Amorphous Robotic Construction Nils Napp nnapp@buffalo.edu November 11th 2014 1 Robots Building Stuff 2 Robotic Construction in Messy Environments 3 Related Work Petersen, Werfel, Nagpal 2011 Rus, Lipson, Yim Khoshnevis 2004 Lindsey, Mellinger, Kumar 2010 D’Andrea 2010 4 Biological Inspiration K. Petersen, N. Napp, J. Chin-Lee, J. Werfel and R. Nagpal, 3D Tracking of Building Processes in Macrotermes , Visual Observation and Analysis of Animal and Insect Behavior, Workshop (ICPR), 2012. 5 Biological Inspiration 6 Outline • Algorithm Design – Adaptive Ramp Building Problem – World and Material Model – Navigable Structures – Ramp Building Algorithm(s) • Experiments – Working in 3D – Deposition Experiments 7 Adaptive Ramp Building Develop algorithms and robots to build in unstructured environments N. Napp, J. M. Wu, O. R. Rappoli, and R. Nagpal, Materials and Mechanisms for Amorphous Robotic Construction. IROS 12 8 Algorithmic Challenges 1. Modeling Amorphous Depositions 2. Planning with Amorphous Depositions 9 Outline • Algorithm Design – Adaptive Ramp Building Problem – World and Material Model – Navigable Structures – Ramp Building Algorithm(s) • Experiments – Working in 3D – Deposition Experiments 10 Modeling Structures : finite building area : robot position : height function 11 Modeling Structures : finite building area : robot position : height function 12 Modeling Amorphous Depositions • Shape defined by the environment • Conforming on bottom • Top defined by shape function: 13 Modeling Amorphous Depositions Deposition operator INPUT: shape function and height function OUTPUT: new height function 14 Outline • Algorithm Design – Adaptive Ramp Building Problem – World and Material Model – Navigable Structures – Ramp Building Algorithm(s) • Experiments – Working in 3D – Deposition Experiments 15 Maximum Climbable Steepness A function is called K-Lipschitz iff 16 Navigable: Almost, Locally, Lipschitz A function is called navigable iff 17 Navigable: Almost, Locally, Lipschitz A function is called navigable iff 18 Navigable: Almost, Locally, Lipschitz A function is called navigable iff 19 Navigable: Almost, Locally, Lipschitz A function is called navigable iff 20 Outline • Algorithm Design – Adaptive Ramp Building Problem – World and Material Model – Navigable Structures – Ramp Building Algorithm(s) • Experiments – Working in 3D – Deposition Experiments 21 Local Reactive Algorithm for Making Navigable Structures Algorithm 1 1. 2. 3. 4. 5. 6. 7. 8. Given Set While violating the navigability condition Set to be point with lower h value (wlog assume ) Pick deposition height Deposit at : Set EndWhile 22 Local Reactive Algorithm for Making Navigable Structures Algorithm 1 1. 2. 3. 4. 5. 6. 7. 8. Given Set While violating the navigability condition Set to be point with lower h value (wlog assume ) Pick deposition height Deposit at : Set EndWhile 23 Stopping for Algorithm 1 Bounded above Guaranteed progress Depositions never add material above . Each deposition has a minimum Volume. Proof based on point selection, Proof based on point selection, and the inequalities and deposition steepness continuity assumptions on and . 24 Adaptive Ramp Building (Alg 2) Algorithm 2 1. 2. 3. 4. 5. 6. 7. 8. 9. Given and navigable terrain around v . Set While Move until are non-navigable or If Move to lower point and deposit according to Alg. 1 Move backward to EndIf EndWhile Proof based on termination of Alg.1 and backing up from depositions that might have altered previously navigable terrain. 25 Adaptive Ramp Building Start 426 Steps N. Napp and R. Nagpal, Distributed Amorphous Ramp Construction in Unstructured Environments . DARS 2012 Goal 26 Outline • Algorithm Design – Adaptive Ramp Building Problem – World and Material Model – Navigable Structures – Ramp Building Algorithm(s) • Experiments – Working in 3D – Deposition Experiments 27 Using Algorithm 2 in 3D Leveling Mechanism Level Deposition with Conical Cross Section 28 Experiment: Messy Leveling Translating Carriage Mixing Nozzle Distance Sensor 29 Experiment: Messy Leveling 30 Foam Depositing Robot 31 Robot Depositing Foam 32 Foam Ramp 7 6 5 4 3 2 1 33 Summary • Amorphous building materials can enable robust construction in irregular terrain • Model terrain with continuous functions • Bound shape uncertainty with shape functions Future Work Construction in Cluttered Terrain • Use models to build other structures • Reliable construction with found objects • Extend to probabilistic setting 35 At UB • Teaching CSE 668: Advanced Robotics – Spring 2015 (MWF 12:00pm) – Previously called (Animate Vision Principles) • Looking for Students – Take my class/work on a project with me – E-mail: nnapp@buffalo.edu – Office hours: Tue/Thur 10:00-11:00am 36