Phanindra Tallapragada

A swimming robot with an internal rotor as a nonholonomic system

Two models of seemingly different classes of under actuated bio-inspired robotic systems are studied in this paper. The first model is that of an aquatic robot that swims like a fish. The second is a modified version of Chaplygins sleigh, a canonical nonholonomic system, that can move on the ground or a rigid surface. It is shown that a governing principle underlying the locomotion of both systems is the existence of a nonholonomic constraint. Having identified the common framework of non integrable constraints, an aquatic robot propelled by an internal rotor is presented.

Integrability of Velocity Constraints Modeling Vortex Shedding in Ideal Fluids

A mathematical model that invokes the Kutta condition to account for vortex shedding from the trailing edge of a free hydrofoil in a planar ideal fluid is compared with a canonical model for the dynamics of a terrestrial vehicle subject to a nonintegrable velocity constraint. The Kutta condition is shown to be nonintegrable in a sense that parallels that in which the constraint on the terrestrial vehicle is nonintegrable. Simulations of the two system’s dynamics reinforce the analogy between the two.

Steering a Chaplygin Sleigh Using Periodic Impulses

The control of the motion of nonholonomic systems is of practical importance from the perspective of robotics. In this paper we consider the dynamics of a cart-like system that is both propelled forward by motion of an internal momentum wheel. This is a modification of the Chaplygin sleigh, a canonical nonholonomic system. For the system considered, the momentum wheel is the sole means of locomotive thrust as well the only control input. We first derive an analytical expression for the change in the heading angle of the sleigh as a function of its initial velocity and angular velocity. We use this solution to design an open loop control strategy that changes the orientation of sleigh to any desired angle. The algorithm utilizes periodic impulsive torque inputs via the motion of the momentum wheel.

An Aquatic Robot Propelled by an Internal Rotor

Unmanned aquatic vehicles and robots are of tremendous importance in a variety of applications. In this paper, we present the model of an underactuated aquatic robot that is propelled by an internal rotor. The propulsion of the robot is based on the exchange of momentum between the body and water that is mediated by the creation of vorticity at the trailing edge of the robot. The robot does not have any external fins, propellers, or articulated joints allowing for very easy fabrication. Experimental data on its locomotion and maneuverability are presented.

The Stick-Slip Motion of a Chaplygin Sleigh With a Piecewise Smooth Nonholonomic Constraint

The Chaplygin sleigh is a canonical problem of mechanical systems with nonholonomic constraints, which arises due to the role of friction. The motion of the cart has often been studied under the assumption that the magnitude of friction is as high as necessary to prevent slipping. We relax this assumption by setting a maximum finite value to the friction. The Chaplygin sleigh is then under a piecewise smooth nonholonomic constraint and transitions between ‘slip’ and ‘stick’ modes. We investigate these transitions and the resulting non smooth dynamics of the system. Further more the piecewise smooth constraint offers the possibility of controlling the speed of the sleigh and we investigate this with numerical simulations.© 2015 ASME

The dynamics of a two link Chaplygin sleigh driven by an internal momentum wheel

A class of aquatic robots have been shown to have a correspondence to terrestrial nonholonomic systems. In particular bodies shaped as a Joukowski foil have been shown to have dynamics similar to a well known nonholonomic system, the Chaplygin sleigh. This inspires several related rigid body nonholonomic systems whose behavior is similar to other aquatic robots with other morphologies. In this paper we investigate the dynamics of one such nonholonomic system, a two-link Chaplygin sleigh that is controlled by an internal momentum wheel. This system is analogous to a similar aquatic robot with a passive tail. We also discuss results related to the accessibility and controllability of the two-link Chaplygin sleigh.

Limit Cycle Analysis and Control of the Dissipative Chaplygin Sleigh

There are many types of systems in both nature and technology that exhibit limit cycles under periodic forcing. Sometimes, especially in swimming robots, such forcing is used to propel a body forward in a plane. Due to the complexity in studying a fluid system it is often useful to investigate the dynamics of an analogous land model. Such analysis can then be useful in gaining insight about and controlling the original fluid system. In this paper we investigate the behavior of the Chaplygin sleigh under the effect of viscous dissipation and sinusoidal forcing. This is shown to behave in a similar manner as certain robotic fish models. We then apply limit cycle analysis techniques to predict the behavior and control the net translational velocity of the sleigh in a horizontal plane.Copyright

Fish Like Aquatic Robot Demonstrates Characteristics of a Linear System

In the recent past the design of many aquatic robots has been inspired by the motion of fish. In some recent work the authors described an underactuated planar swimming robot, that is propelled via the motion of an internal rotor. This robot is inspired by a simplified model of the fluid-body interaction mediated by singular distributions of vorticity. Such a model is a significant simplification of the fluid-structure interaction that can be understood using resource intensive numerical computations of the Navier Stokes equation that are unwieldy from a controls perspective. At the same time the simplified model incorporates the creation of vorticity and interaction of the body with the vorticity which many control theoretical models ignore. In this paper we show that despite the complexity of the interaction between the aquatic robot and the ambient vorticity in a fluid, the response of the robot is a nearly linear function of the control input. This surprisingly simple feature emerges in our theoretical model and is validated by our experimental data of the motion of the robot. This simplifying observation is an important step towards developing control algorithms for aquatic robots. ∗Address all correspondence to this author.

Particle slip velocity influences inertial focusing of particles in curved microchannels

Size based separation and identification of particles in microfluidics through purely hydrodynamic means has gained significant interest due to a number of possible biomedical applications. Curved micro-channels, particularly spiral micro-channels with rectangular cross-section and the dynamics of particles in such channels have been extensively researched to achieve size based separation of particles. In this paper we present evidence that sheds new light on the dynamics of particles in such curved channels; that a unique particle slip velocity is associated with the focusing positions in the cross sections, which leads to a balance of forces. Our experiments therefore imply that the forces acting on the particle lead to convergence to an attractor in both the physical space (the cross section of the channel) and the slip velocity space.

Chaotic dynamics of the Chaplygin sleigh with a passive internal rotor

The Chaplygin sleigh is a classic example of a nonholonomically constrained mechanical system. The sleigh’s motion always converges to a straight line whose slope is entirely determined by the initial configuration and velocity of the sleigh. We consider the motion of a modified Chaplygin sleigh that contains a passive internal rotor. We show that the presence of even a rotor with small inertia modifies the motion of the sleigh dramatically. A generic trajectory of the sleigh in a reduced velocity space exhibits two distinct transient phases before converging to a chaotic attractor. We demonstrate this through numerics. In recent work the dynamics of the Chaplygin sleigh have also been shown to be similar to that of a fish-like body in an inviscid fluid. The influence of a passive degree of freedom on the motion of the Chaplygin sleigh points to several possible applications in controlling the motion of the nonholonomically constrained terrestrial and aquatic robots.