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Motion Planning for Humanoid Robots

Motion Planning for Humanoid Robots. Slides from Li Yunzhen and J. Kuffner. Papers:. Footstep placement

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Motion Planning for Humanoid Robots

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  1. Motion Planning for Humanoid Robots Slides from Li Yunzhen and J. Kuffner NUS CS5247

  2. Papers: Footstep placement J. Kuffner, K. Nishiwaki, S. Kagami, M. Inaba, and H. Inoue. Footstep Planning Among Obstacles for Biped Robots. Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (IROS), 2001. Full-body motion J. Kuffner, S. Kagami, M. Inaba, and H. Inoue. Dynamically-Stable Motion Planning for Humanoid Robots. Proc. Humanoids, 2000 NUS CS5247

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  5. What is Humanoid Robots & its balance constraints? center of mass gravity vector projection of mass center area of support Human-like Robots A configuration q is statically-stable if the projection of mass center along the gravity vector lies within the area of support. NUS CS5247

  6. 1. Footstep Placement Goal: In an obstacle-cluttered environment, compute a path from start position to goal region NUS CS5247

  7. 1.Footstep Placement—Simplifying Assumption • Flat environment floor • Stationary obstacles of known position and height • Foot placement only on floor surface (not on obstacles) • Pre-computed set of footstep placement positions • Orientation changes allow direction changing; forward • and backward motion also NUS CS5247

  8. Footstep Placement—Simplifying Assumption Path = A sequence of feet placements + trajectories for transition between footstep. • Pre-calculate statically stable motion trajectories for transition between footstep and use intermediate postures to reduce the number of transition trajectories. • Define intermediate postures Qright, Qleft, that are single foot stable. All transitions are Q1, Qleft, Q2, Qright, Q3, etc. • Thus, problem is reduced to how to find feet placements (collision-free) Qright == stable NUS CS5247

  9. 1.Footstep Placement—Overall algorithm NUS CS5247

  10. 1.Footstep Placement—Best First Search Initial Configuration • Generate successor nodes from lowest cost node • Prune nodes that result in collisions • Continue until a generated successor node falls in goal region • Number of possible footstep placements is branching factor of the tree Red Leaf nodes are pruned from the search NUS CS5247

  11. 1.Footstep Placement—Cost Heuristic • Cost of path to current configuration • Depth of node in the tree • Penalties for orientation changes, backward steps, and poor foot locations • Cost estimate to reach goal • Straight-line steps from current to goal • Weights favor fewer steps, forward motion • weighting factors are empirically-determined • D() is path length so far, rho() is penalty for rotating or going backward, X() is estimate of remaining cost to goal NUS CS5247

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  13. 1.Footstep Placement—Collision Checking • 2D polygon-polygon intersection test foot vs. attempted position • 3D polyhedral minimum-distance determination Robot vs. Obstacle • Lazy collision checking used: as new candidate state is chosen, check for collision • 15 discrete foot placements, 20 obstacles • Search tree has 6,700 nodes. Brute force search would require 10^21 nodes for 18 step path. NUS CS5247

  14. Full Body Motion • Challenge dues to : • The high number of degrees of freedom • Complex kinematic and dynamic models • Balance constraints that must be carefully maintained in order to prevent the robot from falling down NUS CS5247

  15. Full Body Motion • Given two statically-stable configurations, generate a statically stable, collision-free trajectory between them • --Kuffner, et. al, Dynamically-stable Motion Planning for Humanoid Robots, 2000. NUS CS5247

  16. Object Manipulation • Task: move a target object its new location. • Normally 3 steps: • Reach • Transfer • Release NUS CS5247

  17. Dynamically Stable Motion Planning Using RRT’s Decoupled Approach: Solve for kinematic path, then Transform path to a dynamically stable path NUS CS5247

  18. Rapidly-exploring Random Tree (LaValle ’98) Rendering of an RRT by James Kuffner • Efficient randomized planner for high-dim. spaces with • Algebraic constraints (obstacles) and • Differential constraints (due to nonholonomy & dynamics) • Biases exploration towards unexplored portions of the space NUS CS5247

  19. Full Body Motion—Modified RRT • Randomly select a collision-free, statically stable configuration q. q qinit qgoal NUS CS5247

  20. Full Body Motion—Modified RRT • Select nearest vertex to q already in RRT (qnear). q qinit qnear qgoal NUS CS5247

  21. Full Body Motion—Modified RRT • Make a fixed-distance motion towards q from qnear (qtarget). q qtarget qinit qnear qgoal NUS CS5247

  22. Full Body Motion—Modified RRT • Generate qnew by filtering path from qnear to qtarget through dynamic balance compensator and add it to the tree. q qtarget qinit qnew qnear qgoal NUS CS5247

  23. Extend(T,q) qnear  NEAREST_NEIGHBOR(q,T); If NEW_CONFIG(q,qnear,qnew) then T. add_vertex(qnew); T. add_edge(qnear,qnew); if qnew = q then return Reached; else return Advanced; return Trapped ) NUS CS5247

  24. RRT_CONNECT_STABLE( qinit, qgoal) 1. Ta.init( qinit); Tb.init( qgoal); 2. For k= 1 to K do 3. qrand RANDOM_STABLE_CONFIG(); 4. if not( EXTEND(Ta, qrand = Trapped ) 5. if( EXTEND(Tb, qnew) = Reached ) 6. return PATH(Ta, Tb); 7. SWAP(Ta, Tb); 8. return Failure; NUS CS5247

  25. Full Body Motion—Distance Metric • Don’t want erratic movements from one step to the next. • Encode in the distance metric: • Assign higher relative weights to links with greater mass and proximity to trunk. • A general relative measure of how much the variation of an individual joint parameter affects the overall body posture. NUS CS5247

  26. Full Body Motion—Random Statically stable postures • It is unlikely that a configuration picked at random will be collision-free and statically-stable. • Solution: Generate a set of stable configurations, and randomly choose one from this set then do collision checking. NUS CS5247

  27. Full Body Motion—Random stable postures NUS CS5247

  28. Full Body Motion—Experiment Dynamically-stable planned trajectory for a crouching motion Performance statistics (N = 100 trials) NUS CS5247

  29. Full Body Motion • Algorithm for computing dynamically-Stable collision-free • trajectories given full-body posture goals. • Limitations: • Assumes small set of stable configurations • Paths may need to be smoothed NUS CS5247

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