Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on approximation techniques, their simulation often deviates from real-world physics, especially in the long term. In this paper, we propose to learn a particle-based simulator for complex control tasks. Combining learning with particle-based systems brings in two major benefits: first, the learned simulator, just like other particle-based systems, acts widely on objects of different materials; second, the particle-based representation poses strong inductive bias for learning: particles of the same type have the same dynamics within. This enables the model to quickly adapt to new environments of unknown dynamics within a few observations. We demonstrate robots achieving complex manipulation tasks using the learned simulator, such as manipulating fluids and deformable foam, with experiments both in simulation and in the real world. Our study helps lay the foundation for robot learning of dynamic scenes with particle-based representations. Objects have distinct dynamics. Under the same push, a rigid box will slide, modeling clay will deform, and a cup full of water will fall with water spilling out. The diverse behavior of different objects poses challenges to traditional rigid-body simulators used in robotics BID31 BID30 . Particle-based simulators aim to model the dynamics of these complex scenes BID18 ; however, relying on approximation techniques for the sake of perceptual realism, their simulation often deviates from real world physics, especially in the long term. Developing generalizable and accurate forward dynamics models is of critical importance for robot manipulation of distinct real-life objects.We propose to learn a differentiable, particle-based simulator for complex control tasks, drawing inspiration from recent development in differentiable physical engines BID0 BID3 . In robotics, the use of differentiable simulators, together with continuous and symbolic optimization algorithms, has enabled planning for increasingly complex whole body motions with multi-contact and multi-object interactions BID32 ). Yet these approaches have only tackled local interactions of rigid bodies. We develop dynamic particle interaction networks (DPINets) for learning particle dynamics, focusing on capturing the dynamic, hierarchical, and long-range interactions of particles FIG0 -c). DPI-Nets can then be combined with classic perception and gradient-based control algorithms for robot manipulation of deformable objects FIG0 ).Learning a particle-based simulator brings in two major benefits. First, the learned simulator, just like other particle-based systems, acts widely on objects of different states. DPI-Nets have successfully captured the complex behaviors of deformable objects, fluids, and rigid-bodies. With learned DPINets, our robots have achieved success in manipulation tasks that involve deformable objects of complex physical properties, such as molding plasticine to a target shape.Our project page: http://dpi.csail.mit.edu Perception and control with the learned model. Our system first reconstructs the particle-based shape from visual observation. It then uses gradient-based trajectory optimization to search for the actions that produce the most desired output.Second, the particle-based representation poses strong inductive bias for learning: particles of the same type have the same dynamics within. This enables the model to quickly adapt to new environments of unknown dynamics within a few observations. Experiments suggest that DPI-Nets quickly learn to adapt to characterize a novel object of unknown physical parameters by doing online system identification. The adapted model also helps the robot to successfully manipulate object in the real world.DPI-Nets combine three key features for effective particle-based simulation and control: multi-step spatial propagation, hierarchical particle structure, and dynamic interaction graphs. In particular, it employs dynamic interaction graphs, built on the fly throughout manipulation, to capture the meaningful interactions among particles of deformable objects and fluids. The use of dynamic graphs allows neural models to focus on learning meaningful interactions among particles, and is crucial for obtaining good simulation accuracy and high success rates in manipulation. As objects deform when robots interact with them, a fixed interaction graph over particles is insufficient for robot manipulating non-rigid objects.Experiments demonstrate that DPI-Nets significantly outperform interaction networks BID0 , HRN BID19 , and a few other baselines. More importantly, unlike previous paper that focused purely on forward simulation, we have applied our model to downstream control tasks. Our DPI-Nets enable complex manipulation tasks for deformable objects and fluids, and adapts to scenarios with unknown physical parameters that need to be identified online. We have also performed real-world experiments to demonstrate our model's generalization ability. We have demonstrated that a learned particle dynamics model can approximate the interaction of diverse objects, and can help to solve complex manipulation tasks of deformable objects. Our system requires standard open-source robotics and deep learning toolkits, and can be potentially deployed in household and manufacturing environment. Robot learning of dynamic scenes with particle-based representations shows profound potentials due to the generalizability and expressiveness of the representation. Our study helps lay the foundation for it.A CONTROL ALGORITHM Update A by descending with the gradients ∇ A L state (Ĝ t , G t ) Forward simulation using the current graphĜ t+1 ← Φ(G t ) Make a buffer for storing the simulation results G ←Ḡ ∪Ĝ t+1 for i = t + 1, ..., T − 1 do Forward simulation:Ĝ j+1 ← Φ(Ĝ j ); G ← G ∪Ĝ j+1 end for Updateû t:T by descending with the gradients ∇û t: DISPLAYFORM0
Learning particle dynamics with dynamic interaction graphs for simulating and control rigid bodies, deformable objects, and fluids. 
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