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Robot Locomotion Group




    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.

    We are currently participating in the DARPA Robotics Challenge. Make sure you check out our videos here.

    The Robot Locomotion Group is a part of the CSAIL Center for Robotics.

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Locomotion Group Paper and Multimedia News  

    Control and Verification of High-Dimensional Systems with {DSOS} and {SDSOS} Programming
      by Anirudha Majumdar and Amir Ali Ahmadi and Russ Tedrake

      In this paper, we consider linear programming (LP) and second order cone programming (SOCP) based alternatives to sum of squares (SOS) programming and apply this framework to high-dimensional problems arising in control applications. Despite the wide acceptance of SOS programming in the control and optimization communities, scalability has been a key challenge due to its reliance on semidefinite programming (SDP) as its main computational engine. While SDPs have many appealing features, current SDP solvers do not approach the scalability or numerical maturity of LP and SOCP solvers. Our approach is based on the recent work of Ahmadi and Majumdar [1], which replaces the positive semidefiniteness constraint inherent in the SOS approach with stronger conditions based on diagonal dominance and scaled diagonal dominance . This leads to the DSOS and SDSOS cones of polynomials, which can be optimized over using LP and SOCP respectively. We demonstrate this approach on four high dimensional control problems that are currently well beyond the reach of SOS programming: computing a region of attraction for a 22 dimensional system, analysis of a 50 node network of oscillators, searching for degree 3 controllers and degree 8 Lyapunov functions for an Acrobot system (with the resulting controller validated on a hardware platform), and a balancing controller for a 30 state and 14 control input model of the ATLAS humanoid robot. While there is additional conservatism introduced by our approach, extensive numerical experiments on smaller instances of our problems demonstrate that this conservatism can be small compared to SOS programming.

      Final submission. To appear at CDC 2014.

    Pushbroom Stereo for High-Speed Navigation in Cluttered Environments

      by Andrew J. Barry and Russ Tedrake

      We present a novel stereo vision algorithm that is capable of obstacle detection on a mobile-CPU processor at 120 frames per second. Our system performs a subset of standard block-matching stereo processing, searching only for obstacles at a single depth. By using an onboard IMU and state-estimator, we can recover the position of obstacles at all other depths, building and updating a full depth-map at framerate. Here, we describe both the algorithm and our implementation on a high-speed, small UAV, flying at over 20 MPH (9 m/s) close to obstacles. The system requires no external sensing or computation and is, to the best of our knowledge, the first high-framerate stereo detection system running onboard a small UAV.

      Supplemental materials: http://arxiv.org/abs/1407.7091

      Initial submission. Comments welcome.

    An Architecture for Online Affordance-based Perception and Whole-body Planning

      by Maurice Fallon and Scott Kuindersma and Sisir Karumanchi and Matthew Antone and Toby Schneider and Hongkai Dai and Claudia P\'{e}rez D'Arpino and Robin Deits and Matt DiCicco and Dehann Fourie and Twan Koolen and Pat Marion and Michael Posa and Andr\'{e}s Valenzuela and Kuan-Ting Yu and Julie Shah and Karl Iagnemma and Russ Tedrake and Seth Teller

      The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robot's sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule.

      Final submission. To appear in the Journal of Field Robotics.

    Footstep Planning on Uneven Terrain with Mixed-Integer Convex Optimization

      by Robin Deits and Russ Tedrake

      We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program ({MIQCQP}). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robotÂ’s feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robotÂ’s reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake {MATLAB} toolbox.

      Supplemental materials: http://youtu.be/hGhCTPQuMy4

      Under review. Comments welcome.

    Whole-body Motion Planning with Simple Dynamics and Full Kinematics

      by Hongkai Dai and Andr\'es Valenzuela and Russ Tedrake

      To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full- body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We present an approach to generate whole-body motions using a simple dynamics model, which enforces that the linear and angular momentum of the robot be consistent with the external wrenches on the robot, and a full-body kinematics model that enforces rich geometric constraints, such as end-effector positioning or collision avoidance. We obtain a trajectory for the robot and profiles of contact wrenches by solving a nonlinear optimization problem (NLP). We further demonstrate that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot.

      Supplemental materials: http://youtu.be/2Vry-th8g2s

      Under review. Comments welcome.


Locomotion Group News  

    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!

    June 16, 2014. News. Joe Moore has officially accepted a position at the Johns Hopkins Applied Phsyics Lab. Congratulations Joe!

    May 27, 2014. PhD Defense. Joseph Moore officially defended his PhD. You can watch his defense on the group talks page. Congratulations Joe!

    December 21, 2013. News. Team MIT advances to the next round in the DARPA Robotics Challenge.

    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 Siebel 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!

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