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Robot Locomotion Group
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The goal of our research is to build machines which exploit their
natural dynamics to achieve extraordinary agility and efficiency.
In an age where "big data" is all the rage, we still have relatively limited data from robots in these regimes, and instead rely mostly on
existing models (e.g. from Lagrangian mechanics) and model-based optimization. We believe that deep connections are possible -- enabling very efficient optimization by exploiting structure in the governing equations -- and are working hard on both optimization algorithms and control applications.
Our current projects include dynamics and control for humanoid robots, robotic manipulation, and dynamic walking over rough terrain, flight control for aggressive maneuvers in unmanned aerial vehicles, feedback control for fluid dynamics and soft robotics, and connections between perception and control.
The Robot Locomotion Group is a part of Robotics @ MIT and CSAIL.
Locomotion Group Paper and Multimedia News 
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Verifying Neural Networks with Mixed Integer Programming
- by Vincent Tjeng and Russ Tedrake
Neural networks have demonstrated considerable success in a wide variety of real-world problems. However, the presence of adversarial examples - slightly perturbed inputs that are misclassified with high confidence - limits our ability to guarantee performance for these networks in safety-critical applications. We demonstrate that, for networks that are piecewise affine (for example, deep networks with ReLU and maxpool units), proving no adversarial example exists - or finding the closest example if one does exist - can be naturally formulated as solving a mixed integer program. Solves for a fully-connected MNIST classifier with three hidden layers can be completed an order of magnitude faster than those of the best existing approach. To address the concern that adversarial examples are irrelevant because pixel-wise attacks are unlikely to happen in natural images, we search for adversaries over a natural class of perturbations written as convolutions with an adversarial blurring kernel. When searching over blurred images, we find that as opposed to pixelwise attacks, some misclassifications are impossible. Even more interestingly, a small fraction of input images are provably robust to blurs: every blurred version of the input is classified with the same, correct label.
Posted on arxiv while under review. Comments welcome.
Compositional Verification of Large-Scale Nonlinear Systems via Sums-of-Squares Optimization
- by Shen Shen and Russ Tedrake
We consider the computationally prohibitive problem of stability and invariance verification of large-scale dynamical systems. We exploit the natural interconnected structure often arising from such systems in practice (i.e., they are interconnections of low-dimensional subsystems), and propose a compositional method. We construct independently for each subsystem a Lyapunov-like function, and guarantee that their sum automatically certifies the original high-dimensional system is stable or invariant. For linear time invariant systems, our method produces block-diagonal Lyapunov matrices without structural assumptions commonly found in the literature. For polynomial system tasks, our formulation results in significantly smaller sum-of-squares programs. Demonstrated on numerical and practical examples, our algorithms can handle problems beyond the reach of direct optimizations, and are orders of magnitude faster than existing compositional methods.
Under review. Comments welcome.
NanoMap: Fast, Uncertainty-Aware Proximity Queries with Lazy Search over Local 3D Data
- by Peter R. Florence and John Carter and Jake Ware and Russ Tedrake
We would like robots to be able to safely navigate at high speed, efficiently use local 3D information, and robustly plan motions that consider pose uncertainty of measurements in a local map structure. This is hard to do with previously existing mapping approaches, like occupancy grids, that are focused on incrementally fusing 3D data into a common world frame. In particular, both their fragile sensitivity to state estimation errors and computational cost can be limiting. We develop an alternative framework, NanoMap, which alleviates the need for global map fusion and enables a motion planner to efficiently query pose-uncertainty-aware local 3D geometric information. The key idea of NanoMap is to store a history of noisy relative pose transforms and search over a corresponding set of depth sensor measurements for the minimum-uncertainty view of a queried point in space. This approach affords a variety of capabilities not offered by traditional mapping techniques: (a) the pose uncertainty associated with 3D data can be incorporated in motion planning, (b) poses can be updated (i.e., from loop closures) with minimal computational effort, and (c) 3D data can be fused lazily for the purpose of planning. We provide an open-source implementation of NanoMap, and analyze its capabilities and computational efficiency in simulation experiments. Finally, we demonstrate in hardware its effectiveness for fast 3D obstacle avoidance onboard a quadrotor flying up to 10 m/s.
Supplemental materials: https://www.youtube.com/watch?v=9a0eEscz1Cs
Under review. Comments welcome.
A Pipeline for Generating Ground Truth Labels for Real {RGBD} Data of Cluttered Scenes
- by Pat Marion and Peter R. Florence and Lucas Manuelli and Russ Tedrake
Deep neural network (DNN) architectures have been shown to outperform tradi- tional pipelines for object segmentation and pose estimation using RGBD data, but the performance of these DNN pipelines is directly tied to how representative the training data is of the true data. Hence a key requirement for employing these methods in practice is to have a large set of labeled data for your specific robotic manipulation task, a requirement that is not generally satisfied by existing datasets. In this paper we develop a pipeline to rapidly generate high quality RGBD data with pixelwise labels and object poses. We use an RGBD camera to collect video of a scene from multiple viewpoints and leverage existing reconstruction techniques to produce a 3D dense reconstruction. We label the 3D reconstruction using a human assisted ICP-fitting of object meshes. By reprojecting the results of labeling the 3D scene we can produce labels for each RGBD image of the scene. This pipeline enabled us to collect over 1,000,000 labeled object instances in just a few days. We use this dataset to answer questions related to how much training data is required, and of what quality the data must be, to achieve high performance from a DNN architecture.
Supplemental materials: Marion17sup.pdf , https://www.youtube.com/watch?v=zoSNUAxiqzE , http://labelfusion.csail.mit.edu
Under review. Comments welcome.
Approximate Hybrid Model Predictive Control for Multi-Contact Push Recovery in Complex Environments
- by Tobia Marcucci and Robin Deits and Marco Gabiccini and Antonio Bicchi and Russ Tedrake
Feedback control of robotic systems interacting with the environment through contacts is a central topic in legged robotics. One of the main challenges posed by this problem is the choice of a model sufficiently complex to capture the discontinuous nature of the dynamics but simple enough to allow online computations. Linear models have proved to be the most effective and reliable choice for smooth systems; we believe that piecewise affine (PWA) models represent their natural extension when contact phenomena occur. Discrete-time PWA systems have been deeply analyzed in the field of hybrid Model Predictive Control (MPC), but the straightforward application of MPC techniques to complex systems, such as a humanoid robot, leads to mixed-integer optimization problems which are not solvable at real-time rates. Explicit MPC methods can construct the entire control policy offline, but the resulting policy becomes too complex to compute for systems at the scale of a humanoid robot. In this paper we propose a novel algorithm which splits the computational burden between an offline sampling phase and a limited number of online convex optimizations, enabling the application of hybrid predictive controllers to higher-dimensional systems. In doing so we are willing to partially sacrifice feedback optimality, but we set stability of the system as an inviolable requirement. Simulation results of a simple planar humanoid that balances by making contact with its environment are presented to validate the proposed controller.
Under review. Comments welcome.
Locomotion Group News
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April 26, 2018. Award. Congratulations to Katy Muhlrad for winning the "Audience Choice Award" at the SuperUROP Showcase for her work on "Using GelSight to Identify Objects by Touch".
July 26, 2017. Defense. Frank Permenter successfully defended his thesis, titled "Reduction methods in semidefinite and conic optimization". Congratulations Frank!
May 19, 2017. Award. Pete Florence was awarded the EECS Masterworks award. Congratulations Pete!
May 19, 2017. Award. Sarah Hensley was awarded the 2017 Best SuperUROP Presentation award. Congratulations Sarah!
May 16, 2017. PhD Defense. Michael Posa successfully defended his thesis, titled "Optimization for Control and Planning of Multi-Contact Dynamic Motion". Congratulations Michael!
May 15, 2017. Award. Our paper describing the planning and control that we implemented on Atlas for the DARPA Robotics Challenge was recognized with the IEEE-RAS Technical Commmittee on Whole-Body Control 2016 Best Paper of the Year award.
January 28, 2017. Video. Amara Mesnik put together a great mini-documentary on MIT's entry in the DARPA Robotics Challenge.
May 13, 2016. PhD Defense. Ani Majumdar has successfully defended his PhD thesis. Congratulations Ani! Click on the link to watch his talk, and check the publications page to read his thesis.
February 24, 2016. Media. NOVA's documentary on the DARPA Robotics Challenge, titled "Rise of the Robots" is online now.
December 7, 2015. PhD Defense. Andy Barry has successfully defended his PhD thesis. Congratulations Andy! Click on the link to watch his talk.
November 18, 2015. In the news. NASA's R5 humanoid robot is coming to MIT. We're very excited to have the opportunity to do research on this amazing platform.
November 5, 2015. Award. Our DRC Team's continuous walking with stereo fusion paper just won the Best Paper Award (Oral) at Humanoids 2015. Congratulations all!
November 5, 2015. In the news. Andy's video of high-speed UAV obstacle avoidance (using only onboard processing) got some great coverage this week. This article by the IEEE Spectrum was particularly nice and insightful. .
October 26, 2015. PhD Defense. Andres Valenzuela just successfully defended his PhD thesis. Congratulations Andres!
May 29, 2015. News. We're heading off to the DARPA Robotics Challenge. We've been posting some fun videos to our YouTube site (linked here). Wish us luck!
May 26, 2015. News. Benoit Landry has submitted his Masters Thesis on Aggressive Quadrotor Flight in Dense Clutter. Be sure to check out his cool video.
May 28, 2015. News. Scott Kuindersma has accepted a tenure-track position at Harvard starting this fall. Congratulations Scott!
November 20, 2014. Award. Robin Deits' paper on Mixed-integer optimization for footstep planning just won the Best Paper Award (Oral) at Humanoids 2014. Congratulations Robin!
December 31, 1969. Award. Benoit Landry has been awarded the 2014 Siebel Scholarship. Congratulations Benoit!
June 18, 2014. News. Ram Vasudevan has officially accepted a tenure-track position at the University of Michigan, Ann Arbor. Congratulations Ram! Go Blue!