scholarly journals Vehicle Optimal Velocity Curves for Minimum-Time Maneuver

2014 ◽  
Vol 6 ◽  
pp. 194868 ◽  
Author(s):  
Li-xia Zhang ◽  
Fu-quan Pan ◽  
Xiao-yuan Chen ◽  
Feng-yuan Wang ◽  
Jun Lu ◽  
...  
Keyword(s):  
Optimal Control ◽  
Inverse Dynamics ◽  
Minimum Time ◽  
Curvature Radius ◽  
Minimal Amount ◽  
Optimal Velocity ◽  
Moving Vehicles ◽  
New Perspective ◽  
Vehicle Travel Time ◽  
The Given

A problem in vehicle minimum-time maneuver is the assumption that a vehicle passes through a given path in a minimal amount of time without deviating from the boundary of the given path. Vehicle handling inverse dynamics provides a new perspective to solve such problem. Based on inverse dynamics, this paper transformed the problem of optimal vehicle velocity for minimum-time maneuver into that of optimal control with the objective function of minimum time. The path for minimum vehicle travel time and the optimal control model were established. The optimal velocity curves for three types of paths, namely, monotonically increasing path, monotonically decreasing path, and constant radius path, were analyzed. On this basis, the optimal velocity curves were solved for two kinds of concrete paths: a path of decreasing curvature radius followed by a path of increasing curvature radius and another path of increasing curvature radius followed by a path of decreasing curvature radius. Nine cases of possible optimal velocity curves were acquired. The optimal velocity curve of the given path, that is, a parabola followed by a semicircle, was obtained. Optimal velocity curves can be used as reference for vehicle minimum-time maneuver, which is an important issue for driver safety in fast-moving vehicles.

scholarly journals Minimum Time Approach to Emergency Collision Avoidance by Vehicle Handling Inverse Dynamics

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Wang Wei ◽  
Bei Shaoyi ◽  
Yang Hui ◽  
Wang Yongzhi ◽  
Zhang Lanchun
Keyword(s):  
Optimal Control ◽  
Collision Avoidance ◽  
High Speed ◽  
Inverse Dynamics ◽  
Avoidance Performance ◽  
Control Object ◽  
Minimum Time ◽  
Driving Safety ◽  
Multiple Shooting ◽  
Vehicle Handling

Vehicle driving safety is the urgent key problem to be solved of automobile independent development while encountering emergency collision avoidance with high speed. And it is also the premise and one of the necessary conditions of vehicle active safety. A new technique of vehicle handling inverse dynamics which can evaluate the emergency collision avoidance performance is proposed. Based on optimal control theory, the steering angle input and the traction/brake force imposed by driver are the control variables; the minimum time required to complete the fitting biker line change is the control object. By using the improved direct multiple shooting method, the optimal control problem is converted into a nonlinear programming problem that is then solved by means of the sequential quadratic programming. The simulation results show that the proposed method can solve the vehicle minimum time maneuver problem, and can compare the maneuverability of two different vehicles that complete fitting biker line change with the minimum time and the correctness of the model is verified through real vehicle test.

scholarly journals Optimal Control and Positional Controllability in a One-Sector Economy

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 11
Author(s):  
Nikolai Grigorenko ◽  
Lilia Luk’yanova
Keyword(s):  
Optimal Control ◽  
Production Capacity ◽  
Quality Criterion ◽  
Zero Order ◽  
Suboptimal Control ◽  
Time Interval ◽  
Bounded Control ◽  
Optimal Value ◽  
Current Production ◽  
The Given

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

Optimal control of a laser source to generate a minimum time trajectory of a droplet in a liquid layer

2016 ◽  
Author(s):  
Francesco Biral ◽  
Enrico Bertolazzi ◽  
Paolo Bosetti ◽  
Alberto De Marchi ◽  
Martin M. Hanczyc
Keyword(s):  
Optimal Control ◽  
Liquid Layer ◽  
Minimum Time ◽  
Laser Source

Minimum time overtaking problem of vehicle handling inverse dynamics based on interval mathematics

2018 ◽  
Vol 233 (6) ◽  
pp. 1534-1545 ◽  
Author(s):  
Youqun Zhao ◽  
Wenxin Zhang ◽  
Xinglong Zhang ◽  
Fen Lin
Keyword(s):  
Inverse Dynamics ◽  
Age Groups ◽  
Pseudospectral Method ◽  
Unmanned Vehicles ◽  
Minimum Time ◽  
Vehicle Handling ◽  
Interval Mathematics ◽  
Interval Analysis Method ◽  
Driving Assistance ◽  
Driving Assistance System

To analyze the influence of uncertain factors on minimum time overtaking, interval mathematics is used to describe the uncertainties, and the overtaking safety distance is calculated using interval analysis method. In addition, vehicle handling inverse dynamics is proposed in this paper. In this method, the driver-handling input can be obtained without the modeling of driver. The optimal control problem is first converted into a nonlinear programming problem based on Gauss pseudospectral method. Then sequential quadratic programming is applied to get the solution. The simulation results show that the overtaking behavior will be significantly different, if the drivers’ age groups or vehicles’ braking system parameters are different. Besides, the influence of different drivers’ estimate time is critical. The subjective judgments of the drivers are considered in this paper to realize the user-friendly design. This method may provide a reference for the research of unmanned vehicles and driving assistance system.

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

Optimal Control of a Multirotor Unmanned Aerial Vehicle Based on a Multiphysical Model

2020 ◽  
Author(s):  
Nicolas Michel ◽  
Zhaodan Kong ◽  
Xinfan Lin
Keyword(s):  
Optimal Control ◽  
Unmanned Aerial Vehicle ◽  
Operation Time ◽  
Rigid Body Dynamics ◽  
System Level ◽  
Optimal Velocity ◽  
Rotor Aerodynamics ◽  
Time Optimal ◽  
Aerial Vehicle ◽  
Level Model

Abstract Electric multirotor aircraft with vertical-take-off-and-landing capabilities are emerging as a revolutionary transportation mode. This paper studies optimal control of a multirotor unmanned aerial vehicle based on a system-level multiphysical model. The model considers aerodynamics of the rotor-propeller assembly, electro-mechanical dynamics of the motor and motor controller, and rigid-body dynamics of the vehicle, as control based on a system-level model incorporating all these dynamics and their coupling is missing in literature. A forward flight operation is considered for time-optimal and energy-optimal control, as well as battery voltages of 25 V and 21 V. Energy-optimal control is shown to reduce the energy required for the operation by 38.5% at 25 V, while reducing the battery voltage increases the minimum operation time by 19.8%. The energy-optimal cruise velocity is also examined, demonstrating that the optimal velocity predicted without considering rotor aerodynamics uses 35.2% more energy per meter travelled than is required at the true optimal velocity.

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