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Your search keyword '"TRAJECTORY optimization"' showing total 9 results
9 results on '"TRAJECTORY optimization"'

1. Optimal Model-Based Trajectory Planning With Static Polygonal Constraints.

Author

Martinsen, Andreas B., Lekkas, Anastasios M., and Gros, Sebastien

Subjects
DYNAMICAL systems, TRAJECTORY optimization, POLYGONS, MOBILE robots
Abstract

The main contribution of this article is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph search, i.e., a discrete roadmap method, with convex optimization, i.e., a complete path method. Contrary to past approaches, which have focused on using simple obstacle approximations, or suboptimal spatial discretizations, our approach is able to use the exact geometry of polygonal constraints in order to plan optimal trajectories. The performance and flexibility of the proposed method are evaluated via simulations by planning distance-optimal trajectories for a Dubins car model, as well as time-, distance-, and energy-optimal trajectories for a marine vehicle. [ABSTRACT FROM AUTHOR]

Published
2022
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2. Motion Optimization for Musculoskeletal Dynamics: A Flatness-Based Polynomial Approach.

Author

Richter, Hanz and Warner, Holly

Subjects
*POLYNOMIALS, *MATHEMATICAL optimization, *MATHEMATICAL programming, *NONLINEAR systems, *PARAMETERIZATION, *TRAJECTORY optimization, *COLLOCATION methods
Abstract

A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid-body and muscle dynamics described with a Hill-type model driven by neural control inputs. The objective is to find input and state trajectories that are optimal with respect to a minimum-effort objective and meet constraints associated with musculoskeletal models. The measure of effort is given by the integral of pairwise average forces of the agonist-antagonist muscles. The concepts of flat parameterization of nonlinear systems and sum-of-squares optimization are combined to yield a method that eliminates the numerous set of dynamic constraints present in collocation methods. With terminal equilibrium, optimization reduces to a feasible linear program, and a recursive feasibility proof is given for more general polynomial optimization cases. The methods of the article can be used as a basis for fast, and efficient solvers for hierarchical, and receding-horizon control schemes. Two simulation examples are included to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Published
2021
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3. Strong Stationarity Conditions for Optimal Control of Hybrid Systems.

Author

Hempel, Andreas B., Goulart, Paul J., and Lygeros, John

Subjects
*HYBRID systems, *OPTIMAL control theory, *SYMMETRIC matrices, *TRAJECTORY optimization, *DYNAMIC programming, *NONLINEAR dynamical systems
Abstract

We present necessary and sufficient optimality conditions for finite-time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush–Kuhn–Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine (PWA) system can be written as the optimizer of a mathematical program, which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with PWA dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation. [ABSTRACT FROM AUTHOR]

Published
2017
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4. Parallel Generate Entry Landing Footprint Using Differential Evolution.

Author

Chang, Songtao, Wang, Yongji, and Liu, Lei

Abstract

Landing footprint of an entry vehicle provides critical information for mission planning. Conventional methods calculate it through solving a family of multi-constraints optimal control problems. It is difficult to solve. To generate the boundary of it, we proposed a new scheme based on differential evolution(DE). Utilizing DE's parallelism, each run generates one side instead of one point of the boundary. To get the full boundary, just need run the algorithm two times. The algorithm's merits include accurate, fast, not relying on simplification of the system, all control variables are under consideration and facilitating parallel programming. [ABSTRACT FROM PUBLISHER]

Published
2012
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5. Online predictive control based trajectory optimization of tethered foils for wind energy generator.

Author

Mingwei, Sun, Donghui, Liu, Sheng, Quan, and Zengqiang, Chen

Abstract

Capturing the stable wind energy in the high altitude is a novel green generation approach. Rational trajectory optimization can obtain the maximal power difference between the traction phase and the recovery phase. Receding horizon model predictive control in the offline manner was previously employed to handle this type of problem, however it is time-consuming and lacks of adaptability and flexibility to varying aerodynamic parameters. This paper presents a receding horizon optimization method for the tethered foil generator based on an online searching strategy. The nonlinear optimization problem can be approximately reformulated to a univariate receding horizon sub-optimal issue in a short interval in four phases with different objectives. By using uniform sampling and chaotic search approaches, the sub-optimal solution, subject to the physical constraints, is obtained online. The simulation results demonstrate its effectiveness. This algorithm has the potential to be realized in a parallel pattern. [ABSTRACT FROM PUBLISHER]

Published
2012

6. Trajectory optimization for Missile-borne SAR imaging phase via Gauss Pseudospectral Method.

Author

Zhang, Gang, Zhu, Ming-bo, Zhao, Zhen-bo, and Li, Xiang-ping

Abstract

Azimuth resolution of Missile-borne synthetic aperture radar(SAR) is affected by the trajectory and look angle. In order to acquire the fixed azimuth resolution within a minimum time for SAR imaging seeker, a new approach of solving optimal control problem, that is, Gauss Pseudospectral Method(GPM), is proposed to optimize imaging phase trajectory of Missile-borne SAR. First of all, optimization model of imaging phase is built, the missile command acceleration is used as control variables, the minimum dwell time is used as objective function and expression of objective function, imaging constraint as well as over loading constraint is proposed. And then, the state and control variables is discretized by GPM. Through this transformation, the continuous-time optimal control problem is transcribed to a nonlinear programming (NLP). At last, GPOPS software package based on matlab is used to solve this problem. Simulation results show that a smooth trajectory can be got by GPM, and GPM isn't sensitive to initial value of state and control variables. Compared with genetic algorithm, GPM have a faster solution speed and a better robustness. [ABSTRACT FROM PUBLISHER]

Published
2011
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7. Trajectory Optimization for the Engine–Generator Operation of a Series Hybrid Electric Vehicle.

Author

Nino-Baron, Carlos E., Tariq, Abdul Rehman, Zhu, Guoming, and Strangas, Elias G.

Subjects
*TORQUE, *HYBRID electric vehicles, *ENERGY consumption, *ALGORITHMS, *MATHEMATICAL optimization
Abstract

This paper presents a methodology of calculating the optimal torque and speed commands for the engine–generator system of a series hybrid electric vehicle (HEV). In series HEVs, the engine–generator subsystem provides electrical energy to the dc link. This paper proposes an optimal control strategy of the engine–generator subsystem to generate a desired amount of energy within a given period of time. The optimization algorithm, based on trajectory optimization, determines the torque and speed reference signals for the engine–generator subsystem that achieve maximum efficiency. A simplified version of the controller is also presented for online implementation. The proposed control strategy is compared with nonoptimized control techniques, and simulation results show the improvements in energy efficiency. [ABSTRACT FROM PUBLISHER]

Published
2011
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8. Separation of motion techniques for trajectory optimization in flexible redundant robot manipulators

Author

Seyed Mohammad Reza Faritus, Stanford Shateyi, and Mohammad Hassan Heidari

Subjects
0209 industrial biotechnology, elastic vibration, Optimization problem, redundancy, Computer science, lcsh:Mechanical engineering and machinery, Mechanical Engineering, robot, 02 engineering and technology, Kinematics, Trajectory optimization, Optimal control, 020303 mechanical engineering & transports, 020901 industrial engineering & automation, Maximum principle, 0203 mechanical engineering, Control theory, Redundancy (engineering), Trajectory, lcsh:TJ1-1570, General Materials Science, Boundary value problem, optimization
Abstract

This paper presents a computational method for optimization of trajectory in redundant robot manipulators. For this purpose, all possible answers are acquired based on rigid conditions and redundancy of the robot. Using open loop optimal control method, the trajectory which minimizes the objective function will be obtained. The objective function is considered as an integral index that will be minimized in the entire trajectory. The objective function and constraints of optimization problem will be selected based on conditions of motion. Dynamic equations of the system are constraints of optimization problem in point-to-point motion. For motion conditions in the specified path, kinematic equations will be added. Also, unequal constraints are applied for limiting the velocity and torque. By selecting the state and control signal vectors which are obtained by assuming rigid motion of the robot, the objective function and constraints will be changed to standard form of an optimization problem. Pontryagin’s maximum principle is used to solve equations. So, the equations of classical form will be changed into two-point boundary value problem. Suggested method is applied to point-to-point motion and movement in the specified path. Results demonstrate accuracy and efficiency of suggested method.

Published
2017

9. Stochastic Maximum Principle for Optimal Control Problems of Forward-Backward Systems Involving Impulse Controls.

Author

Wu, Zhen and Zhang, Feng

Subjects
*STOCHASTIC processes, *CONTROL theory (Engineering), *PROCESS control systems, *MATHEMATICAL optimization, *DIFFERENTIAL equations, *MAXIMUM principles (Mathematics), *TRAJECTORY optimization
Abstract

We consider a stochastic optimal control problem of a forward-backward system in which the control variable consists of two components: the continuous control and the impulse control. The domain of the control is assumed to be convex. Necessary optimality conditions of the Pontryagin maximum principle type are obtained for this stochastic optimal control problem. We also give additional conditions, under which the necessary optimality conditions turn out to be sufficient. [ABSTRACT FROM AUTHOR]

Published
2011
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