# Systematic Review of Mecanum and Omni Wheel Technologies for Motor Impairments
## 4 Discussion
### Mathematical and Computational Challenges in Assistive Mobility Systems  
In addition to mechanical and usability considerations, the development of Mecanum and omni wheel-based assistive platforms presents a range of mathematical and computational challenges that are often underexplored in the reviewed literature. As highlighted in the Results, Section 3[39; 41; 42], several studies applied advanced control strategies--including sliding mode control (SMC), field-oriented control (FOC), and kinematic simulations--but offered limited detail regarding their mathematical formulation, implementation complexity, or performance trade-offs. For instance, FOC requires real-time transformations (e.g., Clarke and Park) to manage motor torque and flux independently, which can impose strict timing and processing constraints on embedded systems [41]. This is consistent with findings by [PERSON] et al. [58], who demonstrated how decoupled speed and flux control in FOC architectures enhances fault tolerance but also increases control complexity, requiring careful parameter tuning and stability verification.  
Similarly, SMC and other nonlinear control methods demand accurate modeling of system dynamics and often involve discontinuous control laws, which may introduce numerical instabilities if not properly tuned [39]. Motion planning and system modeling also pose significant analytical demands. Studies like [42] used multibody simulation tools to refine drive configurations, emphasizing that kinematic optimization is crucial for maintaining motion fidelity--especially in environments with constrained space or variable friction.  
In a broader modeling context, [PERSON] et al. [59] proposed a modified inverse kinematics model for systems composed of multiple Mecanum platforms, incorporating slip compensation matrices to enhance positioning accuracy. Their work highlights the importance of precise velocity mapping and simulation-based optimization for robust omnidirectional mobility.  
The integration of biosignal-driven user interfaces introduces additional complexity. Real-time classification of EMG, IMU, or EEG signals--such as those used in gesture-based [36] or brain-computer interface (BCI) control [37; 50]--requires robust signal preprocessing, feature extraction, and machine learning pipelines. A recent study by [PERSON] et al. [60] developed a multimodal human-machine interface for assistive wheelchairs using EEG and EMG inputs, combining signal processing algorithms with adaptive navigation logic. Their results show promising control accuracy but also reveal latency and stability challenges during real-time operation.  
However, only a few studies have provided full algorithmic details or reported accuracy, latency, and reliability under varied conditions. To advance this field, future research should more explicitly document the mathematical models, control algorithms, and signal processing architectures employed in assistive mobility systems. Key elements such as computational load, response time, numerical stability, and robustness should be quantitatively evaluated.