“…where 𝜌, ∅ and ∅ are positive constant matrices and are properties of the human and the environment, respectively. Theorem 1: In the teleoperation system described by equation ( 1) with the control laws (24) and the IEAOB ( 13), (21) and the ASP (7), when the human and environmental forces satisfy (26), the velocities 𝑞 𝑡 , 𝑞 𝑡 and position errors are bounded, provided that 1) 𝐾 , 𝐾 , and 𝐾 are bounded and positive definite matrices, 2) 𝑇 , 𝑇 are bounded and continuous, Proof:…”