Smart navigation of a gravity-driven glider with adjustable centre-of-mass

TL;DR

This work tackles how a compact gravity-driven glider can autonomously navigate to a target while settling in a viscous fluid. By coupling a movable centre-of-mass to a 2D elliptical glider with fully resolved DNS via immersed-boundary methods to a reinforcement-learning framework, it identifies two optimal strategies: inclined settling at small $Ga$ (low $Re_p$) and tumbling at large $Ga$ (high $Re_p$) to generate a horizontal lift. The transition between strategies is governed by hydrodynamic torques and lift generation, with a heuristic tumbling rule capturing the essential dynamics. The findings offer a low-energy, autonomous control mechanism for smart gliders and provide a pathway toward laboratory validation and later extension to three-dimensional geometries and shape-control strategies.

Abstract

Artificial gliders are designed to disperse as they settle through a fluid, requiring precise navigation to reach target locations. We show that a compact glider settling in a viscous fluid can navigate by dynamically adjusting its centre-of-mass. Using fully resolved direct numerical simulations (DNS) and reinforcement learning, we find two optimal navigation strategies that allow the glider to reach its target location accurately. These strategies depend sensitively on how the glider interacts with the surrounding fluid. The nature of this interaction changes as the particle Reynolds number Re$_p$ changes. Our results explain how the optimal strategy depends on Re$_p$. At large Re$_p$, the glider learns to tumble rapidly by moving its centre-of-mass as its orientation changes. This generates a large horizontal inertial lift force, which allows the glider to travel far. At small Re$_p$, by contrast, high viscosity hinders tumbling. In this case, the glider learns to adjust its centre-of-mass so that it settles with a steady, inclined orientation that results in a horizontal viscous force. The horizontal range is much smaller than for large Re$_p$, because this viscous force is much smaller than the inertial lift force at large Re$_p$. *These authors contributed equally.

Figures (8)

• Figure 1: (a) Glider with a movable mass ($\bullet$). Here $\boldsymbol{n}$ is the unit vector along the major axis of the glider, $\theta$ is the tilt angle, and $\boldsymbol{v}$ is the velocity of the geometric centre. (b) Illustration of the forces and torques on a glider. The torques are evaluated with respect to the geometric centre. Buoyancy $\boldsymbol{F}_{\rm b}$ ($\circ$) induces no torque, while gravity $\boldsymbol{F}_{\rm g}$ ($\bullet$), causes the torque $T_g=-d\sin\theta$ because the centre-of-mass is located at distance $d$ along $\boldsymbol{n}$ from the geometric centre. Hydrodynamic forces on the glider surface result in a net force $\boldsymbol{F}_{\rm h}$ and torque $T_{\rm h}$ with respect to the geometric centre. (c) Schematic of active control of a settling glider in a quiescent fluid by adjusting its centre-of-mass. The red star represents the target point.
• Figure 2: Landing position $x$ versus randomly prescribed target points $x_{\rm T}$. The dashed line represents perfect navigation $x=x_{\rm T}$. Parameters: (a) $\mathrm{Ga}=4.4$; (b) $\mathrm{Ga}=35.4$, and (c) $\mathrm{Ga}=283$.
• Figure 3: Glider orientation for optimal strategies at different $\mathrm{Ga}$. The control $d(t)$ (dashed lines) and the tilt angle $\theta(t)$ (solid lines) are shown against time. (a) $\mathrm{Ga}=4.4$; (b) $\mathrm{Ga}=35.4$; (c) $\mathrm{Ga}=283$.
• Figure 4: Glider trajectories corresponding to Fig. \ref{['fig:traj']} (a--c). Ellipses outline the glider at time intervals of action update, $\tau_{\rm u} = 1.41$, coloured by instantaneous gravity torque $T_g$. Black dots mark the centre-of-mass, and the red star indicates the target. The glider size is enlarged by a factor 1.5 for better visualisation. (a) $\mathrm{Ga}=4.4$; (b) $\mathrm{Ga}=35.4$; (c) $\mathrm{Ga}=283$.
• Figure 5: (a) Torques for $\mathrm{Ga}=283$, for the trajectory shown in Fig. \ref{['fig:traj-pos']} (c). Solid line: $T_g$; dashed line: dissipative torque $-c_1 \omega -c_2 |\omega|\omega$; dash-dotted line: fluid-inertia torque, $-c_3 |v|^2 \sin\phi \cos\phi$. The added moment of inertia torque, $-c_4\dot{\omega}$, is negligible (not shown). (b) Maximal horizontal distance covered by a glider when it uses the tumbling strategy [Eq. (\ref{['eq:tumbling']})] ($\square$), or settling with a certain fixed orientation ($\circ$).