Virtual Sphere Algorithms for Orthodrome-based Collision-free & Smooth Robot Motion

Reactive Deformation of Path for Navigation Among Dynamic Obstacles(RDP NADO)Anand TaralikaCollege of ComputingGeorgia TechAtlanta USA

#Problem at hand: navigation / motion among dynamic obstacles, in efficient way, less complex, avoid costs of replanning

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The TitleWhat?A simulator for a reactive planning algorithmWhy?For local robotic motion / path planningFor navigation in an environment that isDynamicUnpredictableHow?Reactively deforming a local patch of the global planned path

#Experimental results of developing a simulator for efficient planning.A dynamic / unpredictable environment such as laboratory, hospital, factory floor.2

Demo

#The Navigation AlgorithmGlobal Planner (A*)Navigate to next waypointIs the next waypoint reachable?Is this a static environment?Failure: No feasible pathIs there an obstacle close to the path?Invoke RDP for obstacle avoidance (Local Planner)YesNoNoYesYesNoCurrent Robot Config.Final Robot Config.Obstacle Positions

#Always making sure that the path is clear of any obstacles4

RDP AlgorithmGlobal Planning

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RDP AlgorithmPrinciple of path deformation

The obstacle has a charge opposite to the charge on the path

Not optimal anymore!Optimal Path

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RDP AlgorithmThe forces acting on the path are:Internal contraction force, FiExternal repulsive force, FeSimulates tension in the pathUsed to determine if the elastic limit of the path is reached before it snaps.Deformation stops when equilibrium is attained, that is when Fi = Fe

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RDP AlgorithmForces make the path taut

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RDP AlgorithmDeformation of the trajectory for the robot to pass through available space

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RDP AlgorithmTrajectory regains shape by retraction

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RDP AlgorithmTrajectory regains shape by snapping

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Simulator ImplementationImplemented in C++User can setStart position of the robotDesired goal position for the robotUser can also disperse obstacles by mouse gestures easily in the environmentObstacles follow a random / unknown trajectory which would be impossible to predictGlobal planning is implemented using A* in C++

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Simulator ImplementationMulti-threaded modelSensor threadMonitors obstacles and their positions relative to the planDetects changes in the environment and notifies the Planner thread about the change.Local Planner threadModifies the plan locally to accommodate the changes in the environmentControl threadMakes the robot navigate along the trajectory defined by global and local planners

#Local Planner thread computes the forces on the path and accordingly decides if the path needs to snap / retract13

ResultsA simulator implementing RDP algorithm was developedThe simulator was run withOne mobile robotVarying number of dynamic obstaclesIn a 800x1000 sq. unit workspaceAt a path update rate between 10 and 100 HzThe more often the path is updated, the more fine grained the control is, however, the algorithm becomes more processor intensive

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ResultsUnforeseen obstacles invalidate a planned path and replanning each time could be costlyRDP is a cheaper alternative!RDP also prevents a robot from getting stuck at local minima since it preserves the global nature of the planRDP is applied on-the-fly, without suspending execution of the task

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ResultsWhat happens when there are large changes in the shape?The robot might not be able to keep upSolution 1: Do not allow large changesInfeasible to find a good limit, so path might get invalidated too often, making it less efficientSolution 2: No limit on changes, but merge with the original path to smooth out the outliers

#Large changes in shape happen due to obstacles suddenly showing up near the path causing spikes in the potentials and thus, making big changes in the paths shape suddenly.16

Future WorkTo be used for navigation of a humanoid / mobile robot in an unpredictable / dynamic environmentUse real-time sensor data and generate path deformationsCoping with uncertainty / errors in sensor dataExtend the simulator to elastic roadmaps that can recover from invalidation of the global plan

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Acknowledgement / ReferencesProf. Mike Stilman @ Humanoids Lab, Georgia TechFor advising on the topic and providing robots to test the simulatorS. Quinlan, and O. Khatib, Elastic bands: Connecting path planning and control, Proc. of IEEE Conf. on Robotics and Automation, 1993.O. Brock and O. Khatib, Elastic strips: A framework for motion generation in human environments, Int. Journal of Robotics Research, vol. 18, no. 6, pp. 10311052, 2002.O. Brock, and O. Kathib, Elastic Strips: A framework for integrated planning and execution, Proceedings of the International Symposium on Experimental Robotics, volume 250 of Lecture Notes in Control and Information Sciences, pp. 328-338, 1999.O. Khatib, Real-Time Obstacle Avoidance for Manipulators and Mobile Robots, IEEE International Conference on Robotics and Automation, St. Louis, Missouri, pp. 500-505, March 25-28, 1990.O. Khatib, Towards integrated planning and control, Proceedings of IFAC Symposium on Robot Control, volume 1, pp 305-313, 1994.

#The proposed simulator differs from these references in that the simulator performs deformation only on a local patch of the plan rather than the entire plan, thereby reducing the computational complexity18