Interactive Adaptation of Probabilistic Virtual Fixtures Using Null Space Kernelized Movement Primitives

Abstract

This thesis presents a probabilistic framework for the interactive adaptation of virtual fixtures (VFs) using Null Space Kernelized Movement Primitives (NS-KMPs). The approach enables real-time modification of learned trajectories during human–robot collaborative tasks. Building on Kernelized Movement Primitives, which can learn generalizable skills from demonstrations, NS-KMPs incorporate a soft null space projector that allows efficient trajectory adaptation without recomputing expensive matrix operations.

The proposed method employs NS-KMP to jointly consider position and orientation components of the robot data on the product manifold R3 × SO3 with a single tangent space (STS) projection, thereby supporting orientation-aware adaptation of the NS-KMP trajectory. Moreover, adaptation to user inputs is supported with distributed inputs, referred to as spread NS actions, which ensure a smooth deflection profile. Additionally, different decoupling strategies of the NS-KMP formulation are employed to process these inputs, namely fully coupled, position–orientation decoupled, and fully decoupled variants.

Within this framework, probabilistic VFs provide force and torque feedback to guide users along a learned trajectory while adapting to operator inputs through NS actions. The system is implemented on the SARA torque-controlled robot arm in a ring placement task representative of industrial assembly scenarios. Simulations and real-world experiments demonstrate the framework's capability to produce compliant, adaptive, and safe robot assistance. Results show that NS-KMP VFs effectively modify their reference trajectories under various decoupling modes and provide smooth trajectory modifications through spread NS actions.

In addition, the proposed framework processes user inputs in a human-in-the-loop manner, enabling the operator to deflect the reference trajectory of the NS-KMP VF as desired to easily adapt to changing production environments. The findings highlight the potential of NS-KMP VFs to provide effective guidance in human–robot interaction while allowing easy and intuitive modification by the operator.