Feedback Equivalence and Control of Mobile Robots Through a Scalable FPGA Architecture

Abstract

The control of mobile robots is an intense research field, having produced a substantial volume of research literature in the past three decades. Mobile robots present a challenge in both theoretical control design as well as hardware implementation. From a theoretical point of view, mobile robots exert highly non-linear kinematics and dynamics, non-holonomy and complex operational environment. On the other hand, hardware designs strive for scalability, downsizing, computational power and low cost. The main control problems in robot motion control can be classified in three general cases; stabilization to a point, trajectory tracking and path following. Point stabilization refers to the stabilization of the robot to a specific configuration in its state space (pose). For example, if the robot at t = t0 is at p0 = (x0, y0, θ0), then find a suitable control law that steers it to a goal point pg=(xg, yg, θg). Apparently p0 must be an equilibrium point of the closed loop system, exerting asymptotic stability (although practical stability can also be sought for). In the path following (or path tracking) problem, the robot is presented with a reference path, either feasible or infeasible, and has to follow it by issuing the appropriate control commands. A path is defined as a geometric curve in the robot’s application space. The trajectory tracking problem is similar, although there is a notable difference; the trajectory is a path with an associated timing law i.e. the robot has to be on specific points at specific time instances. These three problems present challenges and difficulties exacerbated by the fact that the robot models are highly non-linear and non-holonomic (although robots that lift the non-holonomic rolling constraint do exist and are called omni-directional robots. However the most interesting mobile robots present this constraint). The non-holonomy means that there are constraints in the robot velocities e.g. the non-slipping condition, which forces the robot to move tangentially to its path or equivalently, the robot’s heading is always collinear to its velocity vector (this can readily be attested by every driver who expects his car to move at the direction it is heading and not sideways i.e. slip). For amoremotivating example of holonomy, consider a prototypical and pedagogical kimenatic model for motion analysis and control; the unicycle robot, described by the equations,