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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.
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.
Locomotion Group Paper and Multimedia News 
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Planning robust walking motion on uneven terrain via convex optimization
- by Hongkai Dai and Russ Tedrake
In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force/torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit.
Under review. Comments welcome.
Balance control using center of mass height variation: limitations imposed by unilateral contact
- by Twan Koolen and Michael Posa and Russ Tedrake
Maintaining balance is fundamental to legged robots. The most commonly used mechanisms for balance control are taking a step, regulating the center of pressure (ankle strategies), and to a lesser extent, changing centroidal angular momentum (e.g., hip strategies). In this paper, we disregard these three mechanisms, instead focusing on a fourth: varying center of mass height. We study a 2D variable-height center of mass model, and analyze how center of mass height variation can be used to achieve balance, in the sense of convergence to a fixed point of the dynamics. In this analysis, we pay special attention to the constraint of unilateral contact forces. We first derive a necessary condition that must be satisfied to be able to achieve balance. We then present two control laws, and derive their regions of attraction in closed form. We show that one of the control laws achieves balance from any state satisfying the necessary condition for balance. Finally, we briefly discuss the relative importance of CoM height variation and other balance mechanisms.
Under review. Comments welcome.
- by Peter R. Florence and John Carter and Russ Tedrake
We present a method for robust high-speed quadrotor flight through unknown cluttered environments using a fast approximation of collision probabilities. Motivated by experiments in which the difficulty of accurate state estimation was a primary limitati...
Under review. Comments welcome.
Localizing External Contact Using Proprioceptive Sensors: The Contact Particle Filter
- by Lucas Manuelli and Russ Tedrake
In order for robots to interact safely and intelligently with their environment they must be able to reliably estimate and localize external contacts. This paper introduces CPF, the Contact Particle Filter, which is a general algorithm for detecting and localizing external contacts on rigid body robots without the need for external sensing. CPF finds external contact points that best explain the observed external joint torque, and returns sensible estimates even when the external torque measurement is corrupted with noise. We demonstrate the capability of the CPF to track multiple external contacts on a simulated Atlas robot, and compare our work to existing approaches.
Supplemental materials: http://youtu.be/ckvsMK0QhB0
Under review. Comments welcome.
Funnel Libraries for Real-time Robust Feedback Motion Planning
- by Anirudha Majumdar and Russ Tedrake
We consider the problem of generating motion plans for a robot that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, and disturbances. Furthermore, we consider scenarios where these plans must be generated in real-time, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our approach is to pre-compute a library of funnels along different maneuvers of the system that the state is guaranteed to remain within (despite bounded disturbances) when the feedback controller corresponding to the maneuver is executed. We leverage powerful computational machinery from convex optimization (sums-of-squares programming in particular) to compute these funnels. The resulting funnel library is then used to sequentially compose motion plans at runtime while ensuring the safety of the robot. A major advantage of the work presented here is that by explicitly taking into account the effect of uncertainty, the robot can evaluate motion plans based on how vulnerable they are to disturbances. We demonstrate and validate our method using extensive hardware experiments on a small fixed-wing airplane avoiding obstacles at high speed (~12 mph), along with thorough simulation experiments of ground vehicle and quadrotor models navigating through cluttered environments. To our knowledge, the resulting hardware demonstrations on a fixed-wing airplane constitute one of the first examples of provably safe and robust control for robotic systems with complex nonlinear dynamics that need to plan in realtime in environments with complex geometric constraints.
Preliminary version on arxiv. Comments welcome.
Locomotion Group News
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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!
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.