Constraints-based Motion Constraints-based Motion Planning for an Automatic, Planning for an Automatic,

Flexible Laser Scanning Flexible Laser Scanning Robotized PlatformRobotized Platform

Th. Borangiu, A. Dogar, A. DumitracheTh. Borangiu, A. Dogar, A. DumitracheUniversity Politehnica of Bucharest, University Politehnica of Bucharest,

borangiu@cimr.pub.ro, borangiu@cimr.pub.ro, dogar@cimr.pub.rodogar@cimr.pub.ro

a1ex_r0@yahoo.com a1ex_r0@yahoo.com

OverviewOverview

IntroductionIntroduction Platform SimulatorPlatform Simulator Defined Constraints in the Robot CSDefined Constraints in the Robot CS Constraints Motion PlanningConstraints Motion Planning Conclusions and Future WorkConclusions and Future Work

IntroductionIntroduction

RE Platform Components

•Laser probe•6-DOF Robot Arm•Turntable Table•PC•Milling Machine

Platform SimulatorPlatform Simulator

Simulated items:Simulated items: Robot and table motionRobot and table motion Laser probe Laser probe

Simulation modes:Simulation modes: Static simulationStatic simulation AnimationAnimation

Platform Simulator-Static Platform Simulator-Static SimulatorSimulator

Platform Simulator-Static Platform Simulator-Static SimulatorSimulator

The static simulation module allows specifying the The static simulation module allows specifying the robot pose, using one of the three input methods:robot pose, using one of the three input methods:

specify the angular values for each joint and for specify the angular values for each joint and for the rotary table (direct kinematics)the rotary table (direct kinematics)

specify the position in Cartesian coordinates and specify the position in Cartesian coordinates and the orientation in ZYZ’ Euler angles, in the robot’s the orientation in ZYZ’ Euler angles, in the robot’s reference frame (inverse kinematics with respect reference frame (inverse kinematics with respect to robot)to robot)

specify the angle of the rotary table, and the specify the angle of the rotary table, and the position and the orientation of the robot end point position and the orientation of the robot end point in the rotary table’s reference frame (inverse in the rotary table’s reference frame (inverse kinematics with respect to rotary table)kinematics with respect to rotary table)

Motion Simulation ModuleMotion Simulation Module

Motion Simulation ModuleMotion Simulation Module

The motion simulation module lets The motion simulation module lets the user simulate and analyze the the user simulate and analyze the behaviour of the robot using a behaviour of the robot using a sequence of user-defined sequence of user-defined trajectories. trajectories.

The user interface has an editor for The user interface has an editor for the motion sequence, and controls the motion sequence, and controls for generating the animation.for generating the animation.

ExampleExample

Defined ConstraintsDefined Constraints

Hard ConstraintsHard Constraints:: known obstacles in the robot workspaceknown obstacles in the robot workspace articulated robot singularities articulated robot singularities articulated robot joint angle limits.articulated robot joint angle limits. Soft ConstraintsSoft Constraints:: surface avoiding (keeping the minimum surface avoiding (keeping the minimum

allowed scanning distance towards the allowed scanning distance towards the modelled object)modelled object)

flexible reach (avoiding “un-comfortable” flexible reach (avoiding “un-comfortable” positions of the robot arm) positions of the robot arm)

following the computed path.following the computed path.

Constraint-based Motion Constraint-based Motion PlanningPlanning

Two approachesTwo approachesClassic methodsClassic methods:: Roadmap, Roadmap, Cell DecompositionCell Decomposition Potential FieldsPotential Fields Mathematical ProgrammingMathematical Programming Heuristic MethodsHeuristic Methods Probabilistic Roadmaps and Rapidly- exploring Random Trees Probabilistic Roadmaps and Rapidly- exploring Random Trees Level set and Linguistic GeometryLevel set and Linguistic Geometry Artificial Neural NetworkArtificial Neural Network Genetic AlgorithmsGenetic Algorithms Particle Swarm OptimizationParticle Swarm Optimization Ant ColonyAnt Colony Stigmergy Stigmergy Wavelet TheoryWavelet Theory Fuzzy LogicFuzzy Logic Tabu SearchTabu Search

Constraint-based Motion Constraint-based Motion PlanningPlanning

Constraints-based Motion Constraints-based Motion Planning Planning

Input data - scanning toolpaths Input data - scanning toolpaths Output data - joint values of the robotic Output data - joint values of the robotic

arm and the rotary table angle arm and the rotary table angle The problem presented here is the inverse The problem presented here is the inverse

kinematics for a 7-DOF mechanism.kinematics for a 7-DOF mechanism.The computed solution has to satisfy the The computed solution has to satisfy the

following requirements:following requirements: minimize the accelerations and limit the minimize the accelerations and limit the

speed of the rotary table;speed of the rotary table; avoid collisions with any obstacles.avoid collisions with any obstacles.

Constraints-based Motion Constraints-based Motion PlanningPlanning

The configuration space for this problem can The configuration space for this problem can be represented in its discrete form as a two be represented in its discrete form as a two dimensional image, or map, where the dimensional image, or map, where the XX axis axis corresponds to the discrete time, and the corresponds to the discrete time, and the YY axis corresponds to the rotary angle ranging axis corresponds to the rotary angle ranging from –180° to 180° in from –180° to 180° in nn equally spaced equally spaced discrete steps.discrete steps.

Since the rotary table can rotate continuously, Since the rotary table can rotate continuously, without any limit on the number of complete without any limit on the number of complete rotations, the configuration map is periodic on rotations, the configuration map is periodic on the the YY axis. axis.

Constraints-based Motion Constraints-based Motion PlanningPlanning The white (allowed) regions on the map will be named The white (allowed) regions on the map will be named CCfreefree , while the black , while the black

(forbidden) regions will be denoted as (forbidden) regions will be denoted as CCobsobs.. When the robot is close to the limits of When the robot is close to the limits of CCobsobs, the robot is either close to the , the robot is either close to the

limits of its joints, or to the limits of its working envelope, or close to a limits of its joints, or to the limits of its working envelope, or close to a singular point.singular point.

In order to obtain a planning algorithm that does not touches the obstacles, 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 but maintains a sufficient distance, one has either to add borders to CCobsobs, or , or modify the interpretation of the map values in modify the interpretation of the map values in CCfreefree to indicate the to indicate the proximity of an obstacle. proximity of an obstacle.

The values of the map in The values of the map in CCobsobs remain zero, which means that these are remain zero, which means that these are forbidden states. The values in forbidden states. The values in CCfreefree will be in the (0, 1] interval, showing will be in the (0, 1] interval, showing that any of these states are allowed, but also indicating how desirable is that any of these states are allowed, but also indicating how desirable is the state. Therefore, states having higher values are more desirable than the state. Therefore, states having higher values are more desirable than states having lower values. states having lower values.

Conclusions and Future Conclusions and Future WorkWork

The main objective of the planning algorithm The main objective of the planning algorithm is finding a path that avoids the obstacles on is finding a path that avoids the obstacles on the configuration map, and obeys the speed the configuration map, and obeys the speed and acceleration limits. and acceleration limits.

An essential feature of the planning algorithm An essential feature of the planning algorithm will be its ability to run in real time, while the will be its ability to run in real time, while the scanning process takes place. scanning process takes place.

The optimality of the path computed is less The optimality of the path computed is less important, and for this reason, the focus will important, and for this reason, the focus will be on faster, but suboptimal, heuristic be on faster, but suboptimal, heuristic algorithms. algorithms.

Thank you!Thank you!