Towards Autonomous FreeClimbing Robots Tim Bretl JC Latombe

Towards Autonomous Free-Climbing Robots Tim Bretl, JC Latombe and Stephen Rock Aerospace Robotics Lab, Department of Aeronautics and Astronautics, Robotics Laboratory, Computer Science Department Stanford University, Stanford CA 94305, USA presented by: Michał Marzec

Outline Introduction p Previous related works p Description of planar three-limbed robot p Basic algorithm for computing motion p 3 -D four-limbed robot p Simulation p Summary p NUS CS 5247 2

Introduction p p p 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 maintained idea: 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. NUS CS 5247 3

Previous related works p Robots sticking to a flat surface Applications: painting, cleaning, inspection of facades. p Robots exploiting features of the environment such as hole, bars… Applications: construction, repair of bridges… p 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. p NUS CS 5247 4

Description of planar three-limbed robot i, k are supporting holds g 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. NUS CS 5247 5

One-step climbing problem p 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. p PARAMETRIZATION: configuration of the robot can be defined by 8 parameters - position of the pelvis (xp, yp) - joint angles of each limb (teta 1, teta 2) p Friction is modeled. p The motion takes places in a 4 -D subspace Cik. NUS CS 5247 6

Sampling p p p The planner samples the configurations of the contact chain. The position of pelvis is sampled in the intersection of the two discs of radius 2 L centered in i and k. For each (xp, yp) the inverse-kinematics operation yields teta 1 and teta 2 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 NUS CS 5247 7

Equilibrium test p 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. NUS CS 5247 8

Path test p 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 subpaths joining q and qmid, and qmid and q’. NUS CS 5247 9

Feasible space for a given configuration of the contact chain. p 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 = 3 xmin -2 xc/chain and xmax/free= 3 xmax – 2 xc/chain Pelvis location is feasible wrt. the robot’s equilibrium constraint if: NUS CS 5247 10

Basic algorithm p p p 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. NUS CS 5247 11

Example NUS CS 5247 12

Refinement of the algorithm p p We sample pelvis location ONLY. …and we let the free limb move in either Eq 8: Eq 9: NUS CS 5247 13

3 D Four-Limbed Robot p p Lemur II The robot’s self-collision and collision with the environment are not allowed. NUS CS 5247 14

Case of 3 D algorithm 1. 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. NUS CS 5247 15

Simulation results NUS CS 5247 16

Summary p PRM planning algorithm – One-Step-Climbing to compute the motion of a multi-limbed robot climbing vertical terrain. p Moves similar to those developed by human climbers. p 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. NUS CS 5247 17