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85
A New Computational Approach to RealTime Trajectory Generation for Constrained Mechanical Systems
, 2000
"... Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that rea ..."
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Cited by 96 (21 self)
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Preliminary results of a new computational approach to generate aggressive trajectories in realtime for constrained mechanical systems are presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that realtime trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package. Keywords: Realtime optimization, nonlinear control design, optimal control, constrained trajectory generation, guidance. 1
Autonomous Vehicle Technologies for Small Fixed Wing UAVs
 AIAA JOURNAL OF AEROSPACE COMPUTING, INFORMATION, AND COMMUNICATION
, 2003
"... Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for realtime motion planning of small aut ..."
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Cited by 67 (17 self)
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Autonomous unmanned air vehicle flight control systems require robust path generation to account for terrain obstructions, weather, and moving threats such as radar, jammers, and unfriendly aircraft. In this paper, we outline a feasible, hierarchal approach for realtime motion planning of small autonomous fixedwing UAVs. The approach divides the trajectory generation into four tasks: waypoint path planning, dynamic trajectory smoothing, trajectory tracking, and lowlevel autopilot compensation. The waypoint path planner determines the vehicle 's route without regard for the dynamic constraints of the vehicle. This results in a significant reduction in the path search space, enabling the generation of complicated paths that account for popup and dynamically moving threats. Kinematic constraints are satisfied using a trajectory smoother which has the same kinematic structure as the physical vehicle. The third step of the approach uses a novel tracking algorithm to generate a feasible state trajectory that can be followed by a standard autopilot. MonteCarlo simulations were done to analyze the performance and feasibility of the approach and determine realtime computation requirements. A planar version of the algorithm has also been implemented and tested in a lowcost microcontroller. The paper describes a custom UAV built to test the algorithms.
Numerical solution of optimal control problems by direct collocation’, Ed
 In Optimal Control  Calculus of Variation, Optimal Control Theory and Numerical Methods, 111, 129143, International Series of Numerical Mathematics, Birkhäuser
, 1993
"... By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method ..."
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Cited by 56 (2 self)
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By an appropriate discretization of control and state variables, a constrained optimal control problem is transformed into a finite dimensional nonlinear program which can be solved by standard SQPmethods [10]. Convergence properties of the discretization are derived. From a solution of this method known as direct collocation, these properties are used to obtain reliable estimates of adjoint variables. In the presence of active state constraints, these estimates can be significantly improved by including the switching structure of the state constraint into the optimization procedure. Two numerical examples are presented. 1 Statement of problems Systems governed by ordinary differential equations arise in many applications as, e. g., in astronautics, aeronautics, robotics, and economics. The task of optimizing these systems leads to the optimal control problems investigated in this paper. The aim is to find a control vector u(t) and the final time tf that minimize the functional
Nonlinear optimal control via occupation measures and LMI relaxations
 SIAM Journal on Control and Optimization
, 2008
"... Abstract. We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state an ..."
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Cited by 46 (23 self)
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Abstract. We consider the class of nonlinear optimal control problems (OCP) with polynomial data, i.e., the differential equation, state and control constraints and cost are all described by polynomials, and more generally for OCPs with smooth data. In addition, state constraints as well as state and/or action constraints are allowed. We provide a simple hierarchy of LMI (linear matrix inequality)relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Under some convexity assumptions, the sequence converges to the optimal value of the OCP. Preliminary results show that good approximations are obtained with few moments. 1.
SQP Methods And Their Application To Numerical Optimal Control
, 1997
"... . In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown ..."
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Cited by 33 (0 self)
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. In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying generalpurpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. largescale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...
Numerical Optimal Control Of Parabolic PDEs Using DASOPT
, 1997
"... . This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package ..."
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Cited by 15 (6 self)
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. This paper gives a preliminary description of DASOPT, a software system for the optimal control of processes described by timedependent partial differential equations (PDEs). DASOPT combines the use of efficient numerical methods for solving differentialalgebraic equations (DAEs) with a package for largescale optimization based on sequential quadratic programming (SQP). DASOPT is intended for the computation of the optimal control of timedependent nonlinear systems of PDEs in two (and eventually three) spatial dimensions, including possible inequality constraints on the state variables. By the use of either finitedifference or finiteelement approximations to the spatial derivatives, the PDEs are converted into a large system of ODEs or DAEs. Special techniques are needed in order to solve this very large optimal control problem. The use of DASOPT is illustrated by its application to a nonlinear parabolic PDE boundary control problem in two spatial dimensions. Computational resu...
Nonlinear hybrid dynamical systems: modeling, optimal control, and applications
 in Modelling, Analysis and Design of Hybrid Systems, ser. Lecture Notes in Control and Information
, 2002
"... Abstract. Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are ..."
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Cited by 13 (7 self)
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Abstract. Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branchandbound. These are applied to a robotic multiarm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem. 1
Optimal Control of the Industrial Robot Manutec r3
, 1994
"... Minimum time and minimum energy pointtopoint trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct coll ..."
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Cited by 12 (2 self)
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Minimum time and minimum energy pointtopoint trajectories for an industrial robot of the type Manutec r3 are computed subject to state constraints on the angular velocities. The numerical solutions of these optimal control problems are obtained in an efficient way by a combination of a direct collocation and an indirect multiple shooting method. This combination links the benefits of both approaches: A large domain of convergence and a highly accurate solution. The numerical results show that the constraints on the angular velocities become active during large parts of the time optimal motion. But the resulting stress on the links can be significantly reduced by a minimum energy trajectory that is only about ten percent slower than the minimum time trajectory. As a byproduct, the reliability of the direct collocation method in estimating adjoint variables and the efficiency of the combination of direct collocation and multiple shooting is demonstrated. The highly accurate solutions ...
Modeling and Optimal Centralized Control of a LargeSize Robotic Population
, 2006
"... Abstract—This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics ..."
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Cited by 12 (1 self)
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Abstract—This paper describes an approach to the modeling and control of multiagent populations composed of a large number of agents. The complexity of population modeling is avoided by assuming a stochastic approach, under which the agent distribution over the state space is modeled. The dynamics of the state probability density functions is determined, and a control problem of maximizing the probability of robotic presence in a given region is introduced. The Minimum Principle for the optimal control of partial differential equations is exploited to solve this problem, and it is applied to the mission control of a simulated large robotic population. Index Terms—Hybrid automata, multirobot systems, optimal control. I.
Algorithm 733: TOMP  Fortran modules for optimal control calculations
 ACM Trans. Math. Soft
, 1994
"... A great number of analysis and synthesis problems of modern processes can be written as state and control constrained optimal control problems governed by ordinary differential equations with multipoint boundary values. As the software tools for following this attractive approach are still missing o ..."
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Cited by 10 (0 self)
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A great number of analysis and synthesis problems of modern processes can be written as state and control constrained optimal control problems governed by ordinary differential equations with multipoint boundary values. As the software tools for following this attractive approach are still missing or can be used only by experts, the structure and usage of an easytouse software package is described which efficiently solves the given problem Among its features are userorientation, applicability onpersonal computers and mainframes, and robustness with respect to model changes and inaccurate starting values, It has been tested on a number of complex engineering tasks, including aerospace and robotic trajectory planning.