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

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.

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Trajectory optimisation of an aerobatic air race

The Aeronautical Journal ◽

10.1017/s0001924000002724 ◽

2009 ◽

Vol 113 (1139) ◽

pp. 1-8 ◽

Cited By ~ 3

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.

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TIME-OPTIMAL PATH PLANNING MODEL USING GENETIC ALGO- RITHM IN RRR ROBOT

International Journal of Engineering Technologies and Management Research ◽

10.29121/ijetmr.v8.i5.2021.938 ◽

2021 ◽

Vol 8 (5) ◽

pp. 9-18

Author(s):

Hasan Demir ◽

Mehmet R. Tolun ◽

Filiz Sari

Keyword(s):

Path Planning ◽

Optimal Path ◽

Angular Position ◽

Mathematical Expression ◽

Joint Space ◽

Planning Model ◽

Optimal Path Planning ◽

Time Optimization ◽

Time Optimal ◽

Task Time

The mathematical expression of the kinematic equations of each joint is utilized for the path planning using a quantic polynomial in joint space. In this study, a time optimization model for path planning using genetic algorithms with a vari- ety of crossover fraction and mutation rates is investigated. The optimization process is performed with MATLAB. Optimization using boundary conditions is performed with MATLAB. The result of the simulation, smooth speed graphs, angular position graphs, and the time when joint movements will complete the orbit as soon as possible are obtained. As a result of this study, a path planning model that can be applied to any robot is developed in joint space based on time optimization and can be used to shorten the task time, especially in task-based robots.

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Planning Near Time-Optimal Trajectories for Robot Manipulators Along Given Paths

20th Design Automation Conference: Volume 2 — Robust Design Applications; Decomposition and Design Optimization; Optimization Tools and Applications ◽

10.1115/detc1994-0162 ◽

1994 ◽

Author(s):

Héctor H. González-Baños ◽

José-Luis Gordillo

Keyword(s):

Optimal Solution ◽

Robotic Manipulators ◽

Joint Space ◽

Previous Method ◽

Optimal Trajectories ◽

Intermediate Step ◽

Arc Length ◽

Time Optimal ◽

Model Components ◽

Valid Solution

Abstract This paper extends a previous method aimed to compute discrete time-optimal trajectories of “dot-like” robots to consider the general case of robotic manipulators. The resulting trajectories provide the torque command at each actuator for following a given path in minimum time while respecting the constraints imposed by the manipulator model. The proposed method makes use of a modified manipulator dynamic model in terms of γ, the arc length parameter which defines the trajectory in the joint space q. The search for a solution is done in the space specified by γ and its derivative ν (the pseudo-speed scalar). In this space we define the features of the solution in order to design an efficient algorithm to compute the time-optimal trajectory. We determine bounds to the model components, such that the optimal solution lies below a curve limiting the area Ω, area in which all possible solutions fit. The algorithm performs, inside Ω, an ascendent search of the limiting curve; this strategy permits the curve obtained at each intermediate step to be a valid solution.

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

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4002712 ◽

2010 ◽

Vol 133 (1) ◽

Cited By ~ 20

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.

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Smooth and Time-Optimal Trajectory Planning for Industrial Manipulators Along Specified Paths

10.1115/imece1999-0065 ◽

1999 ◽

Author(s):

D. Constantinescu ◽

E. A. Croft

Keyword(s):

Optimization Problem ◽

Optimal Path ◽

Robotic Manipulators ◽

State Dependent ◽

Industrial Manipulators ◽

Control Objective ◽

Time Optimal ◽

Tolerance Method ◽

Optimal Trajectory Planning ◽

Third Derivative

Abstract This paper presents a method for determining smooth and time-optimal path-constrained trajectories for robotic manipulators. The desired smoothness of the trajectory is imposed through limits on the actuator jerks. The third derivative of the path parameter with respect to time, the pseudo-jerk, is the controlled input. The limits on the actuator torques translate into state-dependent limits on the pseudo-acceleration. The time-optimal control objective is cast as an optimization problem by using cubic splines to parameterize the state space trajectory. The optimization problem is solved using the flexible tolerance method.

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