# Detecting and Controlling Slip through Estimation and Control of the Sliding Velocity
## 1 Introduction
In [15], the authors, by endowing a three-fingered hand with the TacTip integrated optical tactile sensor, present a method to perform slip detection based on a support-vector machine (SVM). The decision to adopt a model-based approach here is related to the difficulty of current data-driven methods for robotic slipping detection and avoidance to generalize to manipulated objects made of different types of materials and surface conditions. A re-training of the learning-based strategy is still required for such a class of solutions, especially when surface conditions change due to environmental variability, e.g., moisture or temperature. On the contrary, the superior generalization capabilities of the model-based approach appear to be still attractive to attain a high level of autonomy of the robotic system. Moreover, in all the model-free approaches, after detecting a slip, the reaction designed to stabilize the grasp is of a heuristic type, which means increasing the grasp force until the object stops sliding; the selection of an increasing force of the grasp force should be a trade-off between the desired speed to stop slipping and the caution needed to not damage the object. Differently from the method used in [16] to compute the grasp force to avoid slip, here, the control algorithm, owing to the nonlinear observer, distinguishes the static friction contribution from the viscous one, thus leading to the true minimum amount of grasp force necessary to compensate for the external load and avoid slippage. A recent work proposing this sort of approach is [17], where the slip event was predicted by a classifier based on random forests and the proposed grasp force controller does not compensate for rotational slips. In this paper, we do not follow the learning-based prevailing trend, but following the approach already presented in [9; 16], we present a revisited model-based approach to slip detection/avoidance and controlled sliding. General in-hand manipulation tasks involve both translational and rotational motion; thus, it is necessary to model the relationship between the friction force and torque and the sliding motion. The approach adopted to describe such a relationship, assuming that the contact is planar, is the limit surface concept (LS) [12; 18], which relates the sliding motion, described as a rotational motion about the instantaneous center of rotation (CoR), to the maximum friction force and torque as functions of the normal force. The LS concept is a generalization of the Coulomb friction cone concept when friction torsional torque is involved in the soft contact. In order to perceive the object's motion upon contact with the fingertips using only a force/tactile sensor, it is necessary to estimate the relative velocity between the object and the fingertips. In [19], we introduced a nonlinear observer based on the celebrated [PERSON] dynamic friction model [20; 21] extended to the case of rotational sliding about the CoR. Such a model describes the friction as a pure friction torque with respect to the CoR. The maximum friction torque is provided by the limit surface method. The dynamic model requires the knowledge of the CoR position estimated by using the measurement of the dry friction provided by the force/tactile sensor at the fingertips. The nonlinear observer in [19] has been used in [22] to estimate the sliding velocity with the aim of avoiding object slipping and in [16], where a generalization of the LS method has been proposed by considering not only the effects of the dry friction but also the effects of the viscous one. An additional advantage of the adoption of nonlinear dynamics to model the transition from a no-slip to a slip condition is its numerical stability compared to traditional threshold-based approaches also adopted in tribology, such as in [23].