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Neural Network Control Project
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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Direct Trajectory Optimization of Rigid Body Dynamical Systems Through Contact
- by Michael Posa and Russ Tedrake
Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Most state-of-the-art techniques treat the discontinuous dynamics of contact as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning through contact that eliminates the requirement for an a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem (LCP) for forward simulation, the proposed algorithm leverages Sequential Quadratic Programming (SQP) to resolve contact constraint forces while simultaneously optimizing a trajectory and satisfying nonlinear complementarity constraints. The method scales well to high dimensional systems with large numbers of possible modes. We demonstrate the approach using three increasingly complex systems: rotating a pinned object with a finger, planar walking with the Spring Flamingo robot, and high speed bipedal running on the FastRunner platform.
Under review. Comments welcome.
Robust Online Motion Planning with Regions of Finite Time Invariance
- by Anirudha Majumdar and Russ Tedrake
In this paper we consider the problem of generating motion plans for a nonlinear dynamical system that are guaranteed to succeed despite uncertainty in the environment, parametric model uncertainty, disturbances, and/or errors in state estimation. Furthermore, we consider the case where these plans must be generated online, because constraints such as obstacles in the environment may not be known until they are perceived (with a noisy sensor) at runtime. Our work augments the traditional trajectory library approach by designing controllers that stabilize the nominal trajectories in the library and computing regions of finite time invariance ('funnels') for the resulting closed loop system. We leverage sums-of-squares programming in order to efficiently compute funnels which take into account bounded disturbances and uncertainty. 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 our method on a simulation of a plane flying through a two dimensional forest of polygonal trees. Disturbances are introduced in the form of a bounded 'cross-wind' and parametric model uncertainty takes the form of uncertainty in the speed of the plane.
Under review. Comments welcome.
Algebraic Verification for Parameterized Motion Planning Libraries
- by Anirudha Majumdar and Mark Tobenkin and Russ Tedrake
Recent progress in algorithms for estimating regions of attraction and invariant sets of nonlinear systems has led to the application of these techniques to motion planning in complex environments. In most instances, the verification occurs offline as the algorithms are still too computationally demanding for real-time implementation; as a result any online planner is restricted to applying the finite set of motion plans that were verified offline. In this paper we attempt to present a partial remedy by algebraically verifying families of parameterized feedback controllers, and give a specific example using LQR controllers parameterized by their goal or nominal motion. We formulate this verification using robust region of attraction techniques in sums-of-squares optimization, and show that perturbations of a Lyapunov or Riccati equation can be used to provide algebraically parameterized Lyapunov candidates. The resulting verified “funnels” then provide a parameterized motion library that can be used efficiently in online planning. We present a number of numerical examples to demonstrate the effectiveness of our approach.
Under review. Comments welcome.
Design, Analysis and Learning Control of a Fully Actuated Micro Wind Turbine
- by J. Zico Kolter and Zachary Jackowski and Russ Tedrake
Wind power represents one of the most promising sources of renewable energy, and improvements to wind turbine design and control can have a significant impact on energy sustainability. In this paper we make two primary contributions: first, we develop and present a actuated micro wind turbine intended for research purposes. While most academic work on wind turbine control has largely focused on simulated evaluations, most turbine simulators are quite limited in their ability to model unsteady aerodynamic effects induced by the turbine; thus, there is a huge value to validating wind turbine control methods on a physical system, and the platform we present here makes this possible at a very low cost. The second contribution of this paper a novel policy search method, applied to optimizing power production in Region II wind speeds. Our method is similar in spirit to Reinforcement Learning approaches such as the REINFORCE algorithm, but explicitly models second order terms of the cost function and makes efficient use of past execution data. We evaluate this method on the physical turbine and show it it is able to quickly and repeatably achieve near-optimal power production within about a minute of execution time and without any a priori model of the system.
Under review. Comments welcome.
Finite-time Regional Verification of Stochastic Nonlinear Systems
- by Jacob Steinhardt and Russ Tedrake
Recent trends pushing robots into unstructured environments with limited sensors have motivated considerable work on planning under uncertainty and stochastic optimal control, but these methods typically do not provide guaranteed performance. Here we consider the problem of bounding the probability of failure (defined as leaving a finite region of state space) over a finite time for stochastic nonlinear systems with continuous state. Our approach searches for exponential barrier functions that provide bounds using a variant of the classical supermartingale result. We provide a relaxation of this search to a semidefinite program, yielding an efficient algorithm that provides rigorous upper bounds on the probability of failure for the original nonlinear system. We give a number of numerical examples in both discrete and continuous time that demonstrate the effectiveness of the approach.
Extended journal version of RSS 2011 paper. Under review. Comments welcome.
Locomotion Group News
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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).
August 12, 2010. Video. Lecture videos from the 2010 Dynamic Walking meeting are now available.
July 20, 2010. Award. Rick Cory was named the 2010 Boeing Engineering Student of the Year. Congratulations Rick!! You can watch Boeing's video here.
July 20, 2010. News. Our work on perching was spotlighted on the MIT homepage.
July 16, 2010. MURI. A team with members from MIT, Carnegie Mellon, New York University, Harvard University, and Wageningen was selected for funding on an ONR MURI for UAVs flying through dense forest and urban environments.
July 8, 2010. Dynamic Walking 2010. The dynamic walking meeting was held at MIT. Videos of most of the presentations will be available in the next few days.
June 30, 2010. Talk. Russ gives the Early Career Spotlight Talk at RSS 2010.
May 12, 2010. Thesis Defense. Rick Cory successfully defended his thesis entitled Supermaneuverable Perching Robots. Congratulations Rick! The video is available on the Group Talks page.
May 4, 2010. Award. The IEEE Technical Committee on Robot Learning wins the 2010 Most Active Technical Committee Award
May 1, 2010. Outreach. Rick Cory led a hands-on demonstration with robotic birds at the Cambridge Science Festival.
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