\mathbf{Q}}^2 + \|\mathbf{u}_{i|k}\|_{\mathbf{R}}^2 \quad (14) $$
subject to:

$$ \mathcal{G}\mathbf{q}_{i+1|k} = f(\mathcal{G}\mathbf{q}_{i|k}, u_{i|k}), \quad \mathcal{G}\mathbf{q}_{0|k} = \mathcal{G}\mathbf{q}_k \quad (15) $$

$$ \mathbf{u}_{i|k} \in \mathcal{U}, \quad i \in \{1, \dots, N_p\} \quad (16) $$

where $\mathcal{G}\mathbf{q}_{0|k}$ is the relative pose estimate at sampling time $k$, set as the initial state. $\mathcal{G}\mathbf{q}_{i|k}$ is the predicted state at the $i^{th}$ step of the prediction horizon, from sampling time $k$. Its prediction is performed using the nonlinear evolution model $f$ described in section II-A. The control inputs at the $i^{th}$ step from time $k$, denoted $\mathbf{u}_{i|k}$ are constrained in the set $\mathcal{U}$. The weighting matrices $\mathbf{Q}$ and $\mathbf{R}$ are symmetric positive definite, and are set to shape the PW behavior.

### D. NMPC Implementation

Designing an autonomous PW navigation system requires a smooth and slow system behavior. Indeed, a fast system is not acceptable in a rehabilitation center, or in a PW user's home. The control input constraints were set to $v_{max} = 0.25 \text{ m s}^{-1}$ and $a_{max} = 0.2 \text{ m s}^{-2}$ for linear velocity and acceleration, and to $\omega_{max} = 0.25 \text{ rad s}^{-1}$ and $\alpha_{max} = 0.1 \text{ rad s}^{-2}$ for angular velocity and acceleration. As a consequence, the resolution time in the NMPC controller has to be limited to be able to predict small maneuver trajectories despite small velocity values. We have limited the resolution time to 200 ms, hence a controller frequency of 5 Hz. The prediction horizon was set to $N_p = 20$ in order to predict as far as possible in time, while ensuring a convergence of the COBYLA algorithm within the resolution time. The weighting matrices in the objective cost function are set to $\mathbf{Q} = \text{diag}[1, 2, 1]$ and $\mathbf{R} = \text{diag}[0.5, 0.5]$.

Results of our NMPC controller implementation, using our robust range-domain differences based relative positioning method, are discussed in the following section.

## V. EXPERIMENTAL RESULTS

### A. Experimental Setup

The PW used in the experiments is an off-the-shelf PW from the Medical Sunrise company. Such a PW has six wheels, two of which are differentially actuated, whereas the four others are caster wheels. Four UWB tags are integrated to the PW, as shown in Fig. 3. Four UWB anchors are set in the corners of the room. The UWB sensors are Qorvo DWM1001 development kits, providing range measurements at a 10 Hz rate. A motion capture setup with eight Qualisys cameras provides a PW pose ground truth at a 100 Hz rate.

Our method was validated by performing the stabilization task at reference poses under four conditions:

1) An uncluttered environment, with precise anchor position estimation (namely, *I* for *Ideal conditions*).

2) An uncluttered environment, with poor anchor position estimation (namely, *P* for *anchor Positions*). 10 cm of error was added to the precise anchor positions.

3) A cluttered environment (see Fig. 3 where the television and the survival blanket mask LOS signal propagation), with poor anchor position estimation (namely, *PC* for *anchor Positions and Cluttered environment*).

<figure><img src="image_4.png" /><figcaption>Figure 3. Experimental setup, both in uncluttered (top) and cluttered (bottom) environments. The television and survival blanket are set in a way that masks the line-of-sight signal propagation condition with two out of four anchors.</figcaption></figure>

4) An uncluttered environment, with poor anchor position estimation, and a faulty anchor (namely, *PF* for *anchor Positions and Faulty anchor*).

Two tasks were defined and executed for each condition. The first task consisted in stabilizing the PW to a pose $\mathbf{q}_{centre}^*$, at the center of the room, starting from an initial pose $\mathbf{q}_{centre}^0$. Respectively, the second task consisted in stabilizing the PW to a pose $\mathbf{q}_{edge}^*$, at the edge of the room, starting from an initial pose $\mathbf{q}_{edge}^0$. These poses were recorded using the motion capture system.

Our range-domain differences based NMPC was used to perform both tasks, under all four experimental conditions. In what follows, our proposed NMPC controller will be referred to as NMPC-rdd (for *range-domain differences*). A comparison was made with an NMPC controller that uses a global pose, expressed in $\mathcal{F}_W$, as feedback for the control law. This global pose is estimated using UWB range measurements, with a robust M-estimation technique. In the following, this controller is referred to as NMPC-p (for *pose NMPC*).

Both controllers were tested by conducting ten trials per controller, for the two tasks, for each condition. Hence, a total of 160 trials were conducted to compare and evaluate the performance of both the NMPC-rdd and NMPC-p controllers.

For each experimental condition, and for each task (center and edge of the room), the PW was manually driven to the corresponding reference pose. The UWB reference range measurements $s^*$ were obtained by averaging measured ranges for 10 seconds to mitigate the effect of noise of the sensors. An estimate pose $\tilde{\mathbf{q}}^*$, expressed in $\mathcal{F}_W$, was then computed from $s^*$. The positions of the anchors in the reference frame
$\mathcal{F}_G$ were then estimated from the positions of the anchors in $\mathcal{F}_W$, and $\hat{q}^*$. For the three experimental conditions P, PC and PF, the same anchor position estimation error of $\pm 10$ cm has been introduced on both x-axis and y-axis.

## B. NMPC Results

In this section, we compare the proposed NMPC-rdd controller (described in section IV-D) with the world frame pose-based NMPC-p controller. Both controllers use the same tuning of the objective cost function, as well as the same constraint parameters.

The trajectories followed by the PW for the two different tasks (center and edge of the room), under the experimental condition PC, are shown in Fig. 4. Graphics (a) and (c) represent trajectories resulting from our NMPC-rdd controller, whereas (b) and (d) represent trajectories resulting from the NMPC-p controller. Considering the stabilization at the center of the room ((a) and (b)), the NMPC-p controller provides more scattered trajectories. It also provides larger maneuvers at the end of the stabilization task. Our NMPC-rdd controller provides smoother trajectories, with fewer maneuvers. This is even clearer when considering the stabilization at the edge of the room ((c) and (d)). It is also important to notice that none of the trials, for condition PC, using the NMPC-p controller, had stabilized the PW under one minute.

Fig. 5 shows linear and angular velocities for a trial in condition I, using the NMPC-rdd controller, along with the control input constraints. It can be observed that these constraints are not violated during the execution of the stabilization task. This is the case for all trials conducted in the experiments. The constraints on linear and angular accelerations are also always respected.

In Table I, the mean and standard deviation values of the final planimetric error, final absolute orientation error, and stabilizing time are reported. It shows a decrease in performance toward the edge of the room, which can be attributed to poorer geometric conditions. In both tasks, the proposed NMPC-rdd controller consistently outperforms the NMPC-p controller in the final positioning error (both position and orientation) in all experimental conditions. Only the PF condition at the edge of the room presents a slightly higher mean final planimetric error than NMPC-p, but with a faster stabilization time. Stabilization times of both methods are similar for the center of the room stabilization task, but our method is significantly faster for the edge of the room task.

For comparison, 10 trials using an ideal controller with the ground truth motion capture pose as NMPC input for the center stabilization task resulted in mean performance figures of 1.6 cm, 2.7°, and 19.4 s. Our NMPC-rdd method achieved a mean performance of 4.2 cm, 4.3°, and 31.2 s across the four conditions for the same task. The slightly lower accuracy and the longer stabilization time are primarily due to UWB range measurement errors.

## VI. CONCLUSION

In this paper, we present a low-cost, robust UWB range-based control method for a power wheelchair. This sensor-

based approach leverages reference range measurements learned at a reference pose specified by the user.

A differential relative pose estimator mitigates the effects of uncalibrated biases and imprecise anchor positions, while a robust estimation scheme rejects multipath and NLOS erroneous measurements. The estimated pose error is then fed into an NMPC controller, designed for autonomous power wheelchair stabilization. The NMPC formalism incorporates input control constraints that account not only for physical actuator limitations but also for user comfort and acceptability.

Experimental validation was conducted using an off-the-shelf power wheelchair in various indoor conditions. The results demonstrated good final position accuracy, within a few centimeters, which meets the intended usage requirements, such as autonomous positioning for user transfer from the wheelchair to a bed adapted to their specific needs. Compared to a global pose-based method, the proposed approach provides smoother trajectories with fewer maneuvers and significantly better results in terms of final pose error.

Our method is particularly suited to the constraints of power wheelchair use, offering an alternative to conventional autonomous navigation frameworks such as SLAM-based methods, which are challenging to apply to wheelchair navigation assistance in real-world conditions. The instrumentation of the wheelchair is simplified as UWB sensors are low-cost and discreet. Furthermore, our method represents a step toward autonomous wheelchair navigation as it takes into account acceptability, a key factor for assistive technology adoption. On one hand, it is easily integrable into environments such as rehabilitation centers or home settings. On the other hand, it allows for further developments, such as the NMPC approach for designing new cost functions and constraints. This will enable the creation of control profiles more precisely tailored to user needs and the integration of existing low-cost collision avoidance sensors.

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<figure><img src="image_5.png" /><figcaption>Figure 4. Trajectories followed by the PW for the two tasks (center and edge of the room), under experimental condition PC, for both range-domain differences based ((a) and (c)) and global pose based ((b) and (d)) NMPC controllers.</figcaption></figure>

<table><caption>Table I
MEAN AND STANDARD DEVIATION VALUES OF THE FINAL PLANIMETRIC ERROR, ABSOLUTE FINAL ORIENTATION ERROR, AND STABILIZING TIME, FOR BOTH CONTROLLERS, FOR THE TWO TASKS, UNDER ALL EXPERIMENTAL CONDITIONS. BEST RESULTS ARE DISPLAYED IN BOLD.</caption><thead><tr><th rowspan="2">Task</th><th rowspan="2">Condition</th><th colspan="4">centre</th><th colspan="4">edge</th></tr><tr><th>I</th><th>P</th><th>PC</th><th>PF</th><th>I</th><th>P</th><th>PC</th><th>PF</th></tr></thead><tbody><tr><td rowspan="2">Mean final planimetric error (cm)</td><td>NMPC-rdd</td><td><b>5.8</b> σ=1.5</td><td><b>4.9</b> σ=2.6</td><td><b>2.2</b> σ=1.2</td><td><b>3.9</b> σ=3.2</td><td><b>3.7</b> σ=2.5</td><td><b>8.3</b> σ=6.1</td><td><b>12.6</b> σ=2.1</td><td>19.0 σ=9.4</td></tr><tr><td>NMPC-p</td><td>9.3 σ=3.5</td><td>19.4 σ=3.6</td><td>21.3 σ=3.0</td><td>19.0 σ=3.4</td><td>11.2 σ=3.6</td><td>23.0 σ=8.6</td><td>22.3 σ=4.2</td><td><b>17.2</b> σ=3.5</td></tr><tr><td rowspan="2">Mean absolute final orientation error (deg)</td><td>NMPC-rdd</td><td><b>2.4</b> σ=2.4</td><td><b>7.1</b> σ=4.3</td><td><b>1.8</b> σ=1.2</td><td><b>5.9</b> σ=1.4</td><td><b>2.3</b> σ=1.3</td><td><b>3.4</b> σ=3.5</td><td><b>4.2</b> σ=1.2</td><td><b>3.4</b> σ=2.6</td></tr><tr><td>NMPC-p</td><td><b>2.4</b> σ=2.1</td><td><b>7.1</b> σ=2.9</td><td>2.6 σ=1.3</td><td>8.9 σ=3.1</td><td>13.2 σ=7.9</td><td>7.2 σ=5.9</td><td>8.8 σ=3.7</td><td>5.2 σ=1.8</td></tr><tr><td rowspan="2">Mean stabilizing time (s)</td><td>NMPC-rdd</td><td>36.5 σ=13.2</td><td>31.3 σ=12.8</td><td>27.5 σ=7.1</td><td>29.6 σ=5.8</td><td><b>46.6</b> σ=18.5</td><td><b>43.0</b> σ=12.7</td><td><b>60.6</b> σ=25.5</td><td><b>33.6</b> σ=7.1</td></tr><tr><td>NMPC-p</td><td><b>24.9</b> σ=3.7</td><td><b>28.0</b> σ=6.3</td><td><b>25.7</b> σ=4.0</td><td><b>27.3</b> σ=5.7</td><td>96.1 σ=16.8</td><td>73.6 σ=19.6</td><td>100.0 σ=18.9</td><td>64.5 σ=24.4</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>Figure 5. Linear and angular velocities, for a trial in an uncluttered environment, with a precise estimation of the position of the anchors (condition I), using the range differences based NMPC controller. Linear and angular velocity constraints are represented by black dotted lines.</figcaption></figure>

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