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 empirical success of Reinforcement Learning (RL) in contact-rich manipulation leaves much to be understood from a model-based perspective, where the key difficulties are often attributed to (i) the explosion of contact modes, (ii) stiff, non-smooth contact dynamics and the resulting exploding / discontinuous gradients, and (iii) the non-convexity of the planning problem. The stochastic nature of RL addresses (i) and (ii) by effectively sampling and averaging the contact modes. On the other hand, model-based methods have tackled the same challenges by smoothing contact dynamics analytically. Our first contribution is to establish the theoretical equivalence of the two smoothing schemes for simple systems, and provide qualitative and empirical equivalence on several complex examples. In order to further alleviate (ii), our second contribution is a convex, differentiable and quasi-dynamic formulation of contact dynamics, which is amenable to both smoothing schemes, and has proven through experiments to be highly effective for contact-rich planning. Our final contribution resolves (iii), where we show that classical sampling-based motion planning algorithms can be effective in global planning when contact modes are abstracted via smoothing. Applying our method on a collection of challenging contact-rich manipulation tasks, we demonstrate that efficient model-based motion planning can achieve results comparable to RL with dramatically less computation.
Supplemental materials: https://youtu.be/12Ew4xC-VwA
Preprint. Comments welcome.
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.
Preprint. Comments welcome.
Configuration space (C-space) has played a central role in collision-free motion planning, particularly for robot manipulators. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing collision-free C-space regions with rigorous certificates due to the complexities of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge method for generating such regions and certificates through convex optimization. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parametrization of the configuration space which are guaranteed to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Our regions are generated by alternating between two convex optimization problems: (1) a simultaneous search for a maximal-volume ellipse inscribed in a given polytope and a certificate that the polytope is collision-free and (2) a maximal expansion of the polytope away from the ellipse which does not violate the certificate. The volume of the ellipse and size of the polytope are allowed to grow over several iterations while being collision-free by construction. Our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and scales to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in a 3-DOF example where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa and a 12-DOF bimanual manipulator.
Preprint. Comments welcome.
We introduce the first direct policy search algorithm which provably converges to the globally optimal dynamic filter for the classical problem of predicting the outputs of a linear dynamical system, given noisy, partial observations. Despite the ubiquity of partial observability in practice, theoretical guarantees for direct policy search algorithms, one of the backbones of modern reinforcement learning, have proven difficult to achieve. This is primarily due to the degeneracies which arise when optimizing over filters that maintain internal state. In this paper, we provide a new perspective on this challenging problem based on the notion of informativity, which intuitively requires that all components of a filter's internal state are representative of the true state of the underlying dynamical system. We show that informativity overcomes the aforementioned degeneracy. Specifically, we propose a regularizer which explicitly enforces informativity, and establish that gradient descent on this regularized objective - combined with a ``reconditioning step'' - converges to the globally optimal cost a (1/T). Our analysis relies on several new results which may be of independent interest, including a new framework for analyzing non-convex gradient descent via convex reformulation, and novel bounds on the solution to linear Lyapunov equations in terms of (our quantitative measure of) informativity.
Under review. Comments welcome.
Differentiable simulators promise faster computation time for reinforcement learning by replacing zeroth-order gradient estimates of a stochastic objective with an estimate based on first-order gradients. However, it is yet unclear what factors decide the performance of the two estimators on complex landscapes that involve long-horizon planning and control on physical systems, despite the crucial relevance of this question for the utility of differentiable simulators. We show that characteristics of certain physical systems, such as stiffness or discontinuities, may compromise the efficacy of the first-order estimator, and analyze this phenomenon through the lens of bias and variance. We additionally propose an α-order gradient estimator, with α∈[0,1], which correctly utilizes exact gradients to combine the efficiency of first-order estimates with the robustness of zero-order methods. We demonstrate the pitfalls of traditional estimators and the advantages of the α-order estimator on some numerical examples.
Under review. Comments welcome.
June 17, 2022. PhD Defense. Congratulations to Yunzhu Li for successfully defending his PhD thesis!
June 17, 2022. PhD Defense. Congratulations to Greg Izatt for successfully defending his PhD thesis!
August 15, 2020. Talks on Zoom. For better or worse, most research talks these days 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.
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