NUS CS5247

Towards Autonomous Towards Autonomous Free-Climbing RobotsFree-Climbing Robots

Tim Bretl, JC Latombe and Stephen RockTim Bretl, JC Latombe and Stephen Rock

Aerospace Robotics Lab, Department of Aeronautics and Astronautics, Aerospace Robotics Lab, Department of Aeronautics and Astronautics, Robotics Laboratory, Computer Science DepartmentRobotics Laboratory, Computer Science Department

Stanford University, Stanford CA 94305, USAStanford University, Stanford CA 94305, USA

presented by: Michał Marzecpresented by: Michał Marzec

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Outline Introduction Previous related works Description of planar three-limbed robot Basic algorithm for computing motion 3-D four-limbed robot Simulation Summary

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Introduction Multi-limbed robot vs. vertical surface (rock) with holds (free

climbing). Compute a path such that:

-free limb is brought to a new hold-balance of the robot is maintainedidea: opposition. No strength is required.

-the path = sequence of one-step climbing moves. -robot is pushing or pulling at other holds exploiting contact and

friction (limb end-points). Possible applications: search-and-rescue, planetary exploration.

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Previous related works Robots sticking to a flat surface

Applications: painting, cleaning, inspection of facades.

Robots exploiting features of the environment such as hole, bars… Applications: construction, repair of bridges…

Robots climbing within pipes.

But…none of these techniques scale up to vertical terrain. Problem: move one limb at time, adjusting DOFs.What makes our robot so exceptional? It may be used in natural terrain.

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Description of planar three-limbed robot

i, k are supporting holdsg is a free hold

For the robot to be in quasi-static equilibrium, there must exist reaction forces at the supporting holds whose sum exactly compensates for gravitational force on the robot.

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One-step climbing problem Given a start configuration of the robot and a a hold g compute a path of the robot

connecting the initial position to a configuration that places the foot of the free limb at hold g and such that the robot remains in equilibrium along the entire path.

PARAMETRIZATION:configuration of the robot can be defined by 8 parameters- position of the pelvis (xp, yp) - joint angles of each limb (teta1,teta2)

Friction is modeled.

The motion takes places in a 4-D subspace Cik.

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Sampling The planner samples the configurations of the contact chain. The position of pelvis is sampled in the intersection of the two discs

of radius 2L centered in i and k. For each (xp, yp) the inverse-kinematics operation yields teta1 and

teta2 of the free limb. For two sufficiently close configurations, if the path between them

keeps the robot in equilibrium then the new edge is added to V. Then some smoothing techniques are used to improve the path

produced by the algorithm. Stop condition: free limb in g or maximal size of the roadmap

reached

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Equilibrium test Gravity and the reaction forces are the only external forces acting on

our robot.

Given a configuration q we compute E and xc of CM for this configuration and check if xc is included in E. If it is then it means that the robot is in equilibrium.

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Path test How to test whether a linear path between q and q’ keeps the robot in equilibrium?

-Sample the points at some resolution OR

-Compute and upper-bound ‘gamma’ (length of the path traced out by the CM). If either at q or q’ the min distance between xc and the bounds of E exceeds gamma then accept the path. Otherwise qmid = (q +q’)/2. If the robot is not in equilibrium at qmid then reject the path, else apply the same treatment recursively to the two sub-paths joining q and qmid, and qmid and q’.

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Feasible space for a given configuration of the contact chain.

Analyze the connectivity of the equilibrium configurations of the robot.

Xc must lie in E [xmin, xmax]Xc/free must lie in [xmin/free, xmax/free]xmin/free = 3xmin -2xc/chain and xmax/free= 3xmax – 2xc/chain

Pelvis location is feasible wrt. the robot’s equilibrium constraint if:

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Basic algorithm We use PRM approach to sample equilibrium configurations. Configuration where robot remains in equilibrium is retained as a vertex of

the roadmap. An edge is added to if the robot remain in equilibrium along the path

joining 2 sufficiently close vertices.

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Example

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Refinement of the algorithm We sample pelvis location ONLY. …and we let the free limb move in either

Eq 8:

Eq 9:

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3D Four-Limbed Robot Lemur II The robot’s self-collision and collision with the environment are not allowed.

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Case of 3D algorithm1. The joint limits are such that the inverse kinematics of each limb has at most one

solution.

2. Sampling configurations of the contact chain is much harder than the planar case, so we need to use different techniques.

3. The equilibrium test must be slightly modified.

4. We use PQP to check for self-collision of the robot and collision with the environment.

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Simulation results

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Summary PRM planning algorithm – One-Step-Climbing to compute the motion of a

multi-limbed robot climbing vertical terrain.

Moves similar to those developed by human climbers.

Multi-step planning based on incomplete information about the terrain ahead will also be needed to choose which hold to reach next, when multiple holds are within reach.