Learning Variable Impedance Skills from Demonstrations with Passivity Guarantee

TL;DR

This work tackles learning variable impedance control from demonstrations with guaranteed passivity by estimating time-varying stiffness $K_t$ from human demonstrations and incorporating force sensing to reproduce tasks under new conditions. It introduces a stiffness-learning framework that handles unknown damping, using a symmetric SPD projection and CMA-ES optimization, and learns $K_t$ via a kernelized Cholesky parameterization to enable robust reproduction. Passivity is guaranteed through two novel Lyapunov functions that provide practical stability conditions, avoiding reliance on uncertain damping dynamics. The approach is validated in simulations and on a Franka Emika robot performing a massage task, showing robust stiffness estimation, energy-based safety guarantees, and practical implementability of the tank-based passivity mechanism. The results suggest significant potential for adaptable, safe manipulation in unstructured environments using demonstration-driven variable impedance skills.

Abstract

Robots are increasingly being deployed not only in workplaces but also in households. Effectively execute of manipulation tasks by robots relies on variable impedance control with contact forces. Furthermore, robots should possess adaptive capabilities to handle the considerable variations exhibited by different robotic tasks in dynamic environments, which can be obtained through human demonstrations. This paper presents a learning-from-demonstration framework that integrates force sensing and motion information to facilitate variable impedance control. The proposed approach involves the estimation of full stiffness matrices from human demonstrations, which are then combined with sensed forces and motion information to create a model using the non-parametric method. This model allows the robot to replicate the demonstrated task while also responding appropriately to new task conditions through the use of the state-dependent stiffness profile. Additionally, a novel tank based variable impedance control approach is proposed to ensure passivity by using the learned stiffness. The proposed approach was evaluated using two virtual variable stiffness systems. The first evaluation demonstrates that the stiffness estimated approach exhibits superior robustness compared to traditional methods when tested on manual datasets, and the second evaluation illustrates that the novel tank based approach is more easily implementable compared to traditional variable impedance control approaches.

Figures (13)

• Figure 1: The framework involves learning variable stiffness from demonstrations and implementing variable impedance control on the Franka robot to perform a massage task.
• Figure 2: The process for extracting variable stiffness parameters from demonstration data, followed by the application of these parameters in the implementation of variable impedance control, ensuring the system maintains passivity.
• Figure 3: The demonstrated stiffness ellipsoids are visualized at different time steps.
• Figure 4: Considering a known constant damping, compare the performance of the estimated stiffness using the proposed algorithm with nearest-SPD approximation and the convex optimization.
• Figure 5: With known constant damping, compare the performance of the estimated stiffness using the proposed algorithm with nearest-SPD approximation to that using convex optimization to solve the modified objective function.