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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. We
believe that this challenge involves a tight coupling between
mechanical design and underactuated nonlinear control, and that tools
from machine learning and optimal control can be used to produce this
coupling when classical control techniques fail. Our projects include
minimally-actuated dynamic walking on moderate terrain, quadrupedal
locomotion on extreme terrain, fixed-wing acrobatics, flapping-winged
flight, and feedback control for fluid dynamics.
The Robot Locomotion Group is a part of the CSAIL Center for Robotics.
Locomotion Group Paper and Multimedia News 
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Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures
- by Anirudha Majumdar and Ram Vasudevan and Mark M. Tobenkin and Russ Tedrake
The construction of feedback control laws for underactuated nonlinear robotic systems with input saturation limits is crucial for dynamic robotic tasks such as walking, running, or flying. Existing techniques for feedback control design are either restricted to linear systems, rely on discretizations of the state space, or require solving a non-convex optimization problem that requires feasible initialization. This paper presents a method for designing feedback controllers for polynomial systems that maximize the size of the timelimited backwards reachable set (BRS). In contrast to traditional approaches based on Lyapunovs criteria for stability, we rely on the notion of occupation measures to pose this problem as an infinitedimensional linear program which can then be approximated in finite dimension via semidefinite programs (SDP)s. The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS which is well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on six nonlinear systems. Comparisons to an infinitehorizon linear quadratic regulator approach and an approach relying on Lyapunovs criteria for stability are also included in order to illustrate the improved performance of the presented technique.
Under review. Comments welcome.
An Efficiently Solvable Quadratic Program for Stabilizing Dynamic Locomotion
- by Scott Kuindersma and Frank Permenter and Russ Tedrake
We describe a whole-body dynamic walking controller implemented as a compact, convex quadratic program. The controller minimizes an optimal control condition on a simple model of the walking system while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with an active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve real-time control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas humanoid in the DARPA Virtual Robotics Challenge.
Supplemental materials: http://arxiv.org/abs/1311.1839v1
Under review. Comments welcome.
A Summary of Team {MIT}'s Approach to the Virtual Robotics Challenge
- by R. Tedrake and M. Fallon and S. Karumanchi and S. Kuindersma and M. Antone and T. Schneider and T. Howard and M. Walter and H. Dai and R. Deits and M. Fleder and D. Fourie and R. Hammoud and S. Hemachandra and P. Ilardi and C. P\'erez-D'Arpino and S. Pill
Supplemental materials: http://www.youtube.com/watch?v=CXHLntka5q4
Under review. Comments welcome.
Flying Between Obstacles with an Autonomous Knife-Edge Maneuver
- by Andrew J. Barry and Tim Jenks and Anirudha Majumdar and Huai-Ti Lin and Ivo G. Ros and Andrew Biewener and Russ Tedrake
Supplemental materials: http://www.youtube.com/watch?v=LGel-SdAIRg
Under review. Comments welcome.
Locomotion Group News
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October 2, 2013. Award. Michael Posa has been awarded the 2013 Rolf Locher Graduate Fellowship. Congratulations Michael!
September 14, 2013. News. The Robot Locomotion Group hosted the evening session of the 2014 Boston Barefoot Running Festival.
September 11, 2013. In the News. Tough robo-challenge casts robots as rescuers.
June 27, 2013. In the News. Team MIT Completes First Hurdle in DARPA Robotics Challenge.
May 9, 2013. Award. Ani Majumdar and Amir Ali Ahmadi's paper on nonlinear control design along trajectories just won the Best Paper Award at ICRA 2013. Congratulations!
April 10, 2013. Award. Mike Posa and Mark Tobenkin's paper on SOS Verification of Rigid Bodies through Contact won the Best Paper Award at the 16th International Conference on Hybrid Systems: Computation and Control. Congratulations!
August 20, 2012. Award. Ani Majumdar has been awarded the 2012 Seibel Scholarship. Congratulations Ani!
July 25, 2012. In the News. New Aircraft Capable of Fast, Accurate and Repeatable Flight.
May 20, 2012. Award. Russ is the recipient of the 2012 Ruth and Joel Spira Award for Distinguished Teaching.
May 18, 2012. Thesis Defense. John Roberts has successfully defended his thesis on Control of Fluid-Body Systems via Real-Time PIV. Congraulations John!
March 26, 2012. In the news. Our work on flapping flight and perching was featured in the article "A flapping of wings" in this week's issue of Science Magazine. Photo by Jason Dorfman.
June 2, 2011. Award Finalist. Jacob Steinhardt's RSS 2011 paper on stochastic verification was a finalist for the conference Best Student Paper Award. Congratulations Jacob.
May 25, 2011. RSS Workshop. We are co-organizing a workshop at RSS 2011 on "integrated planning and control". As a part of the workshop, we will give a short tutorial on LQR-Trees and Sums-of-Squares Verification for Feedback Motion Planning, which will include tutorial software.
May 12, 2011. Award. Jacob Steinhardt has been awarded the 2011 Robert M. Fano UROP (Undergraduate Research Opportunities Program) award for his outstanding work as an undergraduate researcher. Congratulations Jacob!
May 12, 2011. Award. Hongkai Dai has been awarded the 2011 Frederick C. Hebbie Teaching Award for his outstandng performance as the TA for 6.832 this spring. Congratulations Hongkai!
April 5, 2011. Award. Andy Barry has been awarded an NSF Graduate Research Fellowship. Congratulations Andy!
April 4, 2011. News. CSAIL has posted a short news item about our MURI project.
February 13, 2011. News. Russ has accepted a courtesy appointment with the MIT Department of Aeronautics and Astronautics.
December 4, 2010. Software. We have posted example code for SOS verification of finite-time invariance (e.g. "funnels") along trajectories.
November 28, 2010. Slideshow. A random collection of images from our group lab space appeared in the Sunday edition of the New York Times (Business Day).
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