Giuseppe Oriolo

WMR control via dynamic feedback linearization: design, implementation, and experimental validation

The subject of the paper is the motion control problem of wheeled mobile robots (WMRs) in environments without obstacles. With reference to the popular unicycle kinematics, it is shown that dynamic feedback linearization is an efficient design tool leading to a solution simultaneously valid for both trajectory tracking and setpoint regulation problems. The implementation of this approach on the laboratory prototype SuperMARIO, a two-wheel differentially driven mobile robot, is described in detail. To assess the quality of the proposed controller, we compare its performance with that of several existing control techniques in a number of experiments. The obtained results provide useful guidelines for WMR control designers.

Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators

An analysis of underactuated manipulators from both the dynamic and the control points of view is presented. While the unactuated joints dynamic equation is recognized to be a nonholonomic constraint in the general case, necessary and sufficient conditions are given to identify special cases in which such a constraint is integrable. In contrast to most examples in the literature, the unactuated joints dynamics is an instance of a second-order nonholonomic constraint. it is shown that smooth feedback stabilization to a single equilibrium point is not possible, and a feedback scheme providing stabilization to a manifold of equilibrium positions is proposed.<<ETX>>

Image-Based Visual Servoing for Nonholonomic Mobile Robots Using Epipolar Geometry

We present an image-based visual servoing strategy for driving a nonholonomic mobile robot equipped with a pinhole camera toward a desired configuration. The proposed approach, which exploits the epipolar geometry defined by the current and desired camera views, does not need any knowledge of the 3-D scene geometry. The control scheme is divided into two steps. In the first, using an approximate input-output linearizing feedback, the epipoles are zeroed so as to align the robot with the goal. Feature points are then used in the second translational step to reach the desired configuration. Asymptotic convergence to the desired configuration is proven, both in the calibrated and partially calibrated case. Simulation and experimental results show the effectiveness of the proposed control scheme

Free-joint manipulators: motion control under second-order nonholonomic constraints

The control problem for robot manipulators having some unactuated joints is addressed. The nonholonomic nature of the constraint expressing the dynamics of the free joints is recognized in the general case, and conditions are derived to identify special cases in which such a constraint is integrable. In contrast to most examples in the literature, the free-joint dynamics is an instance of second-order nonholonomic constraint. It is shown that smooth feedback stabilization to a single equilibrium point is not possible. A feedback scheme achieving stabilization to a manifold of equilibrium positions is proposed. Its correctness is established theoretically as well as confirmed by simulation results.<<ETX>>

Fuzzy maps: A new tool for mobile robot perception and planning

An essential component of an autonomous mobile robot is the exteroceptive sensory system. Sensing capabilities should be integrated with a method for extracting a representation of the environment from uncertain sensor data and with an appropriate planning algorithm. In this article, fuzzy logic concepts are used to introduce a tool useful for robot perception as well as for planning collision-free motions. In particular, a map of the environment is defined as the fuzzy set of unsafe points, whose membership function quantifies the possibility for each point to belong to an obstacle. The computation of this set is based on a specific sensor model and makes use of intermediate sets generated from range measures and aggregated by means of fuzzy set operators. This general approach is applied to a robot with ultrasonic rangefinders. The resulting map building algorithm performs well, as confirmed by a comparison with stochastic methods. The planning problem on fuzzy maps can be solved by defining various path cost functions, corresponding to different strategies, and by searching the map for optimal paths. To this end, proper instances of the A* algorithm are devised. Experimental results for a Nomad 200™ robot moving in a real-world environment are presented.

Feature Depth Observation for Image-based Visual Servoing: Theory and Experiments

In the classical image-based visual servoing framework, error signals are directly computed from image feature parameters, allowing, in principle, control schemes to be obtained that need neither a complete three-dimensional (3D) model of the scene nor a perfect camera calibration. However, when the computation of control signals involves the interaction matrix, the current value of some 3D parameters is requiredfor each considered feature, and typically a rough approximation of this value is used. With reference to the case of a point feature, for which the relevant 3D parameter is the depth Z, we propose a visual servoing approach where Z is observed and made available for servoing. This is achieved by interpreting depth as an unmeasurable state with known dynamics, and by building a non-linear observer that asymptotically recovers the actual value of Z for the selected feature. A byproduct of our analysis is the rigorous characterization of camera motions that actually allow such observation. Moreover, in the case of a partially uncalibrated camera, it is possible to exploit complementary camera motions in order to preliminarily estimate the focal length without knowing Z. Simulations and experimental results are presented for a mobile robot with an on-board camera in order to illustrate the benefits of integrating the depth observation within classical visual servoing schemes.

Trajectory Planning and Control for Planar Robots with Passive Last Joint

We present a method for trajectory planning and control of planar robots with a passive rotational last joint. These underactuated mechanical systems, which are subject to nonholonomic second-order constraints, are shown to be fully linearized and input-output decoupled by means of a nonlinear dynamic feedback. This objective is achieved in a unified framework, both in the presence or absence of gravity. The linearizing output is the position of the center of percussion of the last link. Based on this result, one can plan smooth trajectories joining in finite time any initial and desired final state of the robot; in particular, transfers between inverted equilibria and swing-up maneuvers under gravity are easily obtained. We also address the problem of avoiding the singularity induced by the dynamic linearization procedure through a careful choice of output trajectories. A byproduct of the proposed method is the straightforward design of exponentially stable tracking controllers for the generated trajectories. Simulation results are reported for a 3R robot moving in a horizontal and vertical plane. Possible extensions of the approach and its relationships with the differential flatness technique are briefly discussed.

Control of Wheeled Mobile Robots: An Experimental Overview

The subject of this chapter is the motion control problem of wheeled mobile robots (WMRs). With reference to the unicycle kinematics, we review and compare several control strategies for trajectory tracking and posture stabilization in an environment free of obstacles. Experiments are reported for SuperMARIO, a two-wheel differentially-driven mobile robot. From the comparison of the obtained results, guidelines are provided for WMR end-users.

Local incremental planning for nonholonomic mobile robots

We present a simple approach for planning the motion of nonholonomic robots among obstacles. Existing methods lead to open-loop solutions which are either obtained in two stages, approximating a previously built holonomic path, or computationally intensive, being based on configuration space discretization. Our nonholonomic planner employs a direct projection strategy to modify online the output of a holonomic incremental planner, and generates velocity control inputs that realize the desired motion in a least-squares sense. As a result, a feedback scheme is obtained which can use only local sensor information. The proposed approach is applied to unicycle kinematics, with artificial potential fields or vortex fields as local holonomic planners.<<ETX>>

The Sensor-based Random Graph Method for Cooperative Robot Exploration

We present a decentralized cooperative exploration strategy for a team of mobile robots equipped with range finders. A roadmap of the explored area, with the associate safe region, is built in the form of a sensor-based random graph (SRG). This is expanded by the robots by using a randomized local planner that automatically realizes a tradeoff between information gain and navigation cost. The nodes of the SRG represent view configurations that have been visited by at least one robot, and are connected by arcs that represent safe paths. These paths have been actually traveled by the robots or added to the SRG to improve its connectivity. Decentralized cooperation and coordination mechanisms are used so as to guarantee exploration efficiency and avoid conflicts. Simulations and experiments are presented to show the performance of the proposed technique.