1, 2, 2, 2, 2 Recovery Motion Learning for Single-Armed Mobile Robot in Drive System s Fault Tauku ITO 1, Hitoshi KONO 2, Yusuke TAMURA 2, Atsushi YAM
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1 1, 2, 2, 2, 2 Recovery Motion Learning for Single-Armed Mobile Robot in Drive System s Fault Tauku ITO 1, Hitoshi KONO 2, Yusuke TAMURA 2, Atsushi YAMASHITA 2 and Hajime ASAMA 2 1 Department of Precision Engineering, Faculty of Engineering, The University of Tokyo Hongo, Bunkyo-ku, Tokyo , Japan 2 Department of Precision Engineering, Graduate School of Engineering, The University of Tokyo Hongo, Bunkyo-ku, Tokyo , Japan This study presents a new approach to obtain recovery motion for an arm mounted teleoperated crawler robot in drive system s failure. A robot in drive system s fault and in dangerous areas such as disaster sites needs to move. When one side crawler mechanism is in fault, the robot can use redundancies such as its arm for moving. It calls recovery motion in this study. However, it is difficult to know how to leverage these redundancies and to manipulate the robot. Our approach uses the reinforcement learning which makes robot do trial and error to maximize total reward it receives and finds the motion of purpose. To obtain the recovery motion, in advance by using reinforcement learning in the 3D dynamics simulator is effective for real robots. For reinforcement learning, three types of reward functions are used. In the 3D simulator, experiments on a crawler robot verified this approach. Key Words : Crawler Robot, Learning, Recovery 1. (1) (2) 2011 (3) (3) ito@robot.t.u-tokyo.ac.jp {kono, tamura, yamashita, asama}@robot.t.u-tokyo.ac.jp ASTACO-SoRa (4) 1 (5) CPG Central Pattern Generator (6) (7)
2 No Fig. 1 Single-armed crawler robot Choose action a t from state s t Take action a t Observe reward r t, next state s t+1 Update Q(s t, a t ) s t is terminal? Yes Next episode Fig. 2 Q-learning flow 1 step (8) (9) Q Q 2 3 Q Q 1 2 Q(s t,a t ) (1) TD Temporal Difference δ (2) Q(s t,a t ) s t a t r t max a Q(s t+1,a) s t+1 Q δ = r t + γ maxq(s t+1,a) Q(s t,a t ) (1) a Q(s t,a t ) Q(s t,a t ) + αδ (2) α γ 2 4 s a s S,a A π(s,a) (3) π(s,a) = Q(s,a) exp( T ) b A exp( Q(s,b) T ) (3) T Q T Q Q T 0 T = 1 log(t + 0.1) t (4)
3 2 5 1 (5)(6) r (1) t r (2) t r (3) t t (5) y w y t+1 y t Robot d 1 e d 2 θ t p (x t, y t ) φ t Top view (x t+1, y t+1 ) r t = r (1) t + r (2) t + r (3) t (5) Fig. 3 e (6) p 2 θ( π θ π) (7) p e d 1 e (8) d 2 t t + 1 ϕ t O x t Fig. 3 Goal Line x t+1 Vector reward d 3 x w p = [x t+1 x t y t+1 y t ] T (6) d 1 = p cosθ t (7) Goal distance b t = T (x T, y T ) d 2 = p sinθ t (8) (9) 1 r (1) t r (1) t = ηd 1 λ d 2 τ ϕ t (9) η λ b [m] 4 1 t = T d 3 r (2) t = ζ exp( d 3 ) if robot reached goal line 0 otherwise (10) ζ Top view y w t = 0 (x 0, y 0 ) x w Robot Fig. 4 Goal reward 1 b [m] 2 6 NE (10) (11)
4 Table 1 State s t, Action a t Rolled over G max G Joint Figure 1 State s t Action a t Right crawler 1 Torque (N m) 0.3, 0, -0.3 m/s Swing 2 Joint angle (rad) 0.3, 0, -0.3 rad/s Boom 3 Joint angle (rad) 0.3, 0, -0.3 rad/s Arm 4 Joint angle (rad) 0.3, 0, -0.3 rad/s S NE Q Fig. 5 Input Contact point Normalized energy stability margin Radial Basis Function φ j (x) y = w j ϕ j (x) (13) j RBF 3 (14) RBF [ ϕ j (x) = exp i ] (x i µ i j ) 2 σ 2 j (14) s t a t State s t Action a t φ j (x) w j Output Q(s t, a t ) Action-Value Function Q µ i j σ j j RBF Q(s t,a t ) ŷ (15) E E = 1 2 (ŷ y)2 (15) Fig. 6 RBF network z g z max 5 NE S NE (11) S NE = z max z g (11) S NE (12) r (3) t = ρ exp( S NE ) (12) 1 NE 2 7 Q Q Radial Basis Function RBF (12) 6 RBF w j, µ i j Q α w, α µ α Q w j w j α w E w j (16) µ i j µ i j α µ E µ i j (17) Q TD δ w j w j + α w α 2 δϕ j (x) (18) µ i j µ i j + α µ α 2 x i µ i j δw j σ 2 ϕ j (x) (19) j GUI Choreonoid (13) Choreonoid 3D (14) Ubuntu LTS Intel Core i7-4720hq 2.6GHz
5 Table 2 Experiment setup parameter Parameter Value Learning rate α 0.1 Discount rate γ 0.9 Vector reward η 10 Vector reward λ 0.5 Vector reward τ 0.01 Goal reward ζ 10 Goal distance b 1.5 Rolled over ρ 1.0 RBF update rate α w 0.1 RBF update rate α µ m 1.25m s a 8 s Q a PID RBF ϕ 20 RBF m RBF µ i j 0 1 σ j (x,y) = (0,0) (0, 1) y = (a) 9(b) 9(c)(d) 7 Fig. 7 Robot s trajectory Fig. 8 Total reward 5.
6 (a) (b) (c) Fig. 9 Recovery motion of straight movement (d) ImPACT (1) Vol.32 No.1 (2014), pp (2) Vol.32 No.2 (2014), pp (3) Vol.740 (2011), pp (4) ASTACO- SoRa Vol.117 No.1151 (2014), pp (5) Vol.50 No.3 (2009), pp (6) CPG C Vol.136 No.3 (2016), pp (7) QDSEGA Vol.17 No.4 (2002), pp (8) R. S. Sutton, A. Gbarto,, (2000). (9) Vol.38 No.10 (1999), pp (10) Vol.16 No.8 (1998), pp (11) D. A. Messuri, and C. A. Klein, Automatic body regulation for maintaining stability of a legged vehicle during rough-terrain locomotion IEEE Journal on Robotics and Automation, Vol.1, No.3(1985), pp (12) J. Platt, A Resource-Allocating Network for Function Interpolation Neural Computation, Vol.3, No.2 (1991), pp (13) GUI Choreonoid Vol.31, No.3 (2013), pp (14) 2016, No.16-2 (2016).
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