This paper discusses the energy consumption of three parabolic, trapezoidal, and S-curve profiles when implemented using an embedded system. In addition, it presents an alternative methodology for implementing motion controllers using an Advanced RISC Machine (ARM) microcontroller, which computes the trajectory and performs the control action in hard real-time. We experimented using a linear plant composed of a direct current (DC) motor coupled to an endless screw where a carriage was mounted. It can move mechanically along a rail at a distance of 1.16 m. A 4096 pulses per revolution (PPR) encoder was connected to the motor to calculate position and angular velocity. A Hall-effect-based current sensor was used to assess energy consumption. We conducted 40 tests for each profile to compare the energy consumption for the three motion profiles, considering cases with and without load on the carriage. We determined that the parabolic profile provides $22.19\%$ lower energy consumption than the other profiles considered in this study, whereas the S-curve profile exhibited the highest energy consumption.

The UAV bicopter is a double-propeller system whose main objective is to stabilize a rod at a given angle by precisely controlling the rotation speed of each propeller. This mechanism generates asymmetric thrust forces that induce a torque on the bar, thus allowing its pitch angle to be modified. Since its dynamics involve complex interactions between the thrust generated by the rotors, aerodynamic effects, and the pendulum behavior of the system, the bicopter is classified as a highly nonlinear system sensitive to external disturbances. To address this complexity, the implementation of a fuzzy Takagi–Sugeno–Kang (TSK) controller is proposed. This controller decomposes the nonlinear dynamics into multiple local linear models associated with a specific operating condition, such as different pitch angles and rotor speeds. The control strategy provides accurate trajectory tracking and effectively handles disturbances and varying conditions, making this approach a practical solution for both dynamic and uncertain environments. This strategy ensures precise trajectory tracking and demonstrates robust performance compared to other control methods, such as PID and LQR, which often struggle with disturbances and system nonlinearities. The TSK controller has proven its effectiveness in experimental trajectory tracking tests, achieving root mean square errors (RMSEs) of 0.2049, 0.3269, 0.3899, 0.3335, and 0.2494, which evaluate the average error in degrees of the system concerning the target position, for tracking trajectories of −10 to 10, −12 to 12, −15 to 15, −17 to 17, and −20 to 20 degrees, respectively.

Currently, a wide variety of velocity profiles are used in motion control. Thus, this paper compares the energy consumption of three parabolic, trapezoidal, and S-curve profiles. We studied the case of using embedded systems since they are a powerful solution to monitor and coordinate the movement of devices and machinery in various industries combined with motion control applications. These integrated systems allow precise and efficient control of motors and actuators through control and feedback algorithms. In addition, we propose an alternative methodology for implementing motion controllers using an Advanced RISC Machine (ARM) microcontroller, which computes the trajectory and the control action in real-time. We conducted an experiment using a linear plant composed of a direct current (DC) motor coupled to an endless screw where a carriage is mounted that can move mechanically along a rail a distance of 1.16m. In addition, a 4096 pulses per revolution (PPR) encoder is connected to the motor to measure position and angular velocity, which compute the distance the carriage has moved in meters. A current sensor is used to assess the energy consumption, and 40 tests for each profile were carried out to compare the energy consumption for the three-motion profiles considering cases with and without load on the carriage.

Two-wheeled self-balancing robots (TWSBRs) are difficult to control because they are nonlinear, unstable, and underactuated, particularly when balance, velocity regulation, and line tracking must be achieved simultaneously. This paper proposes a hybrid parallel control architecture for a line-following TWSBR operating on straight segments, ${90}^{\circ }$ curves, and a ${15}^{\circ }$ slope. Balance stabilization is handled by a classical PD loop, while traslational velocity is regulated by an adaptive fuzzy PI controller, and line following is performed with an adaptive fuzzy PD controller. The fuzzy modules adjust the effective gains based on tracking errors, thereby improving robustness to disturbances, sensor noise, and changes in operating conditions. The complete strategy is implemented on a low-cost PIC18F4550 microcontroller. Experiments show that the fuzzy line-following controller reduces the orientation tracking error compared with a conventional controller. At $0.10{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, RMSE decreases from $0.042\mathrm{rad}$ to $0.038\mathrm{rad}$, and at $0.175{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, it decreases from $0.083\mathrm{rad}$ to $0.066\mathrm{rad}$. The fuzzy approach also improves IAE ($1.317{\displaystyle \frac{\mathrm{rad}}{\mathrm{s}}}$ to $1.185{\displaystyle \frac{\mathrm{rad}}{\mathrm{s}}}$) and ISE ($0.242{\displaystyle \frac{{\mathrm{rad}}^2}{\mathrm{s}}}$ to $0.153{\displaystyle \frac{{\mathrm{rad}}^2}{\mathrm{s}}}$) at $0.175{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, while maintaining similar maximum error ($0.299\mathrm{rad}$ to $0.261\mathrm{rad}$). Overall, the proposed hybrid scheme achieves better adaptability without retuning. These results support real-time deployment on resource-limited platforms.

Two-wheeled self-balancing robots exhibit nonlinear and inherently unstable dynamics due to their inverted-pendulum structure, making control design challenging under terrain variations and external disturbances. This paper proposes a hybrid master–slave fuzzy cascade controller with an additional wheel-synchronization loop to improve tracking performance and robustness. The architecture combines a master velocity PI loop with fuzzy-tuned integral action and a slave balance PD loop with fuzzy proportional control, while a differential synchronization mechanism compensates for motor mismatches without affecting the global balance dynamics. Local stability is analyzed through linearization and equivalent gain approximation within a sector-bounded framework. Experimental validation was conducted on an ESP32-based TWSBR under flat, uphill, and downhill conditions at reference velocities of $0.15$, $0.20$, and $0.30{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, including payload tests with additional masses of $0.279$ and $0.375\mathrm{kg}$. For each scenario, 30 independent trials were performed to compute the reported metrics. Compared with a conventional PID controller, the proposed strategy reduced the flat-terrain velocity RMSE from $0.0108$ to $0.0057{\displaystyle \frac{\mathrm{m}}{\mathrm{s}}}$, while also improving angular stabilization and robustness under slope and payload disturbances.

Background: Learning-based, bio-inspired, and hybrid methods report routing improvements, but differences in experimental design complicate comparison. This critical review examines the evidence supporting these claims. Methods: Structured screening and critical synthesis covered 240 journal studies from 2022 to 2026: 43 learning-based, 135 bio-inspired and evolutionary, and 62 hybrid. Full-text assessment using category-specific thresholds yielded 1243 primary decisions, complemented by resource-stage and bio-inspired evaluation analyses. Results: Learning generalization and controlled ablation were Supported in 14/43 and 17/43 studies; none met complete joint resource-accounting or live operational-validation thresholds. Bio-inspired studies reported repeated runs in 104/135 cases and public code with inputs in 9/135; complementary feasibility, fairness, and generalization thresholds were Supported in 10/135, 4/135, and 2/135. Among 56 hybrids with comparative routing outcomes, 39 met neither the matched-budget nor the integration-cost threshold. Conclusions: This review contributes a category-specific framework linking routing improvements to feasibility, experimental controls, computational resources, and validation scope. Under its operational thresholds, these reporting frequencies characterize evidence rather than overall study quality. The framework helps researchers and logistics practitioners distinguish Supported claims from those requiring additional evidence, without pooling incompatible performance results or ranking methodological families.