Video Highlights
Robotics Challenge


Positions Available


Robot Locomotion Group




    The goal of our research is to build machines which exploit their natural dynamics to achieve extraordinary agility, efficiency, and robustness using rigorous tools from dynamical systems, control theory, and machine learning. Our current focus in on robotic manipulation, because the revolution in recent machine learning has opened a pathway in these applications to merging control theory and perception at a level that has never been considered before; ideas like "intuitive physics" and "common-sense reasoning" will meet with rigorous ideas like "model-order reduction" and "robust/adaptive control". It's going to be a great few years!

    Our previous projects have included dynamics and control for humanoid robots, 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.

    Follow us on facebook and/or twitter.


Locomotion Group Paper and Multimedia News  

    Lyapunov-stable neural-network control
      by Hongkai Dai and Benoit Landry and Lujie Yang and Marco Pavone and Russ Tedrake

      Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical success, these controllers still lack theoretical guarantees on their performance, such as Lyapunov stability (i.e., all trajectories of the closed-loop system are guaranteed to converge to a goal state under the control policy). This is in stark contrast to traditional model-based controller design, where principled approaches (like LQR) can synthesize stable controllers with provable guarantees. To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability. Our approach formulates the Lyapunov condition verification as a mixed-integer linear program (MIP). Our MIP verifier either certifies the Lyapunov condition, or generates counter examples that can help improve the candidate controller and the Lyapunov function. We also present an optimization program to compute an inner approximation of the region of attraction for the closed-loop system. We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller. The code is open sourced at https://github.com/StanfordASL/neural-network-lyapunov.

      Final version accepted to RSS.

    Shortest Paths in Graphs of Convex Sets

      by Tobia Marcucci and Jack Umenberger and Pablo A. Parrilo and Russ Tedrake

      Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source to a target vertex. We consider a generalization of this classical problem in which the position of each vertex in the graph is a continuous decision variable, constrained to lie in a corresponding convex set. The length of an edge is then defined as a convex function of the positions of the vertices it connects. Problems of this form arise naturally in road networks, robot navigation, and even optimal control of hybrid dynamical systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong mixed-integer convex formulation based on perspective functions. This formulation has a very tight convex relaxation and allows to efficiently find globally-optimal paths in large graphs and in high-dimensional spaces.

      Supplemental materials: https://arxiv.org/abs/2101.11565

      First arxiv submission. Comments welcome.

    A Convex Quasistatic Time-stepping Scheme for Rigid Multibody Systems with Contact and Friction

      by Pang, Tao and Tedrake, Russ

      Motion planning for robotic manipulation makes heavy use of quasistatic models, but these same models have not yet proven useful for simulation. This is because in many multi-contact situations, the quasistatic models do not describe a unique next state for the system. A planner is able to use these models optimistically (checking only for feasibility of a motion), but simulation requires more. In this work, we enable quasistatic models to uniquely determine contact forces by modeling actuated robots as impedances instead of prescribed motions. Using this model with a well-known convex relaxation for Coulomb friction, time-stepping of quasistatic models can be formulated as a convex Quadratic Program (QP). This convex relaxation does admit mild non-physical behavior between relatively-sliding objects, but through simulations of various complexity, we show that the proposed quasistatic time-stepping scheme generates mostly physically-realistic behaviors, and scales well with the complexity of the simulated systems.

      Supplemental materials: https://youtu.be/gJ5h_Kx8fJc

      Under review. Comments welcome.

    Identifying External Contacts from Joint Torque Measurements on Serial Robotic Arms and Its Limitations

      by Pang, Tao and Umenberger, Jack and Tedrake, Russ

      The ability to detect and estimate external contacts is essential for robot arms to operate in unstructured environments occupied by humans. However, most robot arms are not equipped with adequate sensors to detect contacts on their entire body. What many robot arms do have is torque sensors for individual joints. Through a quantitative analysis, we argue that it is fairly likely for two distinct contacts on the robot’s surface to generate almost identical joint torque measurements. When this happens, the best contact estimate achievable is the set of possible contact positions, all of which would reproduce the measured joint torque. Searching for elements of this set is equivalent to solving to global optimality a nonlinear program. By combining rejection sampling with gradient descent, we propose a contact estimation method which in practice finds all local optima of the nonlinear program at real-time rates. In addition, we propose an active contact exploration method which falsifies spurious contact estimates in the set of local optima by making small motions around the robot’s current configuration. The proposed methods highlight the caveats of contact estimation from only joint torque, which, coupled with known limitations of such estimators, suggest that a more capable sensor is probably needed for robust whole-body contact estimation.

      Supplemental materials: https://youtu.be/3TjevLu55V8

      Under review. Comments welcome.

    Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems

      by Sinha, Aman and O'Kelly, Matthew and Duchi, John and Tedrake, Russ

      Learning-based methodologies increasingly find applications in safety-critical domains like autonomous driving and medical robotics. Due to the rare nature of dangerous events, real-world testing is prohibitively expensive and unscalable. In this work, we employ a probabilistic approach to safety evaluation in simulation, where we are concerned with computing the probability of dangerous events. We develop a novel rare-event simulation method that combines exploration, exploitation, and optimization techniques to find failure modes and estimate their rate of occurrence. We provide rigorous guarantees for the performance of our method in terms of both statistical and computational efficiency. Finally, we demonstrate the efficacy of our approach on a variety of scenarios, illustrating its usefulness as a tool for rapid sensitivity analysis and model comparison that are essential to developing and testing safety-critical autonomous systems.

      Under review. Comments welcome.


Locomotion Group News  

    August 15, 2020. Talks on Zoom. For better or worse, more of our talks are now online. I've posted a handful of links to new talks, including Russ on Lex Fridman's AI Podcast, and at the IFRR Colloquium on the Roles of Physics-Based Models and Data-Driven Learning in Robotics.

    July 20, 2020. PhD Defense. Congratulations to Lucas Manuelli for successfully defending his PhD thesis!

    May 29, 2020. PhD Defense. Congratulations to Shen Shen for successfully defending her thesis!

    September 18, 2019. PhD Defense. Congratulations to Twan Koolen for successfully defending his thesis!

    August 19, 2019. PhD Defense. Congratulations to Pete Florence for successfully defending his thesis!

    October 15, 2018. PhD Defense. Congratulations to Robin Deits for successfully defending his thesis!

    October 3, 2018. Award. Congratulations to Pete Florence and Lucas Manuelli whose paper Dense Object Nets: Learning Dense Visual Object Descriptors By and For Robotic Manipulation won the Conference Best Paper Award at CoRL 2018!

    September 19, 2018. Award. Congratulations to Pete Florence and Lucas Manuelli whose paper Dense Object Nets: Learning Dense Visual Object Descriptors By and For Robotic Manipulation won the first ever Amazon Robotics Best Technical Paper Award (2018).

    June 18, 2018. Award. Congratulations to Ani Majumdar whose paper Funnel libraries for real-time robust feedback motion planning won the first ever International Journal of Robotics Research Paper of the Year (2017).

    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.

For Group Members: