Abstract-Robots are finding new applications where physical interaction with a human is necessary: manufacturing, healthcare, and social tasks. Accordingly, the field of physical humanrobot interaction (pHRI) has leveraged impedance control approaches, which support compliant interactions between human and robot. However, a limitation of traditional impedance control is that-despite provisions for the human to modify the robot's current trajectory-the human cannot affect the robot's future desired trajectory through pHRI. In this paper, we present an algorithm for physically interactive trajectory deformations which, when combined with impedance control, allows the human to modulate both the actual and desired trajectories of the robot. Unlike related works, our method explicitly deforms the future desired trajectory based on forces applied during pHRI, but does not require constant human guidance. We present our approach and verify that this method is compatible with traditional impedance control. Next, we use constrained optimization to derive the deformation shape. Finally, we describe an algorithm for real time implementation, and perform simulations to test the arbitration parameters. Experimental results demonstrate reduction in the human's effort and improvement in the movement quality when compared to pHRI with impedance control alone.

Abstract-This paper comparatively evaluates the effect of real-time velocity estimation methods on passivity and fidelity of virtual walls implemented using haptic interfaces. Impedance width, or Z-width is a fundamental measure of performance in haptic devices. Limited accuracy of velocity estimates from position encoder data is an impediment in improving the Zwidth in haptic interfaces. We study the efficacy of Levant's differentiator as a velocity estimator, to allow passive implementation of higher stiffness virtual walls as compared to some of the commonly used velocity estimators in the field of haptics. We first experimentally demonstrate feasibility of Levant's differentiator as a velocity estimator for haptics applications by comparing Z-width performance achieved with Levant's differentiator and commonly used Finite Difference Method (FDM) cascaded with a lowpass filter. A novel Z-width plotting technique combining passivity and fidelity of haptic rendering is proposed, and used to compare the haptic device performance obtained with Levant's differentiator, FDM+lowpass filter, First Order Adaptive Windowing and Kalman filter based velocity estimation methods. Simulations and experiments conducted on a custom single degree of freedom haptic device demonstrate that the stiffest virtual walls are rendered with velocity estimated using Levant's differentiator, and highest wall rendering fidelity is achieved by First Order Adaptive Windowing based velocity estimation scheme.