Koushil Sreenath

A Compliant Hybrid Zero Dynamics Controller for Stable, Efficient and Fast Bipedal Walking on MABEL

The planar bipedal testbed MABEL contains springs in its drivetrain for the purpose of enhancing both energy efficiency and agility of dynamic locomotion. While the potential energetic benefits of springs are well documented in the literature, feedback control designs that effectively realize this potential are lacking. In this paper, we extend and apply the methods of virtual constraints and hybrid zero dynamics, originally developed for rigid robots with a single degree of underactuation, to MABEL, a bipedal walker with a novel compliant transmission and multiple degrees of underactuation. A time-invariant feedback controller is designed such that the closed-loop system respects the natural compliance of the open-loop system and realizes exponentially stable walking gaits. Five experiments are presented that highlight different aspects of MABEL and the feedback design method, ranging from basic elements such as stable walking and robustness under perturbations, to energy efficiency and a walking speed of 1.5 m s−1 (3.4 mph). The experiments also compare two feedback implementations of the virtual constraints, one based on PD control of Westervelt et al., and a second that implements a full hybrid zero dynamics controller. On MABEL, the full hybrid zero dynamics controller yields a much more faithful realization of the desired virtual constraints and was instrumental in achieving more rapid walking.

Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics

This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models-systems with impulse effects-through control Lyapunov functions. The periodic orbit is assumed to lie in a C1 submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the full-order dynamics of the system with impulse effects have relied on input-output linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the full-order dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions.

MABEL, a new robotic bipedal walker and runner

This paper introduces MABEL, a new platform for the study of bipedal locomotion in robots. One of the purposes of building the mechanism is to explore a novel powertrain design that incorporates compliance, with the objective of improving the power efficiency of the robot, both in steady state operation and in responding to disturbances. A second purpose is to inspire the development of new feedback control algorithms for running on level surfaces and walking on rough terrain. A third motivation for building the robot is science and technology outreach; indeed, it is already included in tours when K-through-12 students visit the College of Engineering at the University of Michigan. MABEL is currently walking at 1.1 m/s on a level surface, and a related monopod at Carnegie Mellon is hopping well, establishing that the testbed has the potential to realize its many objectives.

Trajectory generation and control of a quadrotor with a cable-suspended load - A differentially-flat hybrid system

A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and the system is established to be a differentially-flat hybrid system. Using the flatness property, a trajectory generation method is presented that enables finding nominal trajectories with various constraints that not only result in minimal load swing if required, but can also cause a large swing in the load for dynamically agile motions. A control design is presented for the system specialized to the planar case, that enables tracking of either the quadrotor attitude, the load attitude or the position of the load. Stability proofs for the controller design and experimental validation of the proposed controller are presented.

Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load

A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and a coordinate-free dynamic model, defined on the configuration space SE(3)×S2, is obtained by taking variations on manifolds. The quadrotor-load system is established to be a differentially-flat hybrid system with the load position and the quadrotor yaw serving as the flat outputs. A nonlinear geometric control design is developed, that enables tracking of outputs defined by (a) quadrotor attitude, (b) load attitude, and (c) position of the load. In each case, the closed-loop system exhibits almost-global properties. Stability proofs for the controller design, as well as simulations of the proposed controller are presented.

Embedding active force control within the compliant hybrid zero dynamics to achieve stable, fast running on MABEL

A mathematical formalism for designing running gaits in bipedal robots with compliance is introduced and subsequently validated experimentally on MABEL, a planar biped that contains springs in its drivetrain. The methods of virtual constraints and hybrid zero dynamics are used to design a time-invariant feedback controller that respects the natural compliance of the open-loop system. In addition, it also enables active force control within the compliant hybrid zero dynamics allowing within-stride adjustments of the effective stance leg stiffness. The proposed control strategy was implemented on and resulted in a kneed-biped running record of 3.06 m/s (10.9 kph or 6.8 mph).

Dynamics, Control and Planning for Cooperative Manipulation of Payloads Suspended by Cables from Multiple Quadrotor Robots.

We address the problem of cooperative transportation of a cable-suspended payload by multiple quadrotors. In previous work, quasi-static models have been used to study this problem. However, these approaches are severely limited because they ignore the payload dynamics, and do not explicitly model the underactuation in the control problem. Thus, there are no guarantees on the payload trajectory or the cable tensions, which must be non negative. In this paper, we develop a complete dynamic model for the case when payload is a point load and for the case when the payload is a rigid body. We show in both cases the resulting system is differentially flat when the cable tensions are strictly positive. We also consider the case where the tensions are non negative (including the case with zero tensions) and establish that these systems are differentially flat hybrid systems by considering the switching dynamics induced by the unilateral tension constraints. We use the differential flatness property to find dynamically feasible trajectories for the payload+quadrotors system. We show using numerical and experimental methods that these trajectories are superior to those obtained by quasi-static models.

Avian-Inspired Grasping for Quadrotor Micro UAVs

Micro Unmanned Aerial Vehicles (MAVs) have been used in a wide range of applications [1, 2, 3]. However, there are few papers addressing high-speed grasping and transportation of pay-loads using MAVs. Drawing inspiration from aerial hunting by birds of prey, we design and equip a quadrotor MAV with an actuated appendage enabling grasping and object retrieval at high speeds. We develop a nonlinear dynamic model of the system, demonstrate that the system is differentially flat, plan dynamic trajectories using the flatness property, and present experimental results with pick-up velocities at 2 m/s (6 body lengths / second) and 3 m/s (9 body lengths / second). Finally, the experimental results are compared with observations derived from video footage of a bald eagle swooping down and snatching a fish out of water.Copyright

Identification of a Bipedal Robot with a Compliant Drivetrain

Research in bipedal robotics aims to design machines with the speed, stability, agility, and energetic efficiency of a human. While no machine built today realizes the union of these attributes, several robots demonstrate one or more of them. The Cornell biped is designed to be highly energy efficient.

Torque Saturation in Bipedal Robotic Walking Through Control Lyapunov Function-Based Quadratic Programs

This paper presents a novel method to address the actuator saturation for nonlinear hybrid systems by directly incorporating user-defined input bounds in a controller design. In particular, we consider the application of bipedal walking and show that our method [based on a quadratic programming (QP) implementation of a control Lyapunov function (CLF)-based controller] enables a gradual performance degradation while still continuing to walk under increasingly stringent input bounds. We draw on our previous work, which has demonstrated the effectiveness of the CLF-based controllers for stabilizing periodic gaits for biped walkers. This paper presents a framework, which results in more effective handling of control saturations and provides a means for incorporating a whole family of user-defined constraints into the online computation of a CLF-based controller. This paper concludes with an experimental validation of the main results on the bipedal robot MABEL, demonstrating the usefulness of the QP-based CLF approach for real-time robotic control.