Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

Advances in Underactuated Spacecraft Control

This dissertation addresses the control of a spacecraft which either becomes underactuated due to onboard failures or is made underactuated by design. Successfully controlling an underactuated spacecraft can extend spacecraft operational life in orbit and improve the robustness of space missions. The novel contributions of the dissertation include the following. Firstly, switching feedback controllers are developed for the attitude control of an underactuated spacecraft equipped with two pairs of thrusters, or two reaction wheels (RWs), or two control moment gyros (CMGs). The problem is challenging; e.g., even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method exploits the separation of the system into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables towards the desired pointing configuration. Secondly, nonlinear Model Predictive Control (MPC) is applied to the attitude dynamics of an underactuated spacecraft with two RWs and zero angular momentum. MPC has the remarkable ability to generate control laws that are discontinuous in the state. By utilizing nonlinear MPC, the obstruction to stabilizability is overcome and attitude maneuvers can be performed while enforcing constraints. Thirdly, an unconventional pathway is discussed for recovering the linear controllability of an underactuated spacecraft with two RWs by accounting for the effects of solar radiation pressure (SRP) in the spacecraft attitude model. Necessary and sufficient conditions for recovering linear controllability are given, and with linear controllability restored, conventional controllers can be designed for underactuated spacecraft. Lastly, two sets of coupled translational and rotational equations of motion for a spacecraft in a central gravity field are derived. The spacecraft is assumed to have only internal attitude actuators and the equations of motion are relative with respect to an equilibrium orbit. Under reasonable assumptions on the spacecraft configuration and equilibrium orbit, the coupled dynamics are small-time locally controllable (STLC), which opens a path to utilizing conventional control techniques to move translationally in space by employing attitude control only.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133430/1/cdpete_1.pd

Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially

Modeling, analysis and control of robot-object nonsmooth underactuated Lagrangian systems: A tutorial overview and perspectives

International audienceSo-called robot-object Lagrangian systems consist of a class of nonsmooth underactuated complementarity Lagrangian systems, with a specific structure: an "object" and a "robot". Only the robot is actuated. The object dynamics can thus be controlled only through the action of the contact Lagrange multipliers, which represent the interaction forces between the robot and the object. Juggling, walking, running, hopping machines, robotic systems that manipulate objects, tapping, pushing systems, kinematic chains with joint clearance, crawling, climbing robots, some cable-driven manipulators, and some circuits with set-valued nonsmooth components, belong this class. This article aims at presenting their main features, then many application examples which belong to the robot-object class, then reviewing the main tools and control strategies which have been proposed in the Automatic Control and in the Robotics literature. Some comments and open issues conclude the article