Narrow Results

In this paper, an adaptive backstepping-based control scheme is proposed to perform autonomous lateral maneuvers under significant lateral offset in the center of gravity (c.g.) position in a UAV. It is first shown that the coupled equations of motion arising from lateral c.g. shift can be simplified and cast in block strict feedback form making it amenable to a two-step backstepping control design. Useful nonlinear terms in the equations of motion are identified and retained in the backstepping design to ensure a less conservative control. Adaptation law is incorporated to dynamically adjust to changes in the c.g. position by adding an adaptive term to each step of the backstepping control. Lyapunov’s direct method and LaSalle’s invariance principle are applied to establish asymptotic stability of both tracking errors and errors in the c.g. estimate. To validate the effectiveness of the proposed control strategy, simulation results for horizontal turn maneuver are presented for the fixed wing Aerosonde UAV and maneuver performance is observed to remain highly insensitive to a wide range of lateral c.g. positions on either side of the fuselage centerline. Furthermore, a comparative control performance analysis is carried out against an ad-hoc model-based adaptive backstepping control scheme available in the literature and the results show significant performance enhancement in the proposed scheme. Along with the c.g. variations, the effects of steady crosswind are also investigated and the control formulation is modified to mitigate these effects too. Real-time control hardware in loop simulations are also provided in support of the real time viability of the proposed control.

This study examined the influence of running shoe center of gravity relative position shifting forward and backward in sagittal axis on male amateur runners. Twenty-three adult male runners were recruited through social media with paid to participate in this study. The experimental shoe used was the Li Ning Feidian Challenger 3. Forward center of gravity (FCG), defined as the shoe center of gravity located at 10.8cm (15% before midpoint) from shoe toe to heel. Intermediate center of gravity (ICG), defined as the shoe center of gravity, is located at 14.8cm (midpoint) from shoe toe to heel. Backward center of gravity (BCG), defined as the shoe center of gravity, is located at 23.1cm (15% after midpoint) from shoe toe to heel. Questionnaire collection was used to assess the perception of the center of gravity shifting. Ground contact temporal, peak force/pressure of plantar and kinetics indicators data were simultaneously captured by motion capture system and force platform. Three participants (13.04%) correctly perceived the shoe center of gravity shifting forward and backward simultaneously. Shoes ICG peak force underneath Meta 1 increased significantly than BCG by 7.59% ($p<0.05$). Shoes FCG peak force underneath Meta 2 decreased significantly compared to ICG and BCG by 13.62% and 8.96% ($p<0.05$). Shoes BCG peak force underneath Meta 5 decreased significantly compared to ICG and FCG by 18.18% and 23.78% ($p<0.05$). Shoes FCG peak pressure underneath Meta 2 decreased significantly compared to ICG and BCG by 13.02% and 9.19% ($p<0.05$). Shoes FCG peak pressure underneath Meta 2 decreased significantly compared to ICG and BCG by 11.18% and 9.16% ($p<0.05$). However, there are no significant differences in kinetic indicators. The findings suggest that a fraction of participants can correct perceived shoe center of gravity shifting. Shoes’ FCG reduces force and pressure in the middle metatarsal regions. Shoes’ BCG reduces force in the lateral and medial metatarsal region. Healthcare professionals can optimize the design of footwear accordingly to improve rehabilitation outcomes and reduce injury risks in runners.

Displacement of the center of gravity (COG) of tubular structures with various polygonal cross-sections is numerically investigated under an axial crush using the program code of ANSYS/LS-DYNA. A subroutine is developed using this code to calculate the COG of the deformed shape, during and after the crush. The effect of wall thickness on displacement of the COG is also investigated. Displacement of the COG decreases as the number of edges increases; it is a reasonable symmetric-deformed shape for the number of edges beyond eight. An even number of edges leads to a more symmetric displacement of the COG. The effect of the number of polygonal edges on symmetric deformation of the COG becomes more prominent as the initial wall thickness decreases. The higher number of edges stabilizes the deformed shape and the value of the mass moment of inertia of the deformed shape about the y axis (I_yy). The value of the mass moment of inertia about the x–z axes (I_xz) in comparison with I_yy can be neglected in the case of dealing with an axial crush along the y direction.

• (1)The RAOs of OC4-DeepCWind platform motions are more sensitive to the low-frequency wave than the high-frequency wave. The nonlinear motion responses for platform heave and pitch motions are comparatively remarkable.
• (2)The pitch motion of OC4-DeepCWind platform is much more apparently influenced by the height of center of gravity (COG) than surge and heave motions. The lower COG height within a suitable range leads to a smaller fluctuation amplitude of platform pitch motion in waves.
• (3)A large horizontal displacement abruptly occurs to the OC4-DeepCWind platform when one mooring line is failure. The risk of failure for the other mooring lines significantly increases.

To better understand the hydrodynamic performance of a floating support platform in various wave environments, a two-phase CFD solver naoe-FOAM-SJTU based on the open source CFD toolbox OpenFOAM is applied to investigate the hydrodynamic characteristics and motion performance of the OC4-DeepCWind platform. Moreover, the restoring force and moment of mooring lines are simulated using the solver in time domain. The studies of grid sensitivity and time step refinement are first conducted to determine an appropriate time step and mesh size. Then hydrodynamic responses of the floater in free-decay tests are analyzed and compared with experimental data, and the motion performance of the platform in regular waves with different parameters is also investigated. In addition, the platform motion responses with one mooring line broken and different heights of center of gravity are explored. It is shown that simulation results have good agreement with published data, and several conclusions can be drawn through the study. The RAOs of platform motions are found to be more sensitive to the low-frequency wave than the high-frequency wave. Nonlinear motion responses are comparatively remarkable in platform heave and pitch motions. Besides, the lower height of center of gravity within a suitable range is benefit to the stability of floating platform. Survival condition with broken mooring line should be paid enough attention to avoid the failure of other mooring lines.

This paper mainly studies the comparison of the global vehicle models and the effects of the inertial parameters due to the center of gravity (CG) positions when we consider that the vehicle has only one CG. This paper proposes a new nonlinear model vehicle model which considers both unsprung mass and sprung mass CG. The CG positions and inertial parameters effects are analyzed in terms of the published vehicle dynamics models. To this end, two 14 degree-of-freedom (DOF) vehicle models are developed and compared to investigate the vehicle dynamics responses due to the different CG height and inertial parameters concepts. The proposed models describe simultaneously the vehicle motion in longitudinal, lateral and vertical directions as well as roll, pitch and yaw of the vehicle about corresponding axis. The passive and active moments and the forces acting on the vehicle are also described and they are considered as a direct consequence of acceleration, braking and steering maneuvers. The proposed model $M_1$ takes both the CG of sprung mass, unsprung mass and total vehicle mass into account. The second model $M_2$ assumes that the vehicle is one solid body which has a single CG as reported in majority of literature. The two vehicle models are compared and analyzed to evaluate vehicle ride and handling dynamic responses under braking/acceleration and cornering maneuvers. Simulation results show that the proposed model $M_1$ could offer analytically some abilities and driving performances, as well as improved roll and pitch in a very flexible manner compared to the second model $M_2$.

We study a variation of the hanging chain problem. If one end (or both) of a hanging chain moves with stretching the chain along a path such that an external force(s) supporting the chain does not do any work, what path does the movable end draw? Sketching the path (“the workless curve”) will help students to acquire a qualitative understanding of work. In its mathematical derivation, one has to solve transcendental equations under an approximation including the Lambert $W$ function. It is suitable for undergraduate students in calculus-based physics courses.