Ballistic Motion Planning 20184612 Ian Libao Overview Motivation - - PowerPoint PPT Presentation

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Ballistic Motion Planning 20184612 Ian Libao Overview Motivation - - PowerPoint PPT Presentation

Ballistic Motion Planning 20184612 Ian Libao Overview Motivation Paper 1: Ballistic Motion Planning Paper 2: Single Leg Dynamic Motion Planning with Mixed-Integer Convex Optimization Summary Quiz 2 Motivation Jumping


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Ballistic Motion Planning

20184612 Ian Libao

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Overview

  • Motivation
  • Paper 1: Ballistic Motion Planning
  • Paper 2: Single Leg Dynamic Motion Planning with

Mixed-Integer Convex Optimization

  • Summary
  • Quiz
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Motivation

  • Jumping motion introduces new shortcuts
  • Instead of going around an obstacle block, why not

jump over it?

  • Unreachable locations can become reachable
  • This would increase complexity for the path

planning algorithm

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Paper 1: Ballistic Motion Planning

Mylene Campana | Jean-Paul Laumond IROS 2016

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Key Features

  • Developed a motion planning algorithm for

jumping point robot in arbitrary environment considering slipping and velocity constraints

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Accessible Space

  • Parabola trajectory is determined by takeoff

angle and initial velocity

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Goal Oriented Ballistic Motion

  • Physically-feasible parabolas linking cs and

cg with varying takeoff angles

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Non-sliding Constraints

  • Intersection between parabola plane and friction

cones

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Velocity Constraints

  • ν𝑑 ≀ π‘Š

𝑛𝑏𝑦

  • s
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Motion Planning

  • Probabilistic Roadmap Planner
  • Build Roadmap
  • Link nodes with Steer algorithm
  • Over when start and goal position are connected
  • Steer Algorithm
  • Selection of takeoff angle
  • Beam Algorithm
  • Computes all possible parabola paths
  • Outputs range of permissible angles
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Results

  • https://www.youtube.com/watch?v=vv_K

7HqANmk&feature=youtu.be

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Strengths and Limitations

  • Small computational cost
  • Arbitrary environment
  • Point robot representation limitation
  • No stance dynamics
  • Frictionless Jumps
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Paper 2: Single Leg Dynamic Motion Planning with Mixed-Integer Convex Optimization

Yanran Ding | Chuanzheng Li | Hae-Won Park IROS 2018

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Key Features

  • Used mixed-integer convex

programming formulation for dynamic motion planning

  • Capable of planning

consecutive jumps through challenging terrains

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Phases of Jumping Robot

  • Stance Phase
  • Leg is in contact with the

ground

  • Actuators to apply force
  • Flight Phase
  • Follows ballistic motion
  • Choosing foot holds
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Constraints

  • Joint Torques do not exceed actuator limits
  • Goal region should be reached at the end of the

motion

  • Ground reaction force (GRF) must be within friction

cone

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Point Mass Dynamic Model

  • To simplify dynamics
  • Center of Mass assumed to

be in the Base Center

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Mixed-integer Convex Torque Constraint

  • Workspace Discretization
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Background: Mixed Integer Convex Optimization

  • Non-convex optimization to convex optimization
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Mixed-integer Convex Torque Constraint

  • Convex Outer-Approximation of Torque Ellipsoid
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Mixed-integer Convex Torque Constraint

  • Convex Outer-Approximation of Torque Ellipsoid
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Other Implementation

  • McCormick Envelope Approximation
  • Foothold Position choice
  • GRF Constraints
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Results

  • https://www.youtube.com/watch?v=0pFY

joUKGu0

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Performance

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Summary

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Summary

  • Paper 1: Ballistic Motion Planning
  • Jumping point robot navigating in 3d environment
  • 2 constraints due to the friction cone
  • Constraint to limit takeoff velocity -> robot’s speed

capacity

  • Constraint to limit landing velocity -> impact force

tolerance

  • Paper 2: Single Leg Dynamic Motion Plannning

with Mixed-Integer Convex Optimization

  • Implemented ballistic motion planning for a real robot

and simplifies the non-convexity of actuator torque constraint through Mixed-Integer Convex Optimization