The structural complexity of the bipedal locomotion may be reduced by using mechanisms with fewer actuators, which ideally do not degrade the performance and functionality of the robot. However, when the mechanism design considers conflicting design objectives, the search for design solutions with specific trade-offs becomes hard. This work studies different multi-objective search approaches the dominance-based, the decomposition-based and the metric-driven in the dimensional synthesis of the eight-bar mechanism for the bipedal locomotion application in the sagittal plane stated as a mixed discrete-continuous nonlinear multi-objective optimisation problem. This work also proposes a dominance-based multi-objective differential evolution algorithm called Multi-Objective Specialist Population-based Differential Evolution (MOSPDE), which endows specialised subpopulations to exploit different regions of the Pareto front to favour the search for design trade-offs with a suitable generation of the gait and force transmission during the stance phase. The comparative study includes algorithms reported in the specialised literature based on dominance (MOPSO, MODE variants and NSGA-II), decomposition (MOEA/D-DE) and metric-driven (SMS-EMOA). The statistical analysis reveals that using the Pareto dominance search approach based on differential evolution and the inclusion of exhaustive exploitation can promote the reconfigurability of the bipedal locomotion mechanism with better trade-offs that satisfy the conflicting design objectives.

The increasing heterogeneity of wheeled mobile robot (WMR) architectures, including differential-drive, Ackermann, omnidirectional, and reconfigurable platforms, poses a major challenge for defining a unified, scalable kinematic representation. Most existing formulations are tailored to specific mechanical layouts, limiting analytical coherence, cross-platform interoperability, and the systematic reuse of modeling, odometry, and motion-related algorithms. This work introduces a generalized kinematic modeling framework that provides a mathematically consistent formulation applicable to arbitrary WMR configurations. Wheel–ground velocity relationships and non-holonomic constraints are expressed through a concise vector formulation that maps wheel motions to chassis velocities, ensuring consistency with established models while remaining independent of the underlying mechanical structure. A parameterized wheel descriptor encodes all relevant geometric and kinematic properties, enabling the modular assembly of complete robot models by aggregating wheel-level relations. The framework is evaluated through numerical simulations on four structurally distinct platforms: differential-drive, Ackermann, three-wheel omnidirectional (3, 0), and 4WD. Results show that the proposed formulation accurately reproduces the expected kinematic behavior across these fundamentally different architectures and provides a coherent and consistent representation of their motion. The unified representation further provides a common kinematic backbone that is directly compatible with odometry, motion-control, and simulation pipelines, facilitating the systematic retargeting of algorithms across heterogeneous robot platforms without architecture-specific reformulation. Additional simulation studies under realistic physics-based conditions show that the proposed formulation preserves coherent kinematic behavior during complex trajectory execution and supports the explicit incorporation of geometric imperfections, such as wheel mounting misalignments, when such parameters are available. By consolidating traditionally separate derivations into a single coherent formulation, this work establishes a rigorous, scalable, and architecture-agnostic foundation for unified kinematic modeling of wheeled mobile robots, with particular relevance for modular, reconfigurable, and cross-architecture robotic systems.

This paper presents a unified Euler–Lagrange methodology for deriving the dynamic models of wheeled mobile robots (WMRs) across heterogeneous kinematic architectures. The work extends the authors’ previously developed kinematic methodology to the dynamic level, handling both holonomic platforms, where free roller motion eliminates kinematic constraints, and non-holonomic platforms, where pure-rolling conditions impose non-integrable velocity constraints. Through null-space-based reduction, constraint forces are eliminated, yielding control-affine state-space models that preserve structural properties essential for control synthesis, including inertia matrix symmetry, positive definiteness, and skew symmetry of the Coriolis matrix. The methodology is applied to four canonical architectures: differential drive, Ackermann steering, three-wheeled omnidirectional, and four-wheeled Mecanum drive. Distinct dynamic features are observed across topologies with direct implications for controller design. To confirm the correctness and practical utility of the derived models, trajectory tracking experiments are conducted in both ideal simulation and a realistic ROS2/Gazebo environment, with a model-based controller and a model-free strategy. Both successfully track the reference trajectories across all four architectures, with the model-based controller consistently achieving lower tracking errors.