Time Optimal Trajectory Tracking of Redundant Planar Cable-Suspended Robots Considering Both Tension and Velocity Constraints

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Hamid Reza Fahham ◽  
Mehrdad Farid ◽  
Moosa Khooran
Keyword(s):  
Trajectory Tracking ◽  
Optimal Trajectory ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Hybrid Genetic Algorithm ◽  
Initial State ◽  
Control Approach ◽  
Time Optimal ◽  
Velocity Constraints ◽  
Bang Bang Control

In this paper, time optimal trajectory tracking of redundant planar cable-suspended robots is investigated. The equations of motion of these cable robots are obtained as a system of second order differential equation in terms of path parameter s using the specified path. Besides, the bounds on the cable tensions and cable velocities are transformed into the bounds on the acceleration and velocity along the path. Assuming bang-bang control, the switching points in ṡ2−s plane are obtained. Then the cable tensions are found in terms of path parameter and, subsequently, versus time. The proposed approach is validated and the effect of the number of superfluous cables on the value of minimum time is studied. The next notable challenges include time optimal path planning of cable-suspended robots. By developing a hybrid genetic algorithm and bang-bang control approach, the minimum motion time from initial state to final one and also the corresponding path can be found. The optimum path is the one that minimizes traveling time from initial state to final one, while not exceeding the cable tensions and cable velocities limits, without collision with any obstacles.

Trajectory optimisation of an aerobatic air race

2009 ◽  
Vol 113 (1139) ◽  
pp. 1-8 ◽  
Author(s):  
H. van der Plas ◽  
H. G. Visser
Keyword(s):  
High Performance ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Optimal Solution ◽  
Open Loop ◽  
Receding Horizon ◽  
Mass Model ◽  
Control Approach ◽  
Time Optimal ◽  
Trajectory Optimisation

Abstract This paper deals with the synthesis of optimal trajectories for aerobatic air races. A typical example of an air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescribed slalom course consisting of specially designed inflatable pylons, known as ‘air gates’, in the fastest possible time. The trajectory that we seek to optimise is based on such a course. The air race problem is formulated as a minimum-time optimal control problem and solved in open-loop form using a direct numerical multi-phase trajectory optimisation approach based on collocation and non-linear programming. The multiphase feature of the employed collocation algorithm is used to enable a Receding-Horizon optimisation approach, in which only a limited number of manoeuvres in sequence is considered. It is shown that the Receding-Horizon control approach provides a near-optimal solution at a significantly reduced computational cost relative to trajectory optimisation over the entire course. To avoid the path inclination singularity in the equations of motion based on Euler angles, a point-mass model formulation is used that is based on quaternions. Numerical results are presented for an Extra 300S, a purpose-designed aerobatic aircraft.

An Efficient Approach of Time-Optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Wei Dong ◽  
Ye Ding ◽  
Jie Huang ◽  
Xiangyang Zhu ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Trajectory Tracking ◽  
Linear Programming Problem ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Nurbs Curve ◽  
Tracking Controller ◽  
Time Optimal ◽  
Trajectory Tracking Controller

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Near Time-Optimal Collision-Free Motion Planning of Robotic Manipulators Using an Evolutionary Algorithm

Robotica ◽  
1996 ◽  
Vol 14 (6) ◽  
pp. 621-632 ◽  
Author(s):  
A.S. Rana ◽  
A.M.S. Zalzala
Keyword(s):  
Evolutionary Algorithm ◽  
Equations Of Motion ◽  
Optimal Path ◽  
Robotic Manipulators ◽  
Joint Space ◽  
Open Loop ◽  
Time Histories ◽  
Time Optimal ◽  
Time Planning ◽  
Path Modification

A technique for open-loop minimum time planning of time-histories of control torques for robotic manipulators subject to constraints on the control torques using evolutionary algorithm is presented here. Planning is carried out in joint space of the manipulator and the path is represented as a string of via-points connected by cubic spline polynomial functions. Repeated path modification is done by using the evolutionary algorithm to search for a time-optimal path. Time taken to traverse over a particular path is calculated by reducing the dynamic equations of motion over that path in terms of a path parameter and then calculating the time optimal-control over that path.

Time Optimal Path Planning of Palletizing Robot

2013 ◽  
Vol 470 ◽  
pp. 658-662
Author(s):  
Yong Pan Xu ◽  
Ying Hong
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Optimal Path ◽  
Straight Path ◽  
Optimal Path Planning ◽  
Quintic Polynomial ◽  
Time Optimal ◽  
Acceleration And Deceleration ◽  
Planning Algorithm ◽  
Optimal Trajectory Planning

In order to improve the efficiency and reduce the vibration of Palletizing Robot, a new optimal trajectory planning algorithm is proposed. This algorithm is applied to the trajectory planning of Palletizing manipulators. The S-shape acceleration and deceleration curve is adopted to interpolate joint position sequences. Considering constraints of joint velocities, accelerations and jerks, the traveling time of the manipulator is minimized. The joint interpolation confined by deviation is used to approximate the straight path, and the deviation is decreased significantly by adding only small number of knots. Traveling time is solved by using quintic polynomial programming strategy between the knots, and then time-jerk optimal trajectories which satisfy constraints are planned. The results show that the method can avoid the problem of manipulator singular points and improve the palletize efficiency.

How to Beat Flappy Bird: A Mixed-Integer Model Predictive Control Approach

2017 ◽  
Author(s):  
Matthew Piper ◽  
Pranav Bhounsule ◽  
Krystel K. Castillo-Villar
Keyword(s):  
Optimal Path ◽  
Computation Time ◽  
Planning Horizon ◽  
Mixed Integer ◽  
Worst Case ◽  
Control Approach ◽  
Average Computation Time ◽  
Prediction And Control ◽  
Point Condition ◽  
Velocity Constraints

Flappy Bird is a mobile game that involves tapping the screen to navigate a bird through a gap between pairs of vertical pipes. When the bird passes through the gap, the score increments by one and the game ends when the bird hits the floor or a pipe. Surprisingly, Flappy Bird is a very difficult game and scores in single digits are not uncommon even after extensive practice. In this paper, we create three controllers to play the game autonomously. The controllers are: (1) a manually tuned controller that flaps the bird based on a vertical set point condition; (2) an optimization-based controller that plans and executes an optimal path between consecutive tubes; (3) a model-based predictive controller (MPC). Our results showed that on average, the optimization-based controller scored highest, followed closely by the MPC, while the manually tuned controller scored the least. A key insight was that choosing a planning horizon slightly beyond consecutive tubes was critical for achieving high scores. The average computation time per iteration for the MPC was half that of optimization-based controller but the worst case time (maximum time) per iteration for the MPC was thrice that of optimization-based controller. The success of the optimization-based controller was due to the intuitive tuning of the terminal position and velocity constraints while for the MPC the important parameters were the prediction and control horizon. The MPC was straightforward to tune compared to the other two controllers. Our conclusion is that MPC provides the best compromise between performance and computation speed without requiring elaborate tuning.

scholarly journals Path Planning for Excavator Arm: Fuzzy Logic Control Approach

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Nga Thi-Thuy Vu ◽  
Nam Phuong Tran
Keyword(s):  
Computer Simulation ◽  
Fuzzy Logic ◽  
Fuzzy Logic Control ◽  
Optimal Trajectory ◽  
Optimal Path ◽  
B Spline ◽  
Control Approach ◽  
Logic Control ◽  
Two Phases ◽  
Fuzzy Logic Technique

This paper proposes an algorithm to design the path for automated excavator arm. The path designing is divided into two phases. Firstly, the fuzzy logic technique is used to determine the change of the path to adapt with the variation of the material after each digging period. Secondly, the B-spline algorithm is used to build the optimal trajectory. By this, the excavator can maximize the dug weight although the shape of the material is variation. The effectiveness of the algorithm is verified through computer simulation and real-time experiment. The simulation and experimental results show that the generated optimal path keeps the dug weight around the expected value regardless of the change of the environment.

scholarly journals AlphaPilot: autonomous drone racing

2021 ◽  
Author(s):  
Philipp Foehn ◽  
Dario Brescianini ◽  
Elia Kaufmann ◽  
Titus Cieslewski ◽  
Mathias Gehrig ◽  
...  
Keyword(s):  
Real Time ◽  
Trajectory Planning ◽  
Nonlinear Filtering ◽  
Optimal Trajectory ◽  
Optimal Path ◽  
Data Abstraction ◽  
State Estimate ◽  
World Championship ◽  
Time Optimal ◽  
Optimal Trajectory Planning

AbstractThis paper presents a novel system for autonomous, vision-based drone racing combining learned data abstraction, nonlinear filtering, and time-optimal trajectory planning. The system has successfully been deployed at the first autonomous drone racing world championship: the 2019 AlphaPilot Challenge. Contrary to traditional drone racing systems, which only detect the next gate, our approach makes use of any visible gate and takes advantage of multiple, simultaneous gate detections to compensate for drift in the state estimate and build a global map of the gates. The global map and drift-compensated state estimate allow the drone to navigate through the race course even when the gates are not immediately visible and further enable to plan a near time-optimal path through the race course in real time based on approximate drone dynamics. The proposed system has been demonstrated to successfully guide the drone through tight race courses reaching speeds up to $${8}\,{\hbox {m}/\hbox {s}}$$ 8 m / s and ranked second at the 2019 AlphaPilot Challenge.

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