Task geometry aware assistance for kinesthetic teaching of redundant robots

Kinesthetic teaching of bi-manual tasks with known relative constraints

“…To assist the human-teacher by communicating the directions towards the satisfaction of the RTC, we propose the utilization of penetrable VF initially proposed in [7] for a single robot. In the bi-manual kinesthetic teaching task, the VF are not fixed with respect to the inertial frame but are utilized in the relative space and the control action is distributed in both robotic manipulators using the relative Jacobian (2), (3).…”

“…with D ∈ R 6×6 being a positive definite damping matrix introducing the active damping and U (x R , x c (σ)) : T ×T → R + being the potential function. The following potential function similar to [7] is utilized:…”

“…where the damping term −k d H q ensures that −k d q⊺ N ⊺ R H q ≤ 0 and thus it is dissipative [21]. Remark 1: To ensure passivity of the closed loop system, consisted of (1), ( 2), ( 10), ( 13) and ( 23), one could utilize the notion of energy tanks similarly to [7]. In this case, a portion of the dissipated energy of the closed loop system could have been considered to be stored in an energy tank, which in turn would allow the inertia optimization to be performed when it is not depleted.…”

“…Kinesthetic teaching has been widely used for teaching end-effector skills to single robotic manipulators [3]- [7]. However, in many tasks, a bi-manual solution is required which allows a bigger workspace and an enhanced dexterity/maneuverability owing to the redundant DOFs.…”

“…Task knowledge has been used to assist the human-teacher in demonstrating a single arm task involving contact via virtual fixtures (VF) placed appropriately in the task space [6], [7], [12]- [16]. Moreover, inertia minimization has been utilized in redundant manipulators to reduce the effective end-effector inertia during kinesthetic guidance [17]- [19].…”