scholarly journals Energy based Control Barrier Functions for Robotic Systems

2020 ◽  
Author(s):  
Shishir Kolathaya
Keyword(s):  
Kinetic Energy ◽  
Robotic Systems ◽  
Control Lyapunov Function ◽  
Control Laws ◽  
Lipschitz Continuous ◽  
New Class ◽  
Inertial Parameters ◽  
Affine Control Systems ◽  
Kinematic Models ◽  
The Masses

<div>Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However, due to the presence of model-based terms, they fail to provide guarantees under model perturbations. Therefore, in this paper, we propose a new class of CBFs for robotic systems that augment kinetic energy with the traditional forms. We show that with torque limits permitting, and with the kinematic models accurately known, forward invariance of safe sets generated by kinematic constraints (position and velocity) can be guaranteed. The proposed methodology is motivated by the control Lyapunov function (CLF) based QPs that use the kinetic energy function. By the property of CBF-QPs, we show that the pointwise min-norm control laws obtained are feasible and Lipschitz continuous, and can be derived analytically via the KKT conditions. In order to include stability with safety, we also augment CLF based constraints in the CBF-QPs to realize a unified control law that allows tracking with safety irrespective of the inertial parameters of the robot. We will demonstrate the robustness of this class of CBF-QPs in two robotic platforms: a 1-DOF and a 2-DOF manipulator, by scaling the masses by up to 100, and then simulating the resulting dynamics.</div>

scholarly journals Energy based Control Barrier Functions for Robotic Systems

2020 ◽  
Author(s):  
Shishir Kolathaya
Keyword(s):  
Kinetic Energy ◽  
Robotic Systems ◽  
Control Lyapunov Function ◽  
Control Laws ◽  
Lipschitz Continuous ◽  
New Class ◽  
Inertial Parameters ◽  
Affine Control Systems ◽  
Kinematic Models ◽  
The Masses

<div>Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However, due to the presence of model-based terms, they fail to provide guarantees under model perturbations. Therefore, in this paper, we propose a new class of CBFs for robotic systems that augment kinetic energy with the traditional forms. We show that with torque limits permitting, and with the kinematic models accurately known, forward invariance of safe sets generated by kinematic constraints (position and velocity) can be guaranteed. The proposed methodology is motivated by the control Lyapunov function (CLF) based QPs that use the kinetic energy function. By the property of CBF-QPs, we show that the pointwise min-norm control laws obtained are feasible and Lipschitz continuous, and can be derived analytically via the KKT conditions. In order to include stability with safety, we also augment CLF based constraints in the CBF-QPs to realize a unified control law that allows tracking with safety irrespective of the inertial parameters of the robot. We will demonstrate the robustness of this class of CBF-QPs in two robotic platforms: a 1-DOF and a 2-DOF manipulator, by scaling the masses by up to 100, and then simulating the resulting dynamics.</div>

Decentralized Exergy/Entropy Thermodynamic Control for Collective Robotic Systems

2007 ◽  
Author(s):  
Rush D. Robinett ◽  
David G. Wilson
Keyword(s):  
Decentralized Control ◽  
Direct Method ◽  
Robotic Systems ◽  
Control Law ◽  
Thermodynamic Control ◽  
Order Accuracy ◽  
Control Laws ◽  
Vector Lyapunov Function ◽  
Collective Control ◽  
Plume Tracing

This paper develops a distributed decentralized control law for collective robotic systems. The control laws are developed based on exergy/entropy thermodynamic concepts and information theory. The source field is characterized through second-order accuracy. The proposed feedback control law stability for both the collective and individual robots are demonstrated by selecting a general Hamiltonian based solution developed as Fisher Information Equivalency as the vector Lyapunov function. Stability boundaries and system performance are then determined with Lyapunov’s direct method. A robot collective plume tracing numerical simulation example demonstrates this decentralized exergy/entropy collective control architecture.

scholarly journals Automatic Parking Controller with a Twin Artificial Neural Network Architecture

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Jaeyoung Moon ◽  
Il Bae ◽  
Shiho Kim
Keyword(s):  
Neural Network ◽  
Network Architecture ◽  
Neural Network Architecture ◽  
Control Laws ◽  
Confined Spaces ◽  
Human Driver ◽  
Kinematic Models ◽  
Automatic Parking ◽  
The Subject ◽  
Traditional Approaches

We propose an artificial deep neural network- (ANN-) based automatic parking controller that overcomes a stubborn restriction prevalent in traditional approaches. The proposed ANN learns human-like control laws for automatic parking through supervised learning from a training database generated by computer-aided optimizations or real experiments. By learning the relationships between the instantaneous vehicle states and the corresponding maneuver parameters, the proposed twin controller yields lateral and longitudinal maneuvering parameters for executing automatic parking tasks in confined spaces. The proposed automatic parking controller exhibits a twin architecture comprising a main agent and its cloned agent. Before the main agent assumes a maneuvering action, the cloned agent predicts the consequences of the maneuvering action through a Collision Checking and Adjustment (CCA) system. The proposed parking agent operates like a human driver in a manner that is characterized by an unplanned trajectory. In addition, the kinematics of the subject vehicle is not exactly modelled for parking control. The simulation results demonstrate that the proposed twin agent emulates the attributes of a human driver such as adaptive control and determines the consequences of the tentative maneuvering action under varying kinematic models of the subject vehicle. We validate the proposed parking controller by simulating the software-in-the-loop architecture using a PreScan simulator in which the dynamics of the virtual vehicle’s behavior resemble a real vehicle.

scholarly journals A Closed-Form Approach to Determine the Base Inertial Parameters of Complex Structured Robotic Systems

2015 ◽  
Vol 48 (1) ◽  
pp. 316-321 ◽  
Author(s):  
J. Klodmann ◽  
D. Lakatos ◽  
C. Ott ◽  
A. Albu-Schäffer
Keyword(s):  
Closed Form ◽  
Robotic Systems ◽  
Inertial Parameters ◽  
Base Inertial Parameters ◽  
Form Approach

ORCCAD: software engineering for real-time robotics. A technical insight

Robotica ◽  
1997 ◽  
Vol 15 (1) ◽  
pp. 111-115 ◽  
Author(s):  
D. Simon ◽  
B. Espiau ◽  
K. Kapellos ◽  
R. Pissard-Gibollet
Keyword(s):  
Software Engineering ◽  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Robotic Systems ◽  
Formal Definition ◽  
Programming Environment ◽  
Control Laws ◽  
Low Levels ◽  
Definition Of

The ORCCAD programming environment for robotic systems gathers control laws in continuous time at the low levels and discrete time logical aspects at higher levels. Based upon a formal definition of robotic actions, complex applications can be designed, verified and generated incrementally. The approach and tools prototypes have been validated through several applications.

scholarly journals Path and Control Planning for Autonomous Vehicles in Restricted Space and Low Speed

2020 ◽  
Author(s):  
Maksym Diachuk ◽  
Said Easa ◽  
Joel Bannis
Keyword(s):  
Autonomous Vehicles ◽  
Optimal Solution ◽  
Control Laws ◽  
Low Speed ◽  
Output State ◽  
Original Algorithm ◽  
Nonlinear Motion ◽  
Space Of Constant Curvature ◽  
Kinematic Models ◽  
And Control

The paper presents models of path and control planning for parking, docking, and movement of autonomous vehicles at low speeds considering space constraints. Given the low speed of motion, and in order to test and approve the proposed algorithms, vehicle kinematic models are used. Recent works on the development of parking algorithms for autonomous vehicles are reviewed. Bicycle kinematic models for vehicle motion are considered for three basic types of vehicles: passenger car, long wheelbase truck, and articulated vehicles with and without steered semitrailer axes. Mathematical descriptions of systems of differential equations in matrix form and expressions for determining the linearization elements of nonlinear motion equations that increase the speed of finding the optimal solution are presented. Options are proposed for describing the interaction of vehicle overall dimensions with the space boundaries, within which a maneuver should be performed. An original algorithm that considers numerous constraints is developed for determining vehicle permissible positions within the closed boundaries of the parking area, which are directly used in the iterative process of searching for the optimal plan solution using nonlinear model predictive control (NMPC). The process of using NMPC to find the best trajectories and control laws while moving in a semi-limited space of constant curvature (turnabouts, roundabouts) are described. Simulation tests were used to validate the proposed models for both constrained and unconstrained conditions and the output (state-space) and control parameters' dependencies are shown. The proposed models represent an initial effort to model the movement of autonomous vehicles for parking and has the potential for other highway applications.

scholarly journals ALGORITHM FOR SYNTHESIZING PARAMETERS OF CONTROL LAWS OF TECHNICAL SYSTEMS UNDER POLYNOMIAL APPROXIMATION OF NONLINEARITIES

2018 ◽  
pp. 97-102
Author(s):  
V. F. Shishlakov ◽  
E. Yu. Vataeva ◽  
I. G. Krivolapchuk ◽  
N. V. Reshetnikova
Keyword(s):  
Automatic Control ◽  
Control Systems ◽  
Polynomial Approximation ◽  
Nonlinear Characteristics ◽  
Control Laws ◽  
Software Complex ◽  
Automatic Control Systems ◽  
New Class ◽  
Advantages And Disadvantages ◽  
Direct Variational Method

The paper considers the algorithm for solving the problem of synthesis of automatic control systems (ACS) with nonlinear characteristics for polynomial approximation. As a mathematical apparatus, the inversion of the direct variational method of analysis, Galerkin generalized method, is applied to the solution of the problem. Recurrence relations are obtained that make it possible to extend this method to a new class of dynamical systems with nonlinear elements whose characteristics are approximated polynomially. The advantages and disadvantages of various methods of approximation of automatic control systems with nonlinear characteristics are analyzed. The presented algorithm of the software complex is universal and allows solving the synthesis problem for control systems of different classes and structures from unified mathematical, methodological and algorithmic positions.

Distributed Control of a Planar Discrete Elastic Rod Model for Caterpillar-Inspired Locomotion

2019 ◽  
Author(s):  
Helene Nguewou-Hyousse ◽  
William L. Scott ◽  
Derek A. Paley
Keyword(s):  
Feedback Control ◽  
Distributed Control ◽  
Nearest Neighbor ◽  
Traveling Wave Solutions ◽  
Robotic Systems ◽  
Elastic Rod ◽  
Control Laws ◽  
Simulation Results ◽  
Feedback Laws ◽  
Elastic Rod Model

Abstract During crawling, a caterpillar body stretches and bends, and a wave repeatedly travels from the tail to the head. Recently, caterpillar locomotion has been modeled using the theory of planar discrete elastic rods (PDER). This work takes a similar modeling approach and introduces feedback control laws with communication between neighboring segments. Caterpillar locomotion is modeled first as a network of spring-mass-dampers connected through nearest neighbor interactions and then as a network of linked torsional springs. Feedback laws are designed to achieve consensus and traveling wave solutions. Simulation results show the displacement of each segment of a caterpillar during locomotion. These results show promise for the design of feedback control laws in a network model of soft robotic systems.

scholarly journals Path and Control Planning for Autonomous Vehicles in Restricted Space and Low Speed

2020 ◽  
Vol 5 (5) ◽  
pp. 42 ◽  
Author(s):  
Maksym Diachuk ◽  
Said M. Easa ◽  
Joel Bannis
Keyword(s):  
Autonomous Vehicles ◽  
Optimal Solution ◽  
Control Laws ◽  
Low Speed ◽  
Output State ◽  
Original Algorithm ◽  
Nonlinear Motion ◽  
Space Of Constant Curvature ◽  
Kinematic Models ◽  
And Control

This paper presents models of path and control planning for the parking, docking, and movement of autonomous vehicles at low speeds, considering space constraints. Given the low speed of motion, and in order to test and approve the proposed algorithms, vehicle kinematic models are used. Recent works on the development of parking algorithms for autonomous vehicles are reviewed. Bicycle kinematic models for vehicle motion are considered for three basic types of vehicles: passenger car, long wheelbase truck, and articulated vehicles with and without steered semitrailer axes. Mathematical descriptions of systems of differential equations in matrix form and expressions for determining the linearization elements of nonlinear motion equations that increase the speed of finding the optimal solution are presented. Options are proposed for describing the interaction of vehicle overall dimensions with the space boundaries, within which a maneuver should be performed. An original algorithm that considers numerous constraints is developed for determining vehicle permissible positions within the closed boundaries of the parking area, which are directly used in the iterative process of searching for the optimal plan solution using nonlinear model predictive control (NMPC). The process of using NMPC to find the best trajectories and control laws while moving in a semi-limited space of constant curvature (turnabouts, roundabouts) are described. Simulation tests were used to validate the proposed models for both constrained and unconstrained conditions and the output (state-space) and control parameters’ dependencies are shown. The proposed models represent an initial effort to model the movement of autonomous vehicles for parking and have the potential for other highway applications.

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