Iterative Relaxation of Constraints (IRC) Can’t solve originalCan solve relaxed PRMs sample randomly but… start goal C-obst difficult to sample points in small volume feasible regions Solution Find a solution to a relaxed version of the problem (larger volume feasible regions) and use that solution to help solve the original problem. start goal C-obst start goal start goal start goal Relax constraints Improve Find a Solution To relaxed Version Relax feasibility constraints: set to minimal value Approximate solution: Find a valid solution for the current feasibility constraints Improve Solution: While (Original problem is not solved) Strengthen feasibility constraints Improve current solution End While Feasibility Constraints: collision, penetration, energy Enable the planner to concentrate on important areas by reducing region of C-space for planner to sample Virtual Prototyping Check accessibility Robot is rigid Deformable Objects Avoid collisions by deforming Robot changes its surface Ligand Binding Generate candidate sites Ligand is tree-like articulated robot Applications of IRC Algorithm Virtual Prototyping – Domain I [Bayazit et.al. ICRA’00] [Bayazit.et.al. Autonomous Robots Journal‘01] GIVEN A part in CAD/CAM Design CHECK if the part is accessible from outside Accessibility is checked by taking part outside the assembly Motivation Physical mock-ups are expensive and time consuming Approximate Solution: Find a path that may have collision ( solution to relaxed version) automated manual Improving Approximate Solution: Push the colliding configurations to free space Use a scaled robot Reduces the size of C-Space obstacles, increases the feasible regions Build a roadmap Better connected then the original problem Query to find a path Easier to find obstacle Original robot Scaled robot (easier)Comparison Automated Path Generation User attaches haptic device to robot, and moves it around user feels when robot touches obstacles and adjusts trajectory collision detection too slow (~10 Hz), so distribute process and use extrapolation techniques (almost all) Robot configurations passed to planner automatically sampled at regular intervals C-obstacle pushed path generated by planner approximate path User or Planner generates approximate path P –it may contain collisions Planner “pushes” colliding portions of P to C-free –Both C-space and workspace techniques are available Ligand Binding – Domain II [Bayazit, Song, Amato, IEEE ICRA’01] Given: a description of a ligand molecule (robot) and a protein (obstacle). Find: a configuration of the ligand near the protein where geometric, electro-static and chemical constraints are satisfied. protein ligand Approximate Solution: Generate sample nodes automated manual Improving Approximate Solution: Push nodes to local minima. Use other researchers’ scoring functions to evaluate them. Generate a collision free base Find values for other joint angles for a collision free ligand Keep this configuration if the potential is less than E max Protein Ligand base Create a potential grid. Each grid cell contains contributions of protein atoms. Generate joint angles so that molecules stay in low potential grid cells. Keep this configuration if the potential is less than E max. User attaches haptic device to ligand, and moves it around user feels the forces on ligand ligand is rigid force calculation is too slow, so use extrapolation techniques (grid potential) Ligand configurations (candidate sites) passed to planner automatically sampled at regular intervals when user indicated PHANToM PHANToM haptic device gives a sense of touch through force feedback Comparison of OBPRM-like generation methods for flexible ligands Distance to Binding Configuration *Tried by Singh et al. Able to generate conformations near binding conformation (usually < 4 Angstroms) No prior knowledge of protein is required Geometry-Based generation is usually better ** * We have tested 15+ ligand/protein complexes –fully automated method is successful in generating configurations in the binding site – the haptic user-input often helps speed up the processing Next step is a more rigorous comparison to existing methods, and further refinement of our approach Need to refine haptic interface and understand potential benefit Need to score our conformations with existing scoring methods Our results (conformations) may be used as input to other automated docking programs - they are good at refining and ranking solutions Does a path contains valuable information related to destination configuration? In all the applications, we first find an approximate solution and then improve it. Manual Path Generation Improving Solution Flange Problem Experimental Results l Automatic planners can effectively transform approximate paths to free paths –faster than traditional PRMs –iterative relaxation works well l Heuristic collision detection provides support for approximate path collection –ok since we’re collecting approximate paths Conclusion Deformable Objects – Domain III [Bayazit, Lien, Amato, ICRA’02] Given an object which can deform Find a path taking object from start to goal. The object is allowed to deform to avoid collision. Approximate Solution: Find a path for rigid version, may have collision Improving Approximate Solution: Deform the robot to avoid collision Enable Penetration –Use approximate C-Space penetration Use scaled robots –More than one scaled model. –Smaller (Bigger ) model needs more (less) deformation. 1.Build roadmap by relaxing collision free requirement 2. Extract Approximate Path l may not be feasible for the rigid robot Bounding Box Deformation build a 3D voxel bounding box. —Convert it to ChainMail bounding box (3D grid of springs) —Deform ChainMail Bounding box. —Deform objects using Free Form Deformation based of deformation of the bounding box. Deformed ChainMail Bounding Box Obstacle ChainMail Box Apply FFD Geometric Deformation —Find the colliding surfaces —Move the colliding surfaces of the robot outside the obstacle —Smooth the robot Colliding configuration Blue surface=obstacle Red surface=robot. deformation Approximate Solution Automated Geometry Based Automated Energy Based Manual Node Generation Push nodes to local minima For each node sample n close nodes Choose the node with lowest potential among them Repeat until a local minima or iteration limit is reached Improving Approximate Solution Approximate Solution Improving Approximate SolutionExperiments Bounding Box Geometric Conclusion Approximate Solution Fully automated planner can only solve.85 scaled version. With user input, the solution time reduces.. 96 scaled version uses those results and solves the problem. The original problem is solved by using results of.95. Goal Robot Start Deformable Version Original Problem Penetration Scaled Robot Experiments