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## Towards Autonomous Free-Climbing Robots

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**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 NUS CS5247**Outline**• Introduction • Previous related works • Description of planar three-limbed robot • Basic algorithm for computing motion • 3-D four-limbed robot • Simulation • Summary NUS CS5247**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. NUS CS5247**Previous related works**• Robots sticking to a flat surfaceApplications: 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. NUS CS5247**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 CS5247**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. NUS CS5247**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 NUS CS5247**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. NUS CS5247**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’. NUS CS5247**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: NUS CS5247**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. NUS CS5247**Example**NUS CS5247**Refinement of the algorithm**• We sample pelvis location ONLY. • …and we let the free limb move in either Eq 8: Eq 9: NUS CS5247**3D Four-Limbed Robot**• Lemur II • The robot’s self-collision and collision with the environment are not allowed. NUS CS5247**Case of 3D algorithm**• The joint limits are such that the inverse kinematics of each limb has at most one solution. • Sampling configurations of the contact chain is much harder than the planar case, so we need to use different techniques. • The equilibrium test must be slightly modified. • We use PQP to check for self-collision of the robot and collision with the environment. NUS CS5247**Simulation results**NUS CS5247**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. NUS CS5247