Constraints-based Motion Planning for an Automatic, Flexible Laser Scanning Robotized Platform Th. Borangiu, A. Dogar, A. Dumitrache University Politehnica of Bucharest,

Overview Introduction Introduction Platform Simulator Platform Simulator Defined Constraints in the Robot CS Defined Constraints in the Robot CS Constraints Motion Planning Constraints Motion Planning Conclusions and Future Work Conclusions and Future Work

Introduction RE Platform Components Laser probe 6-DOF Robot Arm Turntable Table PC Milling Machine

Platform Simulator Simulated items: Robot and table motion Robot and table motion Laser probe Laser probe Simulation modes: Static simulation Static simulation Animation Animation

Platform Simulator-Static Simulator

The static simulation module allows specifying the robot pose, using one of the three input methods: specify the angular values for each joint and for the rotary table (direct kinematics) specify the angular values for each joint and for the rotary table (direct kinematics) specify the position in Cartesian coordinates and the orientation in ZYZ’ Euler angles, in the robot’s reference frame (inverse kinematics with respect to robot) specify the position in Cartesian coordinates and the orientation in ZYZ’ Euler angles, in the robot’s reference frame (inverse kinematics with respect to robot) specify the angle of the rotary table, and the position and the orientation of the robot end point in the rotary table’s reference frame (inverse kinematics with respect to rotary table) specify the angle of the rotary table, and the position and the orientation of the robot end point in the rotary table’s reference frame (inverse kinematics with respect to rotary table)

Motion Simulation Module

The motion simulation module lets the user simulate and analyze the behaviour of the robot using a sequence of user- defined trajectories. The motion simulation module lets the user simulate and analyze the behaviour of the robot using a sequence of user- defined trajectories. The user interface has an editor for the motion sequence, and controls for generating the animation. The user interface has an editor for the motion sequence, and controls for generating the animation.

Example

Defined Constraints Hard Constraints: known obstacles in the robot workspace known obstacles in the robot workspace articulated robot singularities articulated robot singularities articulated robot joint angle limits. articulated robot joint angle limits. Soft Constraints: surface avoiding (keeping the minimum allowed scanning distance towards the modelled object) surface avoiding (keeping the minimum allowed scanning distance towards the modelled object) flexible reach (avoiding “un-comfortable” positions of the robot arm) flexible reach (avoiding “un-comfortable” positions of the robot arm) following the computed path. following the computed path.

Constraint-based Motion Planning Two approaches Classic methods: Roadmap, Roadmap, Cell Decomposition Cell Decomposition Potential Fields Potential Fields Mathematical Programming Mathematical Programming Heuristic Methods Probabilistic Roadmaps and Rapidly- exploring Random Trees Probabilistic Roadmaps and Rapidly- exploring Random Trees Level set and Linguistic Geometry Level set and Linguistic Geometry Artificial Neural Network Artificial Neural Network Genetic Algorithms Genetic Algorithms Particle Swarm Optimization Particle Swarm Optimization Ant Colony Ant Colony Stigmergy Stigmergy Wavelet Theory Wavelet Theory Fuzzy Logic Fuzzy Logic Tabu Search Tabu Search

Constraint-based Motion Planning

Constraints-based Motion Planning Input data - scanning toolpaths Input data - scanning toolpaths Output data - joint values of the robotic arm and the rotary table angle Output data - joint values of the robotic arm and the rotary table angle The problem presented here is the inverse kinematics for a 7-DOF mechanism. The computed solution has to satisfy the following requirements: minimize the accelerations and limit the speed of the rotary table; minimize the accelerations and limit the speed of the rotary table; avoid collisions with any obstacles. avoid collisions with any obstacles.

Constraints-based Motion Planning The configuration space for this problem can be represented in its discrete form as a two dimensional image, or map, where the X axis corresponds to the discrete time, and the Y axis corresponds to the rotary angle ranging from – 180° to 180° in n equally spaced discrete steps. The configuration space for this problem can be represented in its discrete form as a two dimensional image, or map, where the X axis corresponds to the discrete time, and the Y axis corresponds to the rotary angle ranging from – 180° to 180° in n equally spaced discrete steps. Since the rotary table can rotate continuously, without any limit on the number of complete rotations, the configuration map is periodic on the Y axis. Since the rotary table can rotate continuously, without any limit on the number of complete rotations, the configuration map is periodic on the Y axis.

Constraints-based Motion Planning The white (allowed) regions on the map will be named C free, while the black (forbidden) regions will be denoted as C obs. The white (allowed) regions on the map will be named C free, while the black (forbidden) regions will be denoted as C obs. When the robot is close to the limits of C obs, the robot is either close to the limits of its joints, or to the limits of its working envelope, or close to a singular point. When the robot is close to the limits of C obs, the robot is either close to the limits of its joints, or to the limits of its working envelope, or close to a singular point. In order to obtain a planning algorithm that does not touches the obstacles, but maintains a sufficient distance, one has either to add borders to C obs, or modify the interpretation of the map values in C free to indicate the proximity of an obstacle. In order to obtain a planning algorithm that does not touches the obstacles, but maintains a sufficient distance, one has either to add borders to C obs, or modify the interpretation of the map values in C free to indicate the proximity of an obstacle. The values of the map in C obs remain zero, which means that these are forbidden states. The values in C free will be in the (0, 1] interval, showing that any of these states are allowed, but also indicating how desirable is the state. Therefore, states having higher values are more desirable than states having lower values. The values of the map in C obs remain zero, which means that these are forbidden states. The values in C free will be in the (0, 1] interval, showing that any of these states are allowed, but also indicating how desirable is the state. Therefore, states having higher values are more desirable than states having lower values.

Conclusions and Future Work The main objective of the planning algorithm is finding a path that avoids the obstacles on the configuration map, and obeys the speed and acceleration limits. The main objective of the planning algorithm is finding a path that avoids the obstacles on the configuration map, and obeys the speed and acceleration limits. An essential feature of the planning algorithm will be its ability to run in real time, while the scanning process takes place. An essential feature of the planning algorithm will be its ability to run in real time, while the scanning process takes place. The optimality of the path computed is less important, and for this reason, the focus will be on faster, but suboptimal, heuristic algorithms. The optimality of the path computed is less important, and for this reason, the focus will be on faster, but suboptimal, heuristic algorithms.

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