Motion Planning for the On-orbit Grasping of a Tumbling Target with - - PowerPoint PPT Presentation

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Motion Planning for the On-orbit Grasping of a Tumbling Target with Large Momentum Roberto Lampariello Institute of Robotics and Mechatronics German Aerospace Center (DLR) Contents Some Past and Current Space Programs Free-flying

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Motion Planning for the On-orbit Grasping of a Tumbling Target with Large Momentum

Roberto Lampariello

Institute of Robotics and Mechatronics German Aerospace Center (DLR)

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Date: 08/01/2005

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Contents

  • Some Past and Current Space Programs
  • Free-flying robots and related problems
  • Motion Planning for Grasping a Tumbling

Target

  • Other applications
  • Conclusion
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Past and Current Space Programs

  • ETS-VII – NASDA
  • Workshop on On-orbit Servicing of

Space Infrastructure Elements Via Automation & Robotics Technology: “Developing a Roadmap”

  • Orbital Recovery – ConeXpress
  • TECSAS
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TECSAS -Technology Satellite for demonstration and Verification of Space Systems

Manipulator (7 D.O.F.) Target satellite Handle Sarah hand (CSA) Target spinning axis (ω = 4 deg/sec) Chaser satellite (thruster controlled)

CHASER TARGET

m m ≈

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Free-flying robot dynamics and related problems

  • free-floating dynamics
  • free-floating vs. free-flying
  • optimal minimum may be

the free-floating solution but this is a priori unknown

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Free-flying robot dynamics and related problems (2)

  • dynamic coupling - potential collision
  • external actions vs. uncertainty – require identification
  • path planning solutions are inertial parameter dependent

Non-expert Semi-expert Planned

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Algorithm (Lampariello, Agrawal – ICRA ‘03) Motivation:

A free-flying robot is generally subject to:

  • spacecraft control actions
  • orbital disturbances (gravity gradient, orbital

dynamics)

  • as well as robot torques

Free-floating approximation is only valid for:

  • local motions or short operations

Require an efficient planner

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Problem Definition

  • Path planning for actuated as well as for non-

actuated spacecraft degrees of freedom

  • Optimal solution for minimal energy
  • Fast solutions for realistic applications
  • Dynamically feasible solutions
  • Point-to-point maneuvers of the robot end-effector

and grasping maneuvers for a moving target

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Algorithm Methodology

  • Spatial model of free-flying robot
  • Initial and final end-effector state defined in inertial

space or a given target motion

  • Final robot configuration unknown & optimized

(no BVP!)

  • Single shooting optimization problem
  • Motion planning in joint space for avoidance of

dynamic singularity problem

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Equations of motion - fully actuated system

State space variables: Kinematics: Dynamics:

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Modeling - rheonomic joints

Let state space variables be: and rheonomically driven variables: New equations:

  • is dependent on , a prescribed function of

time

  • order of equations = 6 - d.o.f.s of base body
  • Free-floating system:
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Trajectory Planning - optimization problem: point-to-point

  • Equality constraints: initial and final end-effector

position and orientation: (kinematics)

  • Inequality constraints:

(inverse dynamics)

  • Cost function:

(base actuation)

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Use of Free-floating solution

  • Local workspace - workspace with no base

actuation free-floating solution = from integration of equations of motion

  • Global workspace - all reachable free space

free-flying solution = free-floating solution + extra parametric function of base states

→ →

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Trajectory Planning Solver

Optimization problem: for

  • one free parameter for each state variable

Parameterization of state variables: E.g. base position free-floating solution + polynomial order 5 Parameters:

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Results - Path in local workspace

  • Initial state:
  • Desired final state:
  • Cost: 8e-3 kg m/s
  • Computational time ~

5-7 seconds

  • Initial guess:
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Results - Path in global workspace

  • Desired final state:
  • Cost: 4460 kg m/s (1815

kg m/s for translational forces)

  • Computational time

~ 10 seconds

  • Initial guess: as previous
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Motion Planning for Grasping a Tumbling Target

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Motion Planning for Grasping a Tumbling Target (2) Three phases:

  • Approach to target
  • Tracking of grasping point – inverse kinematics
  • Grasping and stabilization

Inequality constraints:

  • As previously for the point-to-point problem
  • Inequality constraints on chaser satellite states

(collision avoidance) and end-effector forces

  • Same cost function (base actuation)
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Motion Planning for Grasping a Tumbling Target (3) Motivation for path planning:

  • due to free-floating state, need to guarantee no collision
  • due to tracking phase for minimum impact, need to guarantee

feasibility of solution (joint limits, singularities, etc.)

  • due to large momentum, need to guarantee stabilization of

residual motion

  • can optimize for safety (initial chaser attitude and robot

configuration, chaser actuation, etc.) need a realistic model

→

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Motion Planning for Grasping a Tumbling Target (4)

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Other Applications – Parameter Identification

  • Modeling requirements
  • Experimental design

ETS-VII Experimental Data

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Other Applications Compensation Maneuvers for a 2D platform

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Conclusion - Problems and Demands

  • Path planning method provides optimal solutions for

maneuvers in local and global workspaces but is highly nonlinear

  • Collision avoidance and improve algorithm efficiency
  • Integral modeling environment for all mentioned

functionalities

  • Motion planning problems are diverse and model-

based.

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Thank you!