The Agile Robotics Lab, within the Harvard School of Engineering and Applied Sciences, conducts basic research on optimization, control, and learning algorithms for controlling dynamic walking, manipulating, and flying robots. We design algorithms for the next generation of fast, graceful, and robust robots that will narrow the gap between mechanical and biological performance. Current projects include developing algorithms for robust legged locomotion, control and estimation for small-scale morphing wing aircraft, and real-time optimization of human assistive devices. For more details, check out our research summary and publications

# We completed our first round of wind tunnel tests on our perching UAV prototype

December 6, 2016

More details can be found in our upcoming AIAA SciTech paper.

# Paper accepted to CDC 2016

August 18, 2016

Check out our new paper entitled "Derivative-Free Trajectory Optimization with Unscented Dynamic Programming" here!

# Zac Manchester joins Starshot Advisory Committee

April 14, 2016

Our postdoc, Zachary Manchester, will serve on the Advisory Committee for project Starshot led by Yuri Milner and Stephen Hawking (http://breakthroughinitiatives.org/News/4). Go Zac!

# Paper accepted to ICRA 2016

January 20, 2016

Our paper entitled "Optimization and Stabilization of Trajectories for Constrained Dynamical Systems" was accepted to ICRA 2016. PDF and video here.

# New robotics course @ Harvard in Spring 2016

August 20, 2015

Scott will be teaching a new course entitled CS 284: Optimization Algorithms for Robotics in Spring 2016. Harvard students interested in taking it can find the syllabus in the course catalog.

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## Recent Publications

Z. R. Manchester, J. I. Lipton, R. J. Wood, and S. Kuindersma, “A Variable Forward-Sweep Wing Design for Improved Perching in Micro Aerial Vehicles,” in AIAA SciTech Forum, 2017.Abstract

A micro aerial vehicle with a variable forward-sweep wing is proposed with the goal of enhancing performance and controllability during high-angle-of-attack perching maneuvers. Data is presented from a series of wind tunnel experiments to quantify the aerodynamic effects of forward sweep over a range of angles of attack from -25 degrees to +75 degrees. A nonlinear dynamics model is constructed using the wind tunnel data to gain further insight into aircraft flight dynamics and controllability. Simulated perching trajectories optimized with a direct collocation method indicate that the forward-swept wing configuration can achieve qualitatively different lower-cost perching maneuvers than the straight wing configuration.

P. Marion, et al., “Director: A User Interface Designed for Robot Operation with Shared Autonomy,” Journal of Field Robotics, 2016.Abstract

Operating a high degree of freedom mobile manipulator, such as a humanoid, in a field scenario requires constant situational awareness, capable perception modules, and effective mechanisms for interactive motion planning and control. A well-designed operator interface
presents the operator with enough context to quickly carry out a mission and the flexibility to handle unforeseen operating scenarios robustly. By contrast, an unintuitive user interface can increase the risk of catastrophic operator error by overwhelming the user with unnecessary information. With these principles in mind, we present the philosophy and design decisions behind Director---the open-source user interface developed by Team MIT to pilot the Atlas robot in the DARPA Robotics Challenge (DRC). At the heart of Director is an integrated task execution system that specifies sequences of actions needed to achieve a substantive task, such as drilling a wall or climbing a staircase. These task sequences, developed a priori, make online queries to automated perception and planning algorithms with outputs that can be reviewed by the operator and executed by our whole-body controller. Our use of Director at the DRC resulted in efficient high-level task operation while being fully competitive with approaches focusing on teleoperation by highly-trained operators. We discuss the primary interface elements that comprise the Director and provide analysis of its successful use at the DRC.

Z. Manchester and S. Kuindersma, “Derivative-Free Trajectory Optimization with Unscented Dynamic Programming,” in Proceedings of the 55th Conference on Decision and Control (CDC), 2016.Abstract

Trajectory optimization algorithms are a core technology behind many modern nonlinear control applications. However, with increasing system complexity, the computation of dynamics derivatives during optimization creates a computational bottleneck, particularly in second-order methods. In this paper, we present a modification of the classical Differential Dynamic Programming (DDP) algorithm that eliminates the computation of dynamics derivatives while maintaining similar convergence properties. Rather than relying on naive finite difference calculations, we propose a deterministic sampling scheme inspired by the Unscented Kalman Filter that propagates a quadratic approximation of the cost-to-go function through the nonlinear dynamics at each time step. Our algorithm takes larger steps than Iterative LQR---a DDP variant that approximates the cost-to-go Hessian using only first derivatives---while maintaining the same computational cost. We present results demonstrating its numerical performance in simulated balancing and aerobatic flight experiments.

M. Posa, S. Kuindersma, and R. Tedrake, “Optimization and stabilization of trajectories for constrained dynamical systems,” in Proceedings of the International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, 2016.Abstract

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 a trajectory optimization algorithm (DIRCON) that extends the direct collocation method, naturally incorporating 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 manifold tangent plane. 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.

S. Kuindersma, et al., “Optimization-based locomotion planning, estimation, and control design for Atlas,” Autonomous Robots, vol. 40, no. 3, pp. 429–455, 2016.Abstract

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 built by Boston Dynamics, Inc.

R. Tedrake, S. Kuindersma, R. Deits, and K. Miura, “A closed-form solution for real-time ZMP gait generation and feedback stabilization,” in IEEE-RAS International Conference on Humanoid Robots, Seoul, Korea, 2015.Abstract

Here we present a closed-form 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.

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