We present a novel paradigm and algorithm for optimal design of underactuated robot platforms in highly-constrained nonconvex parameter spaces. We apply this algorithm to two variants of the mature RoboBee platform, numerically demonstrating predicted performance improvements of over 10% in some cases by algorithmically reasoning about variable effective-mechanical-advantage (EMA) transmissions, higher aspect ratio (AR) wing designs, and force-power tradeoffs. The algorithm can currently be applied to any underactuated mechanical system with one actuated degree of freedom (DOF), and can be easily extended to arbitrary configuration spaces and dynamics.

We present the first fully spatial hopping gait of a 12 DoF tailed biped driven by only 4 actuators. The control of this physical machine is built up from parallel compositions of controllers for progressively higher DoF extensions of a simple 2 DoF, 1 actuator template. These template dynamics are still not themselves integrable, but a new hybrid averaging analysis yields a conjectured closed form representation of the approximate hopping limit cycle as a function of its physical and control parameters. The resulting insight into the role of the machines kinematic and dynamical design choices affords a redesign leading to the newly achieved behavior.

The Jerboa, a tailed bipedal robot with two hip-actuated, passive-compliant legs and a doubly actuated tail, has been shown both formally and empirically to exhibit a variety of stable hopping and running gaits in the sagittal plane. In this paper we take the first steps toward operating Jerboa as a fully spatial machine by addressing the predominant mode of destabilization away from the sagittal plane: body roll. We develop a provably stable controller for underactuated aerial stabilization of the coupled body roll and tail angles, that uses just the tail torques. We show that this controller is successful at reliably reorienting the Jerboa body in roughly 150 ms of freefall from a large set of initial conditions. This controller also enables (and appears intuitively to be crucial for) sustained empirically stable hopping in the frontal plane by virtue of its substantial robustness against destabilizing perturbations and calibration errors. The controller as well as the analysis methods developed here are applicable to any robotic platform with a similar doubly-actuated spherical tail joint.

We have built a 4DOF tailed monoped that hops along a boom permitting free sagittal plane motion. This underactuated platform is powered by a hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of “template” reference systems along with data from the physical platform suggesting these templates are “anchored” as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.

This paper explores the design space of simple legged robots capable of leaping culminating in new behaviors for the Penn Jerboa, an underactuated, dynamically dexterous robot. Using a combination of formal reasoning and physical intuition, we analyze and test successively more capable leaping behaviors through successively more complicated body mechanics. The final version of this machine studied here bounds up a ledge 1.5 times its hip height and crosses a gap 2 times its body length, exceeding in this last regard the mark set by the far more mature RHex hexapod. Theoretical contributions include a non-existence proof of a useful class of leaps for a stripped-down initial version of the new machine, setting in motion the sequence of improvements leading to the final resulting performance. Conceptual contributions include a growing understanding of the Ground Reaction Complex as an effective abstraction for classifying and generating transitional contact behaviors in robotics.

We consider the problem of visually servoing a legged vehicle with unicycle-like nonholonomic constraints subject to second-order fore-aft dynamics in its horizontal-plane. We target applications to rugged environments characterized by complex terrain likely to significantly perturb the robot's nominal dynamics. At the same time, it is crucial that the camera avoid “obstacle” poses where absolute localization would be compromised by even partial loss of landmark visibility. Hence, we seek a controller whose robustness against disturbances and obstacle avoidance capabilities can be assured by a strict global Lyapunov function. Since the nonholonomic constraints preclude smooth point stabilizability we introduce an extra degree of sensory freedom, affixing the camera to an actuated panning axis on the robot's back. Smooth stabilizability to the robot-orientation-indifferent goal cycle no longer precluded, we construct a controller and strict global Lyapunov function with the desired properties. We implement several versions of the scheme on a RHex robot maneuvering over slippery ground and document its successful empirical performance.

We propose a new paradigm for reactive wall-following by a planar robot taking the form of an actively steered sensor model that augments the robot's motion dynamics. We postulate a foveated sensor capable of delivering third-order infinitesimal (range, tangent, and curvature) data at a point along a wall (modeled as an unknown smooth plane curve) specified by the angle of the ray from the robot's body that first intersects it. We develop feedback policies for the coupled (point or unicycle) sensorimotor system that drive the sensor's foveal angle as a function of the instantaneous infinitesimal data, in accord with the trade-off between a desired standoff and progress-rate as the wall's curvature varies unpredictably in the manner of an unmodeled noise signal. We prove that in any neighborhood within which the third-order infinitesimal data accurately predicts the local “shape” of the wall, neither robot will ever hit it. We empirically demonstrate with comparative physical studies that the new active sensor management strategy yields superior average tracking performance and avoids catastrophic collisions or wall losses relative to the passive sensor variant.