Perception Based Navigation for Underactuated Robots.

Robot autonomous navigation is a very active field of robotics. In this thesis we propose a hierarchical approach to a class of underactuated robots by composing a collection of local controllers with well understood domains of attraction. We start by addressing the problem of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case. This is accomplished by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide conditions under which the new procedure brings initial configurations to within an arbitrarily small neighborhood of the goal. We summarize with simulation results on a sample of visual servoing problems with a few different perceptual models. We document the empirical effectiveness of the proposed algorithm by reporting the results of its application to outdoor autonomous visual registration experiments with the robot RHex guided by engineered beacons. Next we explore the possibility of adapting the resulting first order hybrid feedback controller to its dynamical counterpart by introducing tunable damping terms in the control law. Just as gradient controllers for standard quasi-static mechanical systems give rise to generalized "PD-style" controllers for dynamical versions of those standard systems, we show that it is possible to construct similar "lifts" in the presence of non-holonomic constraints notwithstanding the necessary absence of point attractors. Simulation results corroborate the proposed lift. Finally we present an implementation of a fully autonomous navigation application for a legged robot. The robot adapts its leg trajectory parameters by recourse to a discrete gradient descent algorithm, while managing its experiments and outcome measurements autonomously via the navigation visual servoing algorithms proposed in this thesis.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/58412/1/glopes_1.pd

Assembly as a noncooperative game of its pieces: analysis of 1D sphere assemblies

We propose an event-driven algorithm for the control of simple robot assembly problems based on noncooperative game theory. We examine rigorously the simplest setting — three bodies with one degree of freedom and offer extensive simulations for the 2 DOF extension. The initial analysis and the accompanying simulations suggest that this approach may indeed, offer an attractive means of building robust event driven assembly systems

ZMP Support Areas for Multicontact Mobility Under Frictional Constraints

International audienceWe propose a method for checking and enforcing multi-contact stability based on the Zero-tilting Moment Point (ZMP). The key to our development is the generalization of ZMP support areas to take into account (a) frictional constraints and (b) multiple non-coplanar contacts. We introduce and investigate two kinds of ZMP support areas. First, we characterize and provide a fast geometric construction for the support area generated by valid contact forces, with no other constraint on the robot motion. We call this set the full support area. Next, we consider the control of humanoid robots using the Linear Pendulum Mode (LPM). We observe that the constraints stemming from the LPM induce a shrinking of the support area, even for walking on horizontal floors. We propose an algorithm to compute the new area, which we call pendular support area. We show that, in the LPM, having the ZMP in the pendular support area is a necessary and sufficient condition for contact stability. Based on these developments, we implement a whole-body controller and generate feasible multi-contact motions where an HRP-4 humanoid locomotes in challenging multi-contact scenarios

Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single robot. Applications can be found in the fields of underwater robotics, air traffic control, intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled mobile robots can be modeled by a nonlinear system having nonholonomic constraints. Due to these constraints, the collaborative robots arc not stabilizable at a point by continuous time-invariant feedback control laws. Therefore, linear control is ineffective, even locally, and innovative design techniques are needed. One possible design technique is feedback control and the principal interest of this thesis is to evaluate the best feedback control technique. Feedback linearization is one of the possible feedback control techniques. Feedback linearization is a method of transforming a nonlinear system into a linear system using feedback transformation. It differs from conventional Taylor series linearization since it is achieved using exact coordinates transformation rather than by linear approximations of the system. Linearization of the collaborative robots system using Taylor series results in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the feedback linearized control strategies result in a stable system. Feedback linearized control strategies can he designed based on state or input, while both state and input linearization can be achieved using static or dynamic feedback. In this thesis, a kinematic model of the collaborative nonholonomic robots is derived, based on the leader-follower formation. The objective of the kinematic model is to facilitate the design of feedback control strategies that can stabilize the system and Minimize the error between the desired and actual trajectory. The leader-follower formation is used in this research since the collaborative robots are assumed to have communication capabilities only. The kinematic model for the leader-follower formation is simulated using MATLAB/Simulink. A comparative assessment of various feedback control strategies is evaluated. The leader robot model is tested using five feedback control strategies for different trajectories. These feedback control strategies are derived using cascaded system theory, stable tracking method based on linearization of corresponding error model, approximation linearization, nonlinear control design and full state linearization via dynamic feedback. For posture stabilization of the leader robot, time-varying and full state dynamic feedback linearized control strategies are used. For the follower robots using separation bearing and separation-separation formation, the feedback linearized control strategies are derived using input-output via static feedback. Based on the simulation results for the leader robot, it is found that the full state dynamic feedback linearized control strategy improves system performance and minimizes the mean of error more rapidly than the other four feedback control strategies. In addition to stabilizing the system, the full state dynamic feedback linearized control strategy achieves posture stabilization. For the follower robots, the input-output via static feedback linearization control strategies minimize the error between the desired and actual formation. Furthermore, the input-output linearized control strategies allow dynamical change of the formation at run-time and minimize the disturbance of formation change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for the leader robot and input-output feedback linearized strategies for the follower robots are found to be more efficient in stabilizing the system