Motion Planning of Uncertain Fully-Actuated Dynamical Systems: An Inverse Dynamics Formulation

2011 ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Nonlinear Programming ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Optimal Motion ◽  
Time Optimal ◽  
New Framework

This work presents a novel nonlinear programming based motion planning framework that treats uncertain fully-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; ignoring uncertainty during design may lead to poor robustness and suboptimal performance. System uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, new design questions related to uncertain dynamical systems can now be answered through the new framework. Specifically, this work presents the new framework through an inverse dynamics formulation where deterministic state trajectories are prescribed and uncertain actuator inputs are quantified. The benefits of the ability to quantify the resulting actuator uncertainty are illustrated in a time optimal motion planning case-study of a serial manipulator pick-and-place application. The resulting design determines a feasible time optimal motion plan—subject to actuator and obstacle avoidance constraints—for all possible systems within the probability space. The forward dynamics formulation (using deterministic actuator inputs and uncertain state trajectories) is presented in a companion paper.

Motion Planning of Uncertain Fully-Actuated Dynamical Systems: A Forward Dynamics Formulation

2011 ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Nonlinear Programming ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Least Square ◽  
Forward Dynamics ◽  
Optimal Motion ◽  
New Framework

This work presents a novel nonlinear programming based motion planning framework that treats uncertain fully-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; ignoring uncertainty during design may lead to poor robustness and suboptimal performance. System uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, new design questions related to uncertain dynamical systems can now be answered through the new framework. Specifically, this work presents the new framework through a forward dynamics formulation where deterministic actuator inputs are prescribed and uncertain state trajectories are quantified. The benefits of the ability to quantify the resulting state uncertainty are illustrated in an effort optimal motion planning case-study of a serial manipulator pick-and-place application. The resulting design determines a feasible effort optimal motion plan—subject to actuator and obstacle avoidance constraints—for all possible systems within the probability space. Variance of the system’s terminal conditions are also minimized in a Pareto optimal sense. The inverse dynamics formulation (using deterministic state trajectories and uncertain actuator inputs) is presented in a companion paper.

Motion Planning of Uncertain Under-Actuated Dynamical Systems: A Hybrid Dynamics Formulation

2011 ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Nonlinear Programming ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Design System ◽  
Double Pendulum ◽  
Hybrid Dynamics ◽  
New Framework

This work presents a novel nonlinear programming based motion planning framework that treats uncertain under-actuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it’s not accounted for in a given design. System uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiencies of this approach enable the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, new design questions related to uncertain dynamical systems can now be answered through the new framework. Specifically, this work presents the new framework through a hybrid dynamics formulation for under-actuated systems where actuated state and unactuated input trajectories are prescribed and uncertain unactuated states and actuated inputs are quantified. The benefits of the ability to quantify the resulting uncertainties are illustrated in a power optimal motion planning case-study for an inverting double pendulum problem. The resulting design determines a motion plan that minimizes the required input power—subject to actuator and terminal condition variance constraints—for all possible systems within the probability space.

scholarly journals Motion Planning of Uncertain Ordinary Differential Equation Systems

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Nonlinear Programming ◽  
Dynamical Systems ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Underactuated Systems ◽  
Forward Dynamics ◽  
Hybrid Dynamics

This work presents a novel motion planning framework, rooted in nonlinear programming theory, that treats uncertain fully and underactuated dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it, and poor robustness and suboptimal performance result if it is not accounted for in a given design. In this work uncertainties are modeled using generalized polynomial chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach enables the inclusion of uncertainty statistics in the nonlinear programming optimization process. As such, the proposed framework allows the user to pose, and answer, new design questions related to uncertain dynamical systems. Specifically, the new framework is explained in the context of forward, inverse, and hybrid dynamics formulations. The forward dynamics formulation, applicable to both fully and underactuated systems, prescribes deterministic actuator inputs that yield uncertain state trajectories. The inverse dynamics formulation is the dual to that of forward dynamics, and is only applicable to fully actuated systems; deterministic state trajectories are prescribed and yield uncertain actuator inputs. The inverse dynamics formulation is more computationally efficient as it requires only algebraic evaluations and completely avoids numerical integration. Finally, the hybrid dynamics formulation is applicable to underactuated systems where it leverages the benefits of inverse dynamics for actuated joints and forward dynamics for unactuated joints; it prescribes actuated state and unactuated input trajectories that yield uncertain unactuated states and uncertain actuated inputs. The benefits of the ability to quantify uncertainty when planning the motion of multibody dynamic systems are illustrated through several case studies. The resulting designs determine optimal motion plans—subject to deterministic and statistical constraints—for all possible systems within the probability space.

scholarly journals Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

2011 ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Dynamical Systems ◽  
Optimal Design ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Parametric Uncertainty ◽  
Least Square ◽  
Optimization Process ◽  
Entire Family ◽  
New Framework

This work presents a novel optimal design framework that treats uncertain dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness and suboptimal performance. In this work uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The uncertainty statistics are explicitly included in the optimization process. Systems that are nonlinear, have active constraints, or opposing design objectives are shown to benefit from the new framework. Specifically, using a constraint-based multi-objective formulation, the direct treatment of uncertainties during the optimization process is shown to shift, or off-set, the resulting Pareto optimal trade-off curve. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design that accounts for the entire family of systems within the associated probability space.

scholarly journals Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Joe Hays ◽  
Adrian Sandu ◽  
Corina Sandu ◽  
Dennis Hong
Keyword(s):  
Dynamical Systems ◽  
Optimal Design ◽  
Initial Conditions ◽  
Practical Importance ◽  
Real Life ◽  
Parametric Uncertainty ◽  
Least Square ◽  
Optimization Process ◽  
Entire Family ◽  
New Framework

This work presents a novel optimal design framework that treats uncertain dynamical systems described by ordinary differential equations. Uncertainty in multibody dynamical systems comes from various sources, such as system parameters, initial conditions, sensor and actuator noise, and external forcing. The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness and suboptimal performance. In this work, uncertainties are modeled using generalized polynomial chaos and are solved quantitatively using a least-square collocation method. The uncertainty statistics are explicitly included in the optimization process. Systems that are nonlinear have active constraints, or opposing design objectives are shown to benefit from the new framework. Specifically, using a constraint-based multi-objective formulation, the direct treatment of uncertainties during the optimization process is shown to shift, or off-set, the resulting Pareto optimal trade-off curve. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design that accounts for the entire family of systems within the associated probability space.

scholarly journals Path Tracking Algorithms for Non-Convex Waiter Motion Problem

2018 ◽  
Vol 62 (1) ◽  
pp. 16-23
Author(s):  
Ákos Nagy ◽  
Gábor Csorvási ◽  
István Vajk
Keyword(s):  
Motion Planning ◽  
Optimization Problem ◽  
Minimum Energy ◽  
Real Life ◽  
Problem Formulation ◽  
Energy Planning ◽  
Special Area ◽  
Time Optimal ◽  
Motion Problem ◽  
Optimal Approach

Originally, motion planning was concerned with problems such as how to move an object from a start to a goal position without hitting anything. Later, it has extended with complications such as kinematics, dynamics, uncertainties, and also with some optimality purpose such as minimum-time, minimum-energy planning. The paper presents a time-optimal approach for robotic manipulators. A special area of motion planning is the waiter motion problem, in which a tablet is moved from one place to another as fastas possible, avoiding the slip of the object that is placed upon it. The presented method uses the direct transcription approach for the waiter problem, which means a optimization problem is formed in order to obtain a time-optimal control for the robot. Problem formulation is extended with a non-convex jerk constraints to avoid unwanted oscillations during the motion. The possible local and global solver approaches for the presented formulation are discussed, and the waiter motion problem is validated by real-life experimental results with a 6-DoF robotic arm.

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