Even though a variety of methods (e.g., RL, MPC, LQR) have been proposed in the literature, efficient and effective latent-space control of physical systems remains an open challenge. A promising avenue would be to leverage powerful and well-understood closed-form strategies from control theory literature in combination with learned dynamics, such as potential-energy shaping. We identify three fundamental shortcomings in existing latent-space models that have so far prevented this powerful combination: (i) they lack the mathematical structure of a physical system, (ii) they do not inherently conserve the stability properties of the real systems. Furthermore, (iii) these methods do not have an invertible mapping between input and latent-space forcing. This work proposes a novel Coupled Oscillator Network (CON) model that simultaneously tackles all these issues. More specifically, (i) we show analytically that CON is a Lagrangian system - i.e., it presses well-defined potential and kinetic energy terms. Then, (ii) we provide formal proof of global Input-to-State stability using Lyapunov arguments. Moving to the experimental side, (iii) we demonstrate that CON reaches SoA performance when learning complex nonlinear dynamics of mechanical systems directly from images. An additional methodological innovation contributing to achieving this third goal is an approximated closed-form solution for efficient integration of network dynamics, which eases efficient training. We tackle (iv) by approximating the forcing-to-input mapping with a decoder that is trained to reconstruct the input based on the encoded latent space force. Finally, we leverage these four properties and show that they enable latent-space control. We use an integral-saturated PID with potential force compensation and demonstrate high-quality performance on a soft robot using raw pixels as the only feedback information.

翻译：尽管文献中已提出多种方法（如强化学习、模型预测控制、线性二次调节器），物理系统在潜空间中的高效控制仍是一个开放挑战。一条有前景的途径是将控制理论中强大且成熟的闭式策略（如势能整形）与学习到的动力学相结合。我们指出现有潜空间模型存在三个根本缺陷，阻碍了这种强强联合的实现：（i）缺乏物理系统的数学结构；（ii）无法固有保持真实系统的稳定性；（iii）输入与潜空间作用力之间缺乏可逆映射。本文提出一种新型耦合振荡器网络模型，能同时解决所有这些问题。具体而言：（i）我们通过解析证明该网络是拉格朗日系统——即具有明确定义的势能与动能项；（ii）利用李雅普诺夫方法给出全局输入-状态稳定性的形式化证明。在实验方面：（iii）我们证明该网络在直接从图像学习机械系统复杂非线性动力学时达到最先进性能。实现第三个目标的方法创新是提出了网络动力学高效积分的近似闭式解，这有助于提升训练效率。针对问题（iv），我们通过训练解码器近似作用力到输入的映射，该解码器能根据编码的潜空间作用力重建输入。最后，我们整合这四个特性，证明其可实现潜空间控制。通过采用带势能力补偿的积分饱和PID控制器，在以原始像素作为唯一反馈信息的软体机器人上展示了卓越的控制性能。