Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

This paper addresses formulation of stabilizability and motion tracking conditions for mechanical systems from the point of view of constraints put on them. We present a new classification of constraints, which includes nonholonomic constraints that arise in both mechanics and control. Based on our classification we develop kinematic and dynamic control models of systems subjected to these constraints. We demonstrate that a property of being a “hard-to-control” nonholonomic system may not be related to the nature of the constraints. It may result from the formulation of control objectives for a system. We examine two control objectives which are stabilization to the target equilibrium by a continuous static state feedback control and motion tracking. Theory is illustrated with examples of control objective formulations for systems with constraints of various types

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

Challenges and Solutions for Autonomous Robotic Mobile Manipulation for Outdoor Sample Collection

In refinery, petrochemical, and chemical plants, process technicians collect uncontaminated samples to be analyzed in the quality control laboratory all time and all weather. This traditionally manual operation not only exposes the process technicians to hazardous chemicals, but also imposes an economical burden on the management. The recent development in mobile manipulation provides an opportunity to fully automate the operation of sample collection. This paper reviewed the various challenges in sample collection in terms of navigation of the mobile platform and manipulation of the robotic arm from four aspects, namely mobile robot positioning/attitude using global navigation satellite system (GNSS), vision-based navigation and visual servoing, robotic manipulation, mobile robot path planning and control. This paper further proposed solutions to these challenges and pointed the main direction of development in mobile manipulation

Performance Investigations of an Improved Backstepping Operational space Position Tracking Control of a Mobile Manipulator

This article implies an improved backstepping control technique for the operational-space position tracking of a kinematically redundant mobile manipulator. The mobile manipulator thought-out for the analysis has a vehicle base with four mecanum wheels and a serial manipulator arm with three rotary actuated joints. The recommended motion controller provides a safeguard against the system dynamic variations owing to the parameter uncertainties, unmodelled system dynamics and unknown exterior disturbances. The Lyapunov’s direct method assists in designing and authenticating the system’s closed-loop stability and tracking ability of the suggested control strategy. The feasibility, effectiveness and robustness of the recommended controller are demonstrated and investigated numerically with the help of computer based simulations. The mathematical model used for the computer-based simulations is derived based on a real-time mobile manipulator and the derived model is further verified with an inbuilt gazebo model in a robot operating system (ROS) environment. In addition, the proposed scheme is verified on an in-house fabricated mobile manipulator system. Further, the recommended controller performance is correlated with the conventional backstepping control design in both computer-based simulations and in real-time experiments

Research on a semiautonomous mobile robot for loosely structured environments focused on transporting mail trolleys

In this thesis is presented a novel approach to model, control, and planning the motion of a nonholonomic wheeled mobile robot that applies stable pushes and pulls to a nonholonomic cart (York mail trolley) in a loosely structured environment. The method is based on grasping and ungrasping the nonholonomic cart, as a result, the robot changes its kinematics properties. In consequence, two robot configurations are produced by the task of grasping and ungrasping the load, they are: the single-robot configuration and the robot-trolley configuration. Furthermore, in order to comply with the general planar motion law of rigid bodies and the kinematic constraints imposed by the robot wheels for each configuration, the robot has been provided with two motorized steerable wheels in order to have a flexible platform able to adapt to these restrictions. [Continues.

Path following for a target point attached to a unicycle type vehicle

In this article, we address the control problem of unicycle path following, using a rigidly attached target point. The initial path following problem has been transformed into a reference trajectory following problem, using saturated control laws and a geometric characterization hypothesis, which links the curvature of the path to be followed with the target point. The proposed controller allows global stabilization without restrictions on initial conditions. The effectiveness of this controller is illustrated through simulations

GRASP News Volume 9, Number 1

A report of the General Robotics and Active Sensory Perception (GRASP) Laboratory

Virtual Constraints and Hybrid Zero Dynamics for Realizing Underactuated Bipedal Locomotion

Underactuation is ubiquitous in human locomotion and should be ubiquitous in bipedal robotic locomotion as well. This chapter presents a coherent theory for the design of feedback controllers that achieve stable walking gaits in underactuated bipedal robots. Two fundamental tools are introduced, virtual constraints and hybrid zero dynamics. Virtual constraints are relations on the state variables of a mechanical model that are imposed through a time-invariant feedback controller. One of their roles is to synchronize the robot's joints to an internal gait phasing variable. A second role is to induce a low dimensional system, the zero dynamics, that captures the underactuated aspects of a robot's model, without any approximations. To enhance intuition, the relation between physical constraints and virtual constraints is first established. From here, the hybrid zero dynamics of an underactuated bipedal model is developed, and its fundamental role in the design of asymptotically stable walking motions is established. The chapter includes numerous references to robots on which the highlighted techniques have been implemented.Comment: 17 pages, 4 figures, bookchapte

Energy-saver mobile manipulator based on numerical methods

The work presents the kinematic and dynamic control of a mobile robotic manipulator system based on numerical methods. The proposal also presents the curvature analysis of a path not parameterized in time, for the optimization of energy consumption. The energy optimization considers two aspects: the velocity of execution in curves and the amount of movements generated by the robotic system. When a curve occurs on the predefined path, the execution velocity is analyzed throughout the system in a unified method to prevent skid e ects from a ecting the mobile manipulator, while the number of movements is limited by the redundancy presented by the robotic system to optimize energy use. The experimental results are shown to validate the mechanical and electronic construction of the system, the proposed controllers, and the saving of energy consumptionThis research was funded by Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia–CEDI