0.55 0.5 0.45 0.4 0.35 0.3 -0.05 X (m) (a) 0.2 -0.2 -0.4 -0.6 -0.8 (c) 0.55 0.5 0.45 0.4 0.35 0.3 0.55 0.5 0.45 0.4 0.35 -0.05 X (m) (e) External Torque Feedforward Torque Feedback Torque -0.2 1 -1 -2 -0.8 0.5 Time (s) (g) 1 -4 -3 0.5 Time (s) (h) Figure 4. A simulation of adaptation to unstable dynamics as in a velocity dependent external force (VF) field. (a) Trajectories in the first and last three iterations in [8]. (b) and (c) Feedback and feedforward joint torques and the torque affected by external forces in [8]. (d) The evolution of feedforward torque in [8]. (e) Trajectories in the first and last three iterations in the proposed method. (f) and (g) Feedback and feedforward joint torques and the torque affected by external forces in the proposed method. (h) The evolution of feedforward torque in the proposed method. (Continued) DECEMBER 2022 * IEEE ROBOTICS & AUTOMATION MAGAZINE * 71 1 0.05 -0.05 X (m) 0.05 1 -1 -2 -3 0.5 Time (s) (f) External Torque Feedforward Torque 1 External Torque Feedforward Torque Feedback Torque -1 -2 -3 0.5 10 0.5 Time (s) 1 Time (s) (d) External Torque Feedforward Torque Feedback Torque 0.05 0.55 0.5 0.45 0.4 0.35 0.3 1 External Torque Feedforward Torque Feedback Torque -1 -2 -3 -0.05 X (m) 0.05 0.5 Time (s) (b) External Torque Feedforward Torque 1 Torque (N.rad) Y (m) Torque (N.rad) Y (m) Y (m) Y (m) Torque (N.rad) Torque (m.rad) Torque (N.rad) Torque (m.rad)