Table 2.

A comparison of the main approaches for variable impedance learning and control.

Approach		Advantages	Disadvantages
Existing	Stability and passivity of VIC	Model-based solutions, where the models are often simplified computational representations, are efficient, and accurate. Guarantee the stability (or passivity) is of importance for safe interactions.	Rely on accurate models of the system under control to work well. Derive accurate models is, in some cases, nontrivial that complicates the overall design and makes the solution less general.
	Human-in-the-loop	During the execution, human can react where the AI algorithms are not confident about the next reaction. Human impedance, estimated via EMG sensors, postural markers, and/or haptic devices, often represents a good target impedance for the robotic arm.	Require prior knowledge on the human anatomy, a complex setup with multiple sensors, and a long calibration time. Moreover, the system can be influenced by possible human error, in addition to lack of repeatability.
	Imitation learning	User-friendly and easy learning framework to teach robots. Humans use variable impedance strategies in many of their daily activities and can naturally demonstrate a proper impedance behavior to solve a specific task.	The quality of learning can be influenced by the teacher performance. Some tasks are complex enough to be demonstrated. Directly transfer the impedance policy from a human to a robot is not always possible and may require sophisticated strategies or hand tuning.
	Iterative learning	These approaches are computationally and data efficient. Convergence to the optimal parameters can be analytically proved.	The target impedance behavior has to be manually defined, which makes hard to generalize the approach to dissimilar tasks. Moreover, standard ILC assumes that the system is already stable or stabilized with a suitable controller. Moreover, it needs multiple task repetitions with the same duration and initial conditions, which is hard to guarantee in real scenarios.
	RL	The robot may potentially discover control policies to solve complex, hard to model tasks. The usage of a specialized policy paramaterization increases the data efficiency and the policy transferability.	Specialized policies, like the ones based on VIC, as well as safety requirements limit the exploration capability of the learning agent increasing the risk to get stuck into a policy far from the optimal one.
Envisioned	• The ideal impedance behavior should be: – stable, accurate, and robust like a control approach, without requiring an accurate model or domain-specific knowledge like in reinforcement learning. – computational and data efficient, as well as easy to setup. • Enhanced generalization capabilities are also required to adapt the robot behavior to different situations. None of the reviewed approaches has all these features. However, some approaches have great potential and deserve to be further investigation. • Manifold learning has shown interesting performance in learning variable impedance behaviors (Abu-Dakka et al., 2018). In many applications, not only in impedance learning, the training data below to a certain manifold, but the underlying structure of the data is typically not properly exploited by the learning algorithm. Manifold learning remains a widely unexplored and rather promising topic. • Stability guarantees are a need when the robot interacts with the environment and the safe reinforcement learning formalism seems the route to learn effective impedance policies. The most powerful reinforcement learning are extremely data greedy that poses several limitations on their applicability. In this context, model-based approaches with stability guarantee seem better suited but their effectiveness has not be fully investigated.