Second Order Averaging Methods for Oscillatory Control of Underactuated Mechanical Systems

This paper considers the stabilization of underactuated mechanical systems via high-amplitude, high-frequency actuation. Using higher order averaging techniques, we extend previous work to the case where symmetric products of order higher than one are necessary for controllability. We first introduce a second order averaged mechanical system model that incorporates higher order terms. Using this result, we obtain trajectory tracking in the average by feeding back an error signal that is constant over whole periods of the oscillatory actuation. A simulation demonstrates the method

Trajectory stabilization for a planar carangiform robot fish

Considers the task of trajectory stabilization for a fish-like robot by means of feedback. We use oscillatory control inputs and apply correction signals at the endpoints of each periodic input signal. Such a strategy can be proven to cause the system to converge to a desired trajectory. We present a specific model of a planar carangiform fish, and verify the stabilization results with simulations and with experiment on a planar robotic fish system that is propelled using carangiform-like movements

Underwater locomotion from oscillatory shape deformations

This paper considers underwater propulsion that is generated by variations in body shape. We summarize and extend some of the emerging approaches for the uniform modeling and control of such underactuated systems. Two examples illustrate these ideas

Using collision cones to assess biological deconfliction methods

Biological systems consistently outperform autonomous systems governed by engineered algorithms in their ability to reactively avoid collisions. To better understand this discrepancy, a collision avoidance algorithm was applied to frames of digitized video trajectory data from bats, swallows and fish (Myotis velifer, Petrochelidon pyrrhonota and Danio aequipinnatus). Information available from visual cues, specifically relative position and velocity, was provided to the algorithm which used this information to define collision cones that allowed the algorithm to find a safe velocity requiring minimal deviation from the original velocity. The subset of obstacles provided to the algorithm was determined by the animal's sensing range in terms of metric and topological distance. The algorithmic calculated velocities showed good agreement with observed biological velocities, indicating that the algorithm was an informative basis for comparison with the three species and could potentially be improved for engineered applications with further study

Controllability and Trajectory Tracking for Classes of Cascade-Form Second Order Nonholonomic Systems

We discuss classes of nonlinear systems with drift that can be reduced to the cascade of a linear system and a drift-free nonholonomic system. Building on previous work with amplitude-modulated sinusoids for trajectory tracking in drift-free systems, we present algorithms for configuration trajectory tracking in these dynamic settings. Results are demonstrated in simulation for representative examples