Acoustic Wave Manipulation Through Sparse Robotic Actuation

TL;DR

This work addresses controlling acoustic waves with sparse robotic actuation by introducing a physics-informed, interpretable latent model that enforces a 1D wave equation in latent space and incorporates a trainable perfectly matched layer for open-space dissipation. The method learns latent wave dynamics via encoders mapping sensor data and robot states to a reduced PDE, and uses model predictive control to achieve energy focusing or suppression with sparse actuators. Key contributions include the integration of physical priors into a data-driven framework, demonstrated long-horizon prediction, and competitive performance against semi-analytical GBO methods while outperforming a neural baseline. The approach advances robotic PDE manipulation with potential applications in ultrasound, material design, and energy harvesting, and is generalizable to other PDE-governed systems.

Abstract

Recent advancements in robotics, control, and machine learning have facilitated progress in the challenging area of object manipulation. These advancements include, among others, the use of deep neural networks to represent dynamics that are partially observed by robot sensors, as well as effective control using sparse control signals. In this work, we explore a more general problem: the manipulation of acoustic waves, which are partially observed by a robot capable of influencing the waves through spatially sparse actuators. This problem holds great potential for the design of new artificial materials, ultrasonic cutting tools, energy harvesting, and other applications. We develop an efficient data-driven method for robot learning that is applicable to either focusing scattered acoustic energy in a designated region or suppressing it, depending on the desired task. The proposed method is better in terms of a solution quality and computational complexity as compared to a state-of-the-art learning based method for manipulation of dynamical systems governed by partial differential equations. Furthermore our proposed method is competitive with a classical semi-analytical method in acoustics research on the demonstrated tasks. We have made the project code publicly available, along with a web page featuring video demonstrations: https://gladisor.github.io/waves/.

Figures (4)

• Figure 1: Schematic representation of interaction between an agent and acoustic wave. The agent observes wave through its 'Sensor' readings, and affects it back by choosing the optimal locations and radii of the cylindrical scatterers (gray blobs) according to its 'Controller' (policy). Wave propagates with the speed of sound according to the Wave PDE, while robot dynamics (actuation of the cylinders) is an order of magnitude slower time scale. 'Excitation' represents an exogenous source of acoustic energy (e.g., speaker). The 'Dissipation' layer prevents wave reflections from the boundaries and allows for the efficient simulation of open space (infinite) environments. Robot's policy is trained to achieve a desired wave configuration such as focusing energy in a particular location or minimizing total scattered energy.
• Figure 2: Encoding Scheme. Left: Sensor observation $X(t_i)$ of the PDE $\zeta$ is encoded by $W$ to the latent initial condition $\mathbf{g}(\bar{x}, t_i)$ and exogenous function $l(\bar{x})$. Right: sequences of robot configurations, $d(t_i), d(t_{i+1}), \cdots$, produced by agent's actions, $a_i(t)$ are individually encoded to latent control functions $c(\bar{x}, t_i), c(\bar{x}, t_{i+1}), \cdots$.
• Figure 3: Long-term prediction of scattered energy over an episode of 0.2 seconds (200 action steps) for the ring configuration (R). The training horizon for the models is 20 actions, which demonstrate generalization of the model to unseen in training horizons.
• Figure 4: Focused and Suppressed Scattered Energy. Both the positions and radii of two fully adjustable scatterers are varied (F, M=2). Source is fixed at location (-10, 0) throughout the simulations. Shading represents ± 0.5 standard deviation from the mean. The mean (solid lines) and variance are calculated with 12 runs with randomized initial conditions. The dashed line is for the ground truth by GBO.