TABLE OF CONTENTS

LIST OF TABLES………………………………………………………………….......................….i

CHAPTER 1: INTRODUCTION…………………………………………………........................…1

CHAPTER 2: HARDWARE AND ELECTRONIC DESIGN………………….……….................6

2.1 Mechanical Frame and Structure………………………………………………..................… 7

2.2 Drive System……………………………………………………….…………...................…….8

2.3 Power Supply……………………………………………………….………….....................….9

2.4 Control and Sensors.........................................................................................................10

2.5 Wiring and Accessories.....................................................................................................11

2.6 System Overview..............................................................................................................11

ABSTRACT

Omni-wheeled mobile robots offer exceptional maneuverability in confined environ-ments due to their ability to move in any direction without changing orientation. However, achieving precise navigation in complex environments remains a significant challenge due to nonlinear system dynamics, dynamic obstacles, and computational demands. This paper presents an integrated path planning and control framework for omni-wheeled mobile robots, aiming to simultaneously address safety, tracking accuracy, and computational efficiency. The framework evaluates advanced path planning algorithms-including RRT*, Informed-RRT*, A*, and Theta*-combined with control strategies such as Nonlinear Model Predictive Con-trol (NMPC), Sliding Mode Control (SMC), and Fuzzy Logic Control (FLC). A particular contribution of this work is the enhancement of RRT* using a shortcutting technique, which simplifies the path and significantly improves NMPC tracking performance. Simulation re-sults across various environments-including cluttered, narrow-gap, maze, and dynamic ob-stacle settings-demonstrate that the Theta*-NMPC pairing delivers superior performance under dynamic conditions. Additionally, the improved RRT* method achieves better path smoothness and reduces tracking error and computation time, particularly in static scenar-ios. This integrated approach provides a robust and efficient solution for autonomous omni-wheeled robot navigation in complex real-world environments.

CHAPTER 1: INTRODUCTION

Omnidirectional mobile robots, particularly those equipped with omni-wheels, have become increasingly prominent in modern autonomous navigation applications due to their unique ability to maneuver in any direction without requiring a change in orientation [1, 2]. This holonomic property makes them particularly well-suited for operating in complex and constrained environments, such as warehouses, laboratories, hospitals, and search-and-rescue scenarios, where high mobility and precise control are essential [3-5]. The ability of omni-wheeled robots to perform agile and smooth movements gives them a distinct advantage over traditional differential-drive or skid-steering robots. However, with these benefits come sig-nificant challenges in the areas of path planning, control, and system integration. Specifically, the nonlinear dynamics of omni-wheeled systems, the need for accurate real-time trajectory tracking, and the unpredictability of dynamic environments all contribute to the difficulty of deploying such systems reliably in real-world applications [6]. A wide range of literature has addressed path planning and control as separate modules. Sampling-based motion plan-ning algorithms, such as the Rapidly-Exploring Random Tree (RRT), RRT*, and their vari-ants, have been widely adopted for high-dimensional and dynamically changing spaces due to their probabilistic completeness and asymptotic optimality. On the control side, methods such as Linear Quadratic Regulation (LQR), Model Predictive Control (MPC), and Sliding Mode Control (SMC) have demonstrated varying degrees of success in tracking trajectories generated by these planners.

Sampling-based algorithms [10] such as Rapidly-exploring Random Tree (RRT) [11, 12] and its optimal variant RRT* have gained prominence due to their efficiency in high-dimensional and dynamic spaces. While the standard RRT* algorithm provides asymptoti-cally optimal paths, variants such as Informed RRT* [13] have been proven to improve con-vergence rates and path quality compared to traditional methods. For dynamic navigation, RRT* has been employed to adapt to real-time changes in the environment and enhance tra-jectory safety to ensure collision-free paths [14].

Recent advancements in path planning included improvements to the traditional RRT* and A* planning methods. Li et al. [19] proposed APSD-RRT: an algorithm that adjusts prob-ability sampling with Dijkstra optimization to balance computing cost and performance. Fan et al. [20] incorporated dual-exploration to informed-RRT* which is BI-Informed-RRT* for mobile robots. Zhu et al. [21] introduced GAO-RRT*: a dual-weighted sampling strategy and variable step size extension to guide trees approaching obstacles while exploring toward targets, showing 38.32% reduction in average path cost compared to standard RRT*. A pa-per by Wang et al. [22] integrated expansion distance, bidirectional search, and smoothing into path planning to A* resulting path planning efficiency by 278%, reduces the number of critical nodes by 91.89% and the number of right-angle turns by 100%.

The applications and integrations of NMPC with trajectory planning are prominent due to the ability to autonomously and automatically navigate. Manoharan et al. [38] address co-operative path planning for multiple autonomous aerial vehicles (AAVs) in GPS-denied areas using NMPC. The main approach combines NMPC with Moving Horizon Estimation (MHE) to form a path planning method and estimate the state of AAVs. A research by Gonzales [39] introduced motion planning for multi-agents by Probably Approximately Correct and NMPC (PAC-NMPC) to address model and measurement uncertainties to achieve robust multi-agent formation control while navigating cluttered environments. A hierarchical framework with Dynamic Window Approach local path planning module and Model Predictive Control (MPC) for the path tracking module was introduced in [40]. This method demonstrated the frame-work’s operational advantages over conventional methods in obstacle avoidance. In terms of FLC development for mobile robot, Kumar et al. [41] applied the krill herd (KH) op-timization algorithm with FLC for both trajectory planning and control of multiple mobile robots. The paper [42] developed a two-layer navigation system with Global Path Planning using Deterministic Constructive Algorithm (DCA) and Local Motion Control using Efficient Fuzzy Logic Controller (EFLC).

This study contributes both a broad and modular experimental framework for evaluat-ing integrated navigation strategies and a concrete, implementable method for improving the synergy between path planning and control. The insights gained not only highlight the mutual dependencies between planning quality and control performance but also provide a founda-tion for future extensions involving adaptive, learning-based, or decentralised approaches to omni-wheeled robot navigation.

CHAPTER 2: HARDWARE AND ELECTRONIC DESIGN

The design of the omni-wheeled mobile robot was carefully guided by the system’s func-tional requirements, real-world implementation constraints, and compatibility with modern control algorithms. Each mechanical and electronic component was chosen not only for per-formance and cost-effectiveness but also for its integration potential, modularity, and suitabil-ity for high-precision control in cluttered or dynamic environments.

2.1 Mechanical Frame and Structure

The robot’s chassis is built using 2020 or 2040 aluminium extrusion profiles, which are widely used in robotic systems due to their lightweight, high structural integrity, and ease of modification. The T-slot nature of aluminium extrusions allows flexible mounting of brackets, sensors, PCBs, or battery packs without permanent drilling or adhesives, making it ideal for rapid prototyping and iterative design.

To enable full holonomic motion, the robot employs four 100mm omni-wheels, mounted in an X-type configuration at 90° intervals. Omni-wheels allow motion in any planar direc-tion without needing to rotate the chassis-this is essential for executing precise trajectory-following tasks while maintaining fixed orientation, as required by NMPC and other predictive controllers.

2.2 Drive System

Each wheel is powered by a DC motor with an integrated rotary encoder, providing both actuation and real-time position/velocity feedback. Motors rated between 200-350 RPM at 12-24V offer a suitable compromise between speed and torque for indoor robot applications. The encoders allow the robot to estimate actual wheel velocities, which are crucial for closed-loop velocity control and odometry estimation.

The robot uses high-current motor drivers such as the BTS7960 or Cytron MD30C, which support bidirectional operation, pulse-width modulation (PWM), and current ratings over 10A. These drivers are robust, easy to integrate with microcontrollers, and reliable in long-term operation. They can handle voltage spikes and motor back-EMF without additional protective circuitry.

2.4 Control and Sensors

At the heart of the control system is a Arduino 328 microcontroller board. It contains everything needed to support the microcontroller; simply connect it to a computer with a USB cable or power it with a AC-to-DC adapter or battery to get started. These microcontrollers are open-source, well-documented, and widely supported by robotics libraries and communities. They are capable of handling real-time motor control, encoder decoding, sensor communica-tion, and basic trajectory logic.

A 9-axis IMU module, such as the MPU6050, is integrated to provide measurements of angular velocity and orientation. These sensors are critical for maintaining stable heading during omni-directional motion and for correcting drift in wheel odometry using sensor fusion techniques such as extended Kalman filters (EKF).

For applications involving obstacle detection or SLAM, the system can integrate range sensors such as ultrasonic modules or 2D LIDARs (e.g., RPLidar A1). These allow the robot to navigate cluttered or dynamic environments by identifying and avoiding obstacles in real time.

2.6 System Overview

Motors are connected to motor drivers and controlled via PWM and direction signals from the MCU. Encoder feedback is read using interrupt-capable pins. IMU and sensors communicate via I2C/UART/SPI. Power is distributed through a regulated system using buck converters to ensure proper voltage for logic and power stages.

Each component in this robot platform is selected with a system-level perspective: mo-tors and encoders are matched for control precision, the chassis is modular for scalability, and sensors are chosen for their role in state estimation and environment perception. The electron-ics are laid out to support clean wiring, real-time control, and future extensibility-ensuring that the platform is suitable for both academic research and applied robotics development.

CHAPTER 3: METHODOLOGY

3.1 Problem Formulation

The problem is formulated as a two-stage optimization process combining path planning with Nonlinear Model Predictive Control (NMPC) for trajectory tracking. The system will be tested in multiple complex environments and dynamic environments

3.1.1 Environment Specifications

Four distinct environments are designed to evaluate system performance under varying complexity levels and temporal dynamics:

1. Maze Environment (ℰ₁): Complex corridor navigation with 12 wall segments forming maze-like structure. Start: (0.4, 4.6), Goal: (4.6, 0.4)

2. Gap Environment (ℰ₂): Strategic gap navigation with 5 wall barriers creating controlled passages. Start: (2.5, 2.5), Goal: (6.0, 2.5)

3. Scattered Environment (ℰ₃): Cluttered space with 15 randomly distributed rectangular obstacles. Start: (0, 0), Goal: (5, 5)

5. 3D Environment (ℰ₅): A 3D space with low and high terrain regions located between the start and goal points. Start: (-8, -8, Z_start + 1.5), Goal: (8, 8, Z_goal + 1.5)

For static environments , the obstacle set is denoted as O_j = {O₁, O₂, . . . , O_nj } where each obstacle O_i is a rectangular region with safety buffer d_s.

For the dynamic environment ℰ₄, the obstacle configuration evolves as:

O₄(t) = O_4,s ∪ O_4,d(t)                                      (3.1)

Circular motion:                            

p_i(t) = c_i + r_i[cos(ω_it), sin(ω_it)]^T                    (3.3)

Where f (t) implements boundary reflection for linear motion, c_i is the circle center, r_i is the radius, and ω_i is the angular frequency.

For the 3D enviroment E₅, the terrain is created using the meshgrid function in MAT-LAB, with X,Y ∈ [-10, 10] m and a resolution of 0.5 m.

+ The terrain is normalized to ensure Z > 0:

Z = Z - min(Z) + 0.5

3.1.2 Path Fitness

The path fitness evaluation framework encompasses multiple quantitative metrics to as-sess the quality and performance of generated paths and their tracking performance across different algorithms and environmental conditions.

Where N is the number of waypoints in the path P = {p₁, p₂, . . . , p_N}.

Number of Waypoints: The total number of waypoints generated by the planning algo-rithm:

N_waypoints = |P |                                                                             (3.6)

Computation Time: The total time required by the planning algorithm to generate a feasible path:

Tplanning = tend – tstart                                                                 (3.7)

Replanning Frequency: The number of replanning events triggered during mission execution:

Freplan = Nreplanning_events                                                         (3.13)

A mission is considered successful if:

+ Path Finding Success: A feasible path is found within the maximum planning iterations

+ Collision-Free Navigation: N_collision = 0

+ Goal Reaching:  x _final − x_goal  ≤ ε_goal

+ Safety Compliance: C_min ≥ d_{sa f ety_threshold}

Where ε_goal is the goal tolerance and d_{sa f ety_threshold} is the minimum required safety distance.

3.2 Mobile Robot Mathematical Modeling

Accurate mathematical modeling is essential for designing an effective NMPC con-troller. The omni-wheeled mobile robot is modeled both kinematically and dynamically. Fig-ure 3.1 and table 3.1 demonstrate reference coordinator and physical design of the robot.

3.2.1 Kinematics

The kinematic model relates the wheel angular velocities to the robot’s translational and rotational velocities. The state vector is defined as:

x_k=[x_k yk ϕk ω_(1,k) ω_(2,k) ω_(3,k) ω_(4,k) ]^T                                    (3.16)

Where (x_k, y_k) denote position, φ_k the orientation, and ω_i,k the angular velocities of the

The state updates are performed using:

x_(k+1)=x_k+R(ϕ_k ) V_k Δt,                                                      (3.19)

3.2.3 Dynamic Model

The continuous dynamics are discretized using Euler integration for controller imple-mentation. The continuous-time state-space representation is:

x˙(t) = f(x(t), u(t)),                                                                    (3.20)

3.3 Related Method for Omniwheeled Mobile Robot Control

3.3.1 Nonlinear Model Predictive Control (NMPC)

NMPC is a nonlinear control strategy that optimizes future control actions by solving a finite-horizon control problem at each sampling step. In this situation, the controller is used to

Enforce a fixed orientation of the robot while tracking the desired path, thereby leveraging the omnidirectional capabilities of the robot’s kinematics and dynamics. NMPC is built upon the dynamic model described in Section 3.2.2 and utilizes the nonlinear state-space representation of the robot to predict its future states.

Where:

+ U = [u₀, u₁, . . . , u_Np−1]^⊤ is the sequence of control inputs over the prediction horizon.

+ e_k = x_k - x_desired,k is the tracking error at step k.

+ Q is the state error weighting matrix.

+ R is the control effort weighting matrix.

+ u_min, u_max: constrains on control inputs.

+ ω_min, ω_max: constrains on wheel angular velocities.

The cost function J(U) aims to minimize the cumulative tracking error and control ef-fort over the prediction horizon. The weighting matrices Q and R balance the trade-off be-tween accuracy and energy efficiency. The higher positional errors weights ensure that the robot closely follows the path, while the orientation weight maintains, demonstrating the om-nidirectional capability by allowing movement in any direction without altering the robot’s orientation.

3.3.3 Fuzzy Logic Control (FLC)

Fuzzy Logic Control provides an intuitive approach to handle nonlinear systems by in-corporating human-like reasoning through linguistic rules. For the omni-wheeled mobile robot, FLC offers adaptive control capabilities that can handle uncertainties and provide smooth control actions without requiring precise mathematical models.

The FLC system consists of three main components: fuzzification, inference engine, and defuzzification. The position and orientation errors serve as inputs to the fuzzy system:

e_x = x_d – x                                              (3.38)

e_y = y_d – y                                              (3.39)

e_ϕ = ϕ_d − ϕ                                             (3.40)

Fuzzification: Triangular membership functions are used to convert crisp inputs into fuzzy sets. For each error signal, five linguistic variables are defined: Negative Large (NL), Negative Small (NS), Zero (Z), Positive Small (PS), and Positive Large (PL).

Inference Engine: The fuzzy rule base consists of conditional statements of the form:

IF e is A_i AND e˙ is B_j THEN u is C_k                           (3.45)

The rule strength is computed using the minimum operator:

α_{i j} = min(µ_Ai (e), µ_Bj (e˙))                                           (3.46)

The fuzzy control outputs for each direction are computed independently:

u_{x, f uzzy} = FuzzyInference(e_x, e˙_x)                                     (3.49)

u_{y, f uzzy} = FuzzyInference(e_y, e˙_y)                                     (3.50)

u_{ϕ, f uzzy} = FuzzyInference(e_ϕ, e˙_ϕ )                                   (3.51)

3.4 Path Planning algorithms

3.4.1 RRT*

RRT^∗ is an optimal and collision-free path planning algorithm that incrementally builds a tree rooted at the start position, exploring the space toward the goal. It samples, extends, and rewires to optimize the path cost. Key parameters like the maximum number of iterations, step size, and goal bias are carefully tuned to enhance efficiency.

Algorithm 1 RRT* Path Planning Algorithm

Require: Start s_start, Goal s_goal, Maximum iterations N_max, Step size δ , Goal bias p_goal, Ob-stacle set O

Ensure: Path P

1: Initialize tree T with root s_start

2: for iter = 1 to N_max do

3:  Sample random configuration s_rand with bias p_goal

4:  Find nearest node s_nearest in tree T

5:  Steer towards s_rand to generate new node s_new

6:  if Collision-free from s_nearest to s_new then

19:  return Path P

20:  end if

21: end for

22: return No path found

3.4.3 A*

Algorithm 3 A* Path Planning Algorithm

Require: Start cell (i_s, j_s), Goal cell (i_g, j_g), Grid map G , Heuristic function h(·)

Ensure: Path P or failure

1: Initialize open_set = {(i_s, j_s)}, closed_set = 0/

2: Initialize g(i_s, j_s) = 0, f (i_s, j_s) = h(i_s, j_s)

16:  Calculate g_tentative = g(i_c, j_c) + cost((i_c, j_c), (i_n, j_n))

17: if (i_n, j_n) ∈/ open_set then

18:  Add (i_n, j_n) to open_set

24: f (i_n, j_n) = g(i_n, j_n) + h(i_n, j_n)

25: end for

26: end while

27: return No path found

A* is a graph-based search algorithm that finds the optimal path from start to goal by systematically exploring nodes with the lowest estimated total cost. It uses a heuristic function to guide the search toward the goal. The algorithm maintains optimality when the heuristic function is consistent.

* Cost Function: f (n) = g(n) + h(n)

Where g(n) is the actual cost from start to node n, and h(n) is the heuristic estimate from

. Neighbor Expansion: For 8-connectivity, each cell (i, j) has up to 8 neighbors:

N (i, j) = {(i + ∆i, j + ∆ j) : ∆i, ∆ j ∈ {−1, 0, 1},            (3.59)

(∆i, ∆ j) ̸= (0, 0)}

. Optimality Condition: A* finds the optimal path if the heuristic satisfies:

h(n) ≤ h^∗(n)       ∀n ∈ G

Where h^∗(n) is the true minimum cost from n to goal.

3.4.5 Predictive Dynamic Obstacle Avoidance

Predictive dynamic obstacle avoidance extends static path planning by incorporating temporal dynamics of moving obstacles and implementing proactive replanning strategies. The system continuously monitors obstacle trajectories, predicts future positions, and triggers replanning when collisions are anticipated within a specified lookahead horizon.

* Trajectory Prediction: For lookahead horizon T_h and prediction time step ∆t_p, generate predicted positions:

Ôi(t_k + j∆t_p) = {pˆ_i(t_k + j∆t_p) : j = 0, 1, . . . , ⌊T_h/∆t_p⌋}

* Collision Prediction Algorithm: For current path segment P_remaining = {p_ℓ, p_ℓ+1, . . . , p_N}:

* Adaptive Replanning Strategy: The replanning frequency adapts based on environment dynamics:

Δt_replan (t)=Δt_base⋅(1+α⋅(N_rep1an (t))/t)^-1

Where α is an adaptation parameter and N_replan(t) is the cumulative number of replans up to time t.

3.5 Path Post-Processing Methodology

This section presents the methodology for path post-processing techniques applied to enhance the planned trajectories from the four path planning algorithms. The post-processing methods aim to improve path smoothness, reduce path length, and decrease the number of waypoints while maintaining collision-free navigation. The post-processing framework con-sists of four distinct methods applied to each successfully planned path: (1) None (baseline),

(2) Bézier curve smoothing, (3) B-spline smoothing, and (4) Shortcutting optimization. Each method is evaluated based on safety preservation, computational efficiency, and trajectory improvement metrics.

Require: Current time t_k, Robot position xrobot, Current path Pcurrent, Path index ℓ, Dy-namic obstacles Oii = 1ⁿd , Lookahead horizon T_h, Prediction step ∆t_p, Safety distance d_s

Ensure: Replanning decision and updated path

1: Initialize collision_detected = False

2: Set J = ⌊T_h/∆t_p⌋

3: for j = 0 to J do

4:  t_pred = t_k + j · ∆t_p

5:  for i = 1 to n_d do

18:  end for

19:  if collision_detected then

20: break

21: end if

22: end for

23:  if collision_detected and (t_k − t_{last_replan} ≥ ∆t_replan) then

24: Update tlast_replan = tk

25:  Get current obstacle configuration: O_current = UpdateObstacles(t_k)

32: return (False, P_current) // Replanning failed

33: end if

34: else

35: return (False, P_current) // No replanning needed

36: end if

3.5.1 Bézier Curve Smoothing

The Bézier curve smoothing method transforms the discrete waypoint sequence into a smooth continuous curve using Bernstein polynomials.

Given an original path P = {p₁, p₂, . . . , p_n}, the algorithm selects m control points where m = min(6, n) to maintain computational efficiency while preserving path characteristics. The control points are selected as:

C = {p₁, p_i2 , p_i3 , . . . , p_im−1 , p_n}                               (3.61)

Where the intermediate indices i _j are uniformly distributed along the original path.

The number of sample points is determined adaptively based on the original path length:

n_samples = max(20, min(100, ⌊L_original × 10⌋))                    (3.63)

 Where L_original is the length of the original path in meters.

3.5.3 Shortcutting Optimization

The shortcutting method iteratively removes intermediate waypoints to create more di-rect paths while maintaining collision-free navigation.

The algorithm attempts to connect non-adjacent waypoints directly, bypassing interme-diate points when collision-free paths exist. For each waypoint p_i, the method tests connec-tions to waypoints p_{i+ j} where j ∈ {2, 3, . . . , min(5, n − i)}.

1: Poptimized ← Poriginal

2: for iter = 1 to max_iterations do

3:  improved ← false

4:  i ← 1

15: end while

16: if not improved then

17:  break

18: end if

 19: end for

CHAPTER 4: RESULTS AND DISCUSSION

In this section, we compare path planning algorithms: Standard RRT*, Informed-RRT* and A*, Theta* integrated with controllers NMPC, SMC, FLC and post-processing Bezier, Bspline and Shortcut to see the adaptation and robustness of proposed framework within com-plex and dynamic enviroments.

4.1 Static environment

4.1.1 Narrow Gap Environment

Table 4.1 and figure 4.1 presents a comprehensive evaluation of four motion planning algorithms: Theta*, A*, RRT*, and I-RRT*-within narrow gap environments. The narrow gap environment presented unique challenges where the solution to find a path from start to goal must through a gap opposit to goal (see figure 4.1). Results indicate that only grid-based methods (A* and Theta*) successfully finding feasible paths and both RRT-based algorithms failed to navigate through constrained passages, highlighting limita-tions in goal-bias of the algorithm for the environment. A* generates up to 2,494 nodes,

While Theta* only generates 2,148 nodes, indicating that Theta* is more suitable for systems requiring optimization in computational time (see figure 4.1. However, Theta* is not compat-ible with any post-processing methods. In contrast, A* demonstrates effectiveness across all post-processing techniques, particularly when combined with Bezier and Bspline. The most notable performance is observed when integrated with the SMC controller, achieving the low-est RMSE of 0.0613. Nevertheless, this comes at the cost of high control energy, reaching up to 955,881 units.

4.1.3 Cluttered Enviroment

Table 4.3 and Figure 4.9 provide a comprehensive comparison of the performance of four navigation algorithms-Theta*, A*, RRT*, and Informed RRT*-in cluttered environments with dense static obstacles.

Although A* generates up to 1,496 nodes, it achieves the overall shortest path compared to the other algorithms, particularly when combined with Bezier or Bspline and the SMC con-troller-resulting in a path length of only 117 units. In contrast, Theta* generates only 175 nodes; however, it completely fails when applying path smoothing techniques, demonstrating poor compatibility with Bezier, Bspline, and Shortcut methods.

Comes at the cost of significantly increased computational complexity, generating 3,903 nodes. This sharp increase in node count indicates extensive exploration and refinement, which con-tribute to path optimality but present serious challenges for real-time implementation. RRT* produces only 111 nodes-35 times fewer than Informed RRT*-and achieves a very low RMSE of 0.0585 (the lowest across all configurations when no post-processing is applied and SMC is used). However, it results in the longest path at 184 units, highlighting high speed but low path quality.

4.2 Dynamic environment

Figure 4.14 illustrates the real-time tracking performance of NMPC controllers inte-grated with different path planning algorithms in the dynamic environment. Table 4.4 com-pares the performance of each integrated method in dynamic environment. The dynamic environment evaluation revealed the superior adaptability and robustness of the integrated predictive framework when confronted with moving obstacles. Theta* combined with NMPC demonstrated exceptional performance, achieving minimal replanning requirements (only 1 replan event), while maintaining the highest average safety clearance.

The visualization clearly demonstrates how each algorithm-controller combination han-dles trajectory following while simultaneously avoiding dynamic obstacles. With integration of all planning algorithm, SMC seems to show noisier performance and unstable tracking compare to NMPC. In dynamic planning, tracking performance help to effectively avoid col-lision. We can observe that unstable tracking performance leads to collisions. Figure 4.14 is also well-aligned with the result where NMPC control require the least effort and perform the smoothest tracking and FLC performance is better than SMC. The results highlighting that improvements need to be made in the future to enable better planning strategy to adapt dynamic environment and improvment to SMC.

4.3 3D Enviroment

The image shows that the robot has moved from the starting point (marked by a green circle) to the goal point (marked by a red circle). The planned path (solid blue line) and the NMPC-adjusted path (dashed red line) indicate that the robot successfully completed its jour-ney through the 3D terrain. The robot’s trajectory demonstrates good adaptability to terrain variations, avoiding high peaks and selecting a reasonable route.

The appearance of the 3D robot model at the goal point demonstrates that the simulation successfully visualized the robot’s posture in accordance with the terrain, including its ability to align with elevation and slope.

CHAPTER 5: CONCLUSION

This paper presented a comprehensive and integrated navigation framework for omni-wheeled mobile robots operating in complex static and dynamic environments. The frame-work combines global path planning algorithms-RRT*, Informed-RRT*, A*, and Theta*-with advanced nonlinear control strategies including Nonlinear Model Predictive Control (NMPC), Sliding Mode Control (SMC), and Fuzzy Logic Control (FLC). The design emphasizes the mutual interaction between planning and control modules, where the characteristics of the generated path directly influence the performance of the tracking controller.

A key contribution of this work is the enhancement of RRT* through a shortcutting tech-nique, which significantly improves path smoothness and reduces the number of waypoints without compromising collision avoidance. This improvement reduces computational burden on NMPC and enhances its tracking performance. When the improved RRT* is combined with NMPC, results show that path length is shortened, the number of waypoints is reduced by up to 90%, and tracking Root Mean Square Error (RMSE) is significantly decreased in all tested environments.

Simulation results across various environments-such as cluttered, maze-like, and narrow-gap configurations-demonstrate that the proposed framework performs reliably and effi-ciently. Among all planner-controller combinations, Theta*-NMPC consistently outperformed others by achieving the lowest tracking error, shortest execution time, and most stable mo-tion. Particularly in dynamic environments, where moving obstacles were introduced, Theta*-NMPC required the fewest replanning events (only one) and successfully avoided all collisions while maintaining the highest minimum safety distance.

These findings confirm the importance of path-control synergy in robot navigation. Smooth and feasible paths from algorithms like Theta* or improved RRT* not only simplify the controller’s optimization process but also lead to better orientation tracking and energy-efficient movement. Conversely, well-tuned controllers such as NMPC benefit from reduced path complexity and can execute trajectories more accurately and safely under real-time con-straints.

The integration of predictive obstacle avoidance further strengthens the system’s capabil-ity to operate in dynamic environments. By forecasting future positions of moving obstacles, the system can proactively replan paths, improving safety without sacrificing responsiveness.

In conclusion, the proposed framework not only demonstrates strong performance across diverse planning and control pairings but also highlights the critical role of bidirectional in-teraction between modules in achieving robust, precise, and computationally efficient au-tonomous navigation. Future work will involve real-world implementation on physical omni-wheeled robot platforms, integration of adaptive or learning-based planners, and extension to decentralized multi-robot coordination in dynamic and uncertain environments.

REFERENCES

[1]. Ye, C., Wang, H., Yu, S., Ma, X., & Zhou, R. (2024). Design and Implementation of a Land-Air Omnidirectional Mobile Robot. Aerospace, 11(7), 576.

[2]. S. NOGA. (2006). Omni-Wheeled Mobile Robots: Kinematics and Dynamics. Kinemat-ics and dynamics of some selected two-wheeled mobile robots, 6(3), 55-70.

3]. Pere, G., Celaya, E., & Ros, L. L. (2023). The Otbot project: Dynamic modelling, parameter identification, and motion control of an omnidirectional tire-wheeled robot. arXiv.org.

[4]. Zhuolun, L., Jiajun, L., Ximan, Z., Chengyuan, G., Shixing, J., Zheng, Z., & Zhen, J. (2023). Experimental Characterization and Comparison of Three Typical Omnidirec-tional Mobile Robots. 2023 International Conference on Advanced Robotics and Mecha-tronics (ICARM), 1162-1168.

[5]. Seder, M., Petrovic´, L., Persˇic´, J., Popovic´, G., Petkovic´, T., Sˇelek, A., Bic´anic´, B., Cvisˇic´, I., Josic´, D., Markovic´, I., Petrovic´, I., & Muhammad, A. (2019). Open Plat-form Based Mobile Robot Control for Automation in Manufacturing Logistics. IFAC-PapersOnLine, 52(22), 95-100.

[6]. Zhang, Y., Zhao, W., Wang, J., & Yuan, Y. (2024). Recent Progress, Challenges and Future Prospects of Applied Deep Reinforcement Learning: A Practical Perspective in Path Planning. Neurocomputing, 608, 128423.

[7]. Massoud, M.M., Abdellatif, A., & Atia, M.R.A. (2022). Different Path Planning Tech-niques for an Indoor Omni-Wheeled Mobile Robot: Experimental Implementation, Com-parison and Optimization. Applied Sciences, 12(24), 12951.

[8]. B. Zhou, K. Zhang, Z. Yang, and M. Wang, “A Safe Reinforcement Learning Approach for Autonomous Navigation of Mobile Robots in Dynamic Environments,” IET Cyber-Systems and Robotics, vol. 5, no. 2, pp. 97–106, 2023..

"TẢI VỀ ĐỂ XEM ĐẦY ĐỦ ĐỒ ÁN"