# Variable Admittance Control in Sliding Mode for Robust Physical Human-Robot Interaction
###### Abstract  
Intuitive and comfortable physical human-robot interaction (pHRI) can be realized by changing impedance/admittance parameters corresponding to human interaction. However, this dynamic adjustment may result in drastically changed system dynamics, which usually give rise to system instability. We introduce a power envelope regulation strategy designed to constrain the variability of admittance parameters, thereby ensuring system passivity and mitigating the risk of instability. Then, sliding mode control (SMC) is employed to yield stable and robust performance. A new sliding surface is proposed based on feedback linearization, which shows improved tracking performance and stability compared to a conventional sliding surface. The effectiveness of the proposed sliding surface and associated control is theoretically validated. Notably, our modified sliding surface works universally, regardless of the order of the desired admittance equation. The trade-off between system chattering and robustness is effectively managed using a variable-boundary approach, which dynamically adjusts system constraints to optimize performance. In addition, a control algorithm combining acceleration feedback and sliding mode is proposed, showing improved robustness and tracking accuracy performance compared with applying the proposed SMC algorithm exclusively. The efficacy of these methodologies is substantiated through numerical simulations and empirical experiments. physical human-robot interaction; human intention adaptation; variable admittance control (VAC); passivity and stability; power envelope; sliding mode control (SMC); acceleration feedback +
Footnote †: journal: _sciences_  
and [PERSON] selected the time derivative of interaction force to infer the human's future intention (i.e., acceleration and deceleration) where the damping decreases according to a suddenly increased force and vice versa [22]. A similar force-dependent approach was proposed in [18], where the direction of force and velocity was introduced to detect acceleration and deceleration. A common disadvantage of these methods is that the user must continuously exert higher force to maintain a long-duration, faster motion. [PERSON] and [PERSON] [16] addressed this issue by proposing an updating rule for damping that saves the user's efforts. Virtual stiffness is usually omitted because restoring the forces in a virtual spring is not desirable when the human leads the robot to move in free space. Inducing a stiffness force term renders a less compliant behavior of the robot. In contrast, the stiffness term is essential to maintain small position tracking errors upon disturbance if a trajectory is prescribed. In [23; 24], active stiffness combined with reference trajectory deduced from human intended motion yields a compliant and effort-saving interaction. Virtual inertia has less direct contributions to human perception of robot motion but critically impacts the system's stability, as discussed in [25; 26]. A lower value of inertia is appealing in acceleration and fast movement. Intuitively, small inertia may yield a rapid change in speed to be perceived immediately by the user if the control frequency is high. However, experimental results observed in [16] suggested no significant improvement in human perception experience by increasing inertia. The selection of admittance parameters not only affects the performance (i.e., adaptation to human intention [10; 18; 22; 27; 28]) but also impacts the stability of interaction [29; 30; 31; 32]. Human intention adaptation determines the intuitiveness of pHRI but cannot take stability into consideration. Passivity is a sufficient condition for a robot's stability when interacting with a passive environment [31], whereas it is a necessary condition in interaction with humans [16].