Research
Feedback Control of a Bipedal Walker and Runner
Designing controllers that allow for robustly stable, energy efficient, and fast locomotion over unstructured terrain is essential for applications, such as first response, and disaster robotics. My research contributes to the theoretical foundations of robotic bipedal locomotion and advances the experimental state of the art as well.
On the theoretical side, a mathematical formalism for designing provably stable, walking and running gaits in bipedal robots with compliance is developed. A key contribution is a novel method of force control in robots with compliance, which results in combining the analytical tractability afforded by the hybrid zero dynamics framework, with physically intuitive compliance control to induce reliable, fast running, as well as large unexpected step-down’s while walking. This is the first formal control design, with experimental validity, for bipedal runners with non-trivial morphologies.
On the experimental side, my controllers are validated on MABEL, a planar bipedal test bed with no feet, weighing 65 Kg, 1 m tall at the hips, and having a novel transmission with compliance. MABEL is a high degree-of-freedom, nonlinear, hybrid system, with several degrees of underactuation and subject to unilateral ground constraints. Current research has accomplished the following:
On the theoretical side, a mathematical formalism for designing provably stable, walking and running gaits in bipedal robots with compliance is developed. A key contribution is a novel method of force control in robots with compliance, which results in combining the analytical tractability afforded by the hybrid zero dynamics framework, with physically intuitive compliance control to induce reliable, fast running, as well as large unexpected step-down’s while walking. This is the first formal control design, with experimental validity, for bipedal runners with non-trivial morphologies.
On the experimental side, my controllers are validated on MABEL, a planar bipedal test bed with no feet, weighing 65 Kg, 1 m tall at the hips, and having a novel transmission with compliance. MABEL is a high degree-of-freedom, nonlinear, hybrid system, with several degrees of underactuation and subject to unilateral ground constraints. Current research has accomplished the following:
- Stable, robust walking - The walking controller preserves the natural compliance of the system as a dominant characteristic of the closed-loop system.
- Energy efficient walking - The resulting mechanical efficiency is within a factor of 2 of humans, and over 11 times better than Honda’s ASIMO.
- Fast walking - Walking at sustained speeds of 1.5 m/s (5.4 Km/hr or 3.4. mph) has been demonstrated.
- Fast Running - A compliant hybrid zero dynamics based controller with active force control enabled MABEL to run at a peak speed of 3.06 m/s (10.9 km/hr or 6.8 mph), creating a world running record for bipedal robots with non-trivial morphologies in August 2011. The resulting videos were viewed over 500,000 times, with significant press coverage from CNN, ESPN, Discovery Channel, Fox, and CBS.
Videos: Walking
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Videos: Running
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Select Publications
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Embedding active force control within the compliant hybrid zero dynamics to achieve stable, fast running on MABEL. The International Journal of Robotics Research (IJRR), 32(3):324–345, March 2013. Details | pdf
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Compliant hybrid zero dynamics controller for achieving stable, efficient and fast bipedal walking on MABEL. The International Journal of Robotics Research (IJRR), 30(9):1170–1193, August 2011. Details | pdf
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Identification of a bipedal robot with a compliant drivetrain: Parameter estimation for control design. IEEE Control Systems Magazine (CSM), 31(2):63–88, April 2011. Details | pdf
Nonlinear Geometric Control for Aerial Manipulation
The introduction of inexpensive micro unmanned aerial vehicles (UAV) in recent years provides a novel opportunity for easy transportation of loads using one or more UAVs. My research considers a quadrotor with a cable-suspended load, an underactuated, and hybrid system, with the dynamics evolving on SE(3) x S^2. My work extends differential-flatness to hybrid systems and establishes that this system is a differentially-flat hybrid system with the load position being a flat output. By taking variations on manifolds, a coordinate-free dynamical model is developed. Next, employing a singular perturbation argument, a nonlinear geometric controller is developed that can achieve any of the following:
By extending this to a planar setting, and with a specially designed gripper, we can use a quadrotor to demonstrate high-speed grasping and retrieval of a ground-based object.
- Almost-global exponential tracking of the quadrotor attitude, or
- Almost-global exponential tracking of the load attitude, or
- Almost-global exponential attractivity of the load position.
By extending this to a planar setting, and with a specially designed gripper, we can use a quadrotor to demonstrate high-speed grasping and retrieval of a ground-based object.
Videos
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Video of a simulation with 178 degree error in load and quadrotor attitude (load and quadrotor flipped), and large error in load position. The almost-global exponential attractivity of the load position tracking controller ensures convergence to the desired load position trajectory.
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Select Publications
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Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In IEEE Conference on Decision and Control (CDC), submitted, 2013. Details | pdf
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Geometric control of cooperating multiple quadrotor UAVs with a suspended payload. In IEEE Conference on Decision and Control (CDC), submitted, 2013. Details | pdf
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Trajectory generation and control of a quadrotor with a cable-suspended load – a differentially-flat hybrid system. In IEEE International Conference on Robotics and Automation (ICRA), to appear, 2013. Details | pdf
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Dynamics, control and planning for cooperative manipulation of payloads suspended by cables from multiple quadrotor robots. In Robotics: Science and Systems (RSS), submitted, 2013. Details | pdf
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Avian-inspired grasping for quadrotor micro uavs. In ASME International Design Engineering Technical Conference (IDETC), to appear, 2013. Details | pdf
Walking with Lyapunov Functions
Walking is a periodic orbit in the state-space of a system with impulse effects, which is a special class of hybrid systems. To date, there have been only three approaches for controller design for stabilizing these periodic orbits, with these methods typically employing high-gain controllers and resulting in large control spikes as the system deviates from the periodic orbit. In collaboration with Aaron Ames at Texas A&M, and Jessy Grizzle at Michigan, my work establishes that a sufficiently rapidly exponentially stabilizing control Lyapunov function (CLF) guarantees stabilization to the periodic orbit, thereby extending the class of controllers to infinitely many. My contribution in particular was the experimental validation of the controller on MABEL, demonstrating that CLFs yield better real-world controllers than earlier approaches. Moreover, my work extends this result to explicitly incorporate control bounds by posing a minimum-norm controller as a constrained quadratic program. This enables graceful degradation of walking under bounded control, which is important when you have a dying battery.
Videos
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Select Publications
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Rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics. IEEE Transactions on Automatic Control (TAC), accepted, 2013. Details | pdf
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Torque saturation in bipedal robotic walking through control lyapunov function based quadratic programs. IEEE Transactions on Robotics (TRO), submitted, 2013. Details | pdf
Whole Body Locomotion
Humans are able to walk rapidly upto a car, brace against the roof, and swivel their body to rapidly get into a sitting position. However, there exists no controller that is able to ascribe such dynamic motions to humanoid systems. My work extends virtual constraints to enable swiveling a humanoid about an axis formed by the contact locations of the hand and foot, resulting in the described dynamic motion.
Moreover, my work also considers the problem of bipedal walking on stochastically varying terrain, where the change in terrain gradient is only partially observable (due to poor and noisy sensors.) To enable walking on terrain with varying slopes, the problem is formulated as a partially observable hybrid model, and solved through a partially observable Markov decision process.
Moreover, my work also considers the problem of bipedal walking on stochastically varying terrain, where the change in terrain gradient is only partially observable (due to poor and noisy sensors.) To enable walking on terrain with varying slopes, the problem is formulated as a partially observable hybrid model, and solved through a partially observable Markov decision process.
Videos
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Walking over deterministic variation in terrain slopes of up to 10 degrees.
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Walking over stochastically varying terrain slopes of up to 10 degrees
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Select Publications
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A partially observable hybrid system model for bipedal locomotion for adapting to terrain variations. In Hybrid Systems: Computation and Control (HSCC), pages 137–142, Philadelphia, PA, April 2013. Details | pdf
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Rapid transition from walking to sitting for a 3d biped with arms. In Humanoids, in preparation, 2013. Details | pdf
Trajectory Planning with Homotopy / Homology Constraints
Specifying topological constraints for either trajectory generation for mobile robots, or for searching for a periodic walking gait in a specific region of the state-space would be extremely useful. However, a topological constraint, such as homotopy of a trajectory, has a gradient of zero almost everywhere, making standard gradient decent algorithms infeasible for searching for trajectories that respect the specified topological constraint. Collaborating with a student, we formulate the problem as a constrained mixed-integer quadratic program, that is easily solved by a convex optimizer.
Select Publications
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Optimal trajectory generation under homology class constraints. In IEEE Conference on Decision and Control (CDC), pages 3157–3164, Maui, HI, December 2012. Details | pdf
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Trajectory planning for systems with homotopy class constraints. In Latest Advances in Robot Kinematics (ARK), pages 83–90, Innsbruck, Austria, June 2012. Springer, Netherlands. Details | pdf
Adaptive Sampling with Mobile Sensor Networks
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Sensor networks have been used to predict the direction and intensity of tsunamis, and forest fires, the density of marine colonies, air pollutants, and other spatially, temporally distributed environmental fields. My Masters work developed systematic methods for optimally estimating environmental parametric fields using multiple mobile sensors, while also simultaneously addressing the issues of localization and deadlock that arise as a consequence of increased autonomy, mobility and actuation in the sensor network. This work has been summarized in a book published by IET.
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Select Publications
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Adaptive Sampling with Mobile WSN: Simultaneous robot localisation & mapping of parametric spatio-temporal fields. Control Engineering Series. IET, February 2011. ISBN 978-1-84919-257-6. Details | Table of contents
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Simultaneous adaptive localization of a wireless sensor network. ACM SIGMOBILE Mobile Computing and Communications Review (M2CR), 11(2):14–28, April 2007. Details | pdf
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Avoiding shared resource conflicts in mobile sensor networks with multiple missions. IET Control Theory & Applications (CTA), 1(3):665–674, May 2007. Details | pdf