Robot Locomotion Group
The Robot Locomotion Group is a part of the CSAIL Center for Robotics.
Here we present a closed-form solution solution to the continuous time-varying linear quadratic regulator (LQR) problem for the zero-moment point (ZMP) tracking controller. This generalizes previous analytical solutions for gait generation by allowing 'soft' tracking (with a quadratic cost) of the desired ZMP, and by providing the feedback gains for the resulting time-varying optimal controller. This enables extremely fast computation, with the number of operations linear in the number of spline segments representing the desired ZMP. Results are presented using the Atlas humanoid robot where dynamic walking is achieved by recomputing the optimal controller online.
Under review. Comments welcome.
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
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.
Under review. Comments welcome.
This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot designed by Boston Dynamics, Inc.
Under review. Comments welcome.
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 exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. 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. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance.
Supplemental materials: https://www.youtube.com/watch?v=l3TEnNAyjmg
To appear in Humanoids 2014.
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.
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.