-- In imitation learning for robotics, cotraining with demonstration data generated both in simulation and on real hardware has emerged as a powerful recipe to overcome the "sim2real gap". This work seeks to elucidate basic principles of this sim-and-real cotraining to help inform simulation design, sim-and-real dataset creation, and policy training. Focusing narrowly on the canonical task of planar pushing from camera inputs enabled us to be thorough in our study. These experiments confirm that cotraining with simulated data can dramatically improve performance in real, especially when real data is limited. The results also suggest that reducing the domain gap in physics may be more important than visual fidelity for nonprehensile manipulation tasks. Perhaps surprisingly, having some visual domain gap actually helps the cotrained policy - binary probes reveal that high-performing policies learn to distinguish simulated domains from real. We conclude by investigating this nuance and mechanisms that facilitate positive transfer between sim-and-real. In total, our experiments span over 40 real-world policies (evaluated on 800+ trials) and 200 simulated policies (evaluated on 40,000+ trials). Foundation models trained on large datasets have transformed natural language processing [2]][3] and computer vision [4]. However, this data-driven recipe has been challenging to replicate in robotics since real-world data for imitation learning can be expensive and time-consuming to collect [5]. Fortunately, alternative data sources, such as simulation and video, contain useful information for robotics. In particular, simulation is promising since it can automate robot-specific data collection.

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm.