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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. 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.

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Locomotion Group Paper and Multimedia News  

    Optimization and stabilization of trajectories for constrained dynamical systems
      by Michael Posa and Scott Kuindersma and Russ Tedrake

      Contact constraints, such as those between a foot and the ground or a hand and an object, are inherent in many robotic tasks. These constraints define a manifold of feasible states; while well understood mathematically, they pose numerical challenges to many algorithms for planning and controlling whole-body dynamic motions. In this paper, we present an approach to the synthesis and stabilization of complex trajectories for both fully-actuated and underactuated robots subject to contact constraints. We introduce an extension to the direct collocation trajectory optimization algorithm that naturally incorporates the manifold constraints to produce a nominal trajectory with third-order integration accuracy— a critical feature for achieving reliable tracking control. We adapt the classical time-varying linear quadratic regulator to produce a local cost-to-go in the tangent plane of the manifold. Finally, we descend the cost-to-go using a quadratic program that incorporates unilateral friction and torque constraints. This approach is demonstrated on three complex walking and climbing locomotion examples in simulation.

      Supplemental materials: https://youtu.be/62GIUJC60P4

      Under review. Comments welcome.

    Aggressive Quadrotor Flight through Cluttered Environments Using Mixed Integer Programming

      by Benoit Landry and Robin Deits and Peter R. Florence and Russ Tedrake

      Quadrotor flight has typically been limited to sparse environments due to numerical complications that arise when dealing with large numbers of obstacles. We hypothesized that it would be possible to plan and robustly execute trajecto- ries in obstacle-dense environments using the novel Iterative Regional Inflation by Semidefinite programming algorithm (IRIS), mixed-integer semidefinite programs (MISDP), and a model-based controller. Unlike sampling-based approaches, the algorithm guarantees non-penetration of the trajectories even with small obstacles such as strings. We present experimental validation of this hypothesis by aggressively flying a small quadrotor (34g, 92mm rotor to rotor) in a series of indoor environments including a cubic meter volume containing 20 interwoven strings.

      Supplemental materials: https://www.youtube.com/watch?v=v-s564NoAu0

      Under review. Comments welcome.

    A closed-form solution for real-time {ZMP} gait generation and feedback stabilization

      by Tedrake, Russ and Kuindersma, Scott and Deits, Robin and Miura, Kanako

      Here we present a closed-form solution to the continuous time-varying linear-quadratic regulator problem for zero-moment point (ZMP) tracking. This generalizes previous analytical solutions for gait generation by allowing ``soft

      Under review. Comments welcome.

    Planning and Control for Quadrotor Flight through Cluttered Environments

      by Benoit Landry

      Previous demonstrations of autonomous quadrotor flight have typically been limited to sparse environments due to the computational burden associated with planning for a large number of obstacles. We hypothesized that it would be possible to do efficient planning and robust execution in obstacle-dense environments using the novel Iterative Regional Inflation by Semidefinite programming algorithm (IRIS), mixedinteger semidefinite programs (MISDP), and model-based control approaches. Here, we present experimental validation of this hypothesis using a small quadrotor in a series of indoor environments including a cubic meter volume containing 20 interwoven strings. We chose one of the smallest hardware platforms available on the market (34g, 92mm rotor to rotor), allowing for these dense environments and explain how to overcome the many system identification, state estimation, and control problems that result from the small size of the platform and the complexity of the environments.

      Supplemental materials: https://www.youtube.com/watch?v=v-s564NoAu0

    Synthesis and optimization of force closure grasps via sequential semidefinite programming

      by Hongkai Dai and Anirudha Majumdar and Russ Tedrake

      In this paper we present a novel approach for synthesizing and optimizing both positions and forces in force closure grasps. This problem is a non-convex optimization problem in general since it involves constraints that are bilinear; in particular, computing wrenches involves a bilinear product between grasp contact points and contact forces. Thus, conventional approaches to this problem typically employ general purpose gradient-based nonlinear optimization. The key observation of this paper is that the force closure grasp synthesis problem can be posed as a Bilinear Matrix Inequality (BMI), for which there exist efficient solution techniques based on semidefinite programming. We show that we can synthesize force closure grasps on different geometric objects, and by maximizing a lower bound of a grasp metric, we can improve the quality of the grasp. While this approach is not guaranteed to find a solution, it has a few distinct advantages. First, we can handle non-smooth but convex positive semidefinite constraints, which can often be important. Second, in contrast to gradient-based approaches we can prove infeasibility of problems. We demonstrate our method on a 15 joint robot model grasping objects with various geometries. The code is included in https://github.com/RobotLocomotion/drake

      Under review. Comments welcome.

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