Safety control for impedance haptic interfaces

Abstract

Instability in haptic systems due to behaviors of human operators or unknown virtual environments can present safety issues. For example, a haptic stylus may be ejected at a high speed which may cause injury if manipulated inappropriately. Three safety control approaches are thus proposed in the paper to tackle the issues. The first approach is based on a simple velocity and force dependent controller, while the other two are derived from a grasp force model exploiting the state of the haptic stylus, including acceleration, velocity and penetration force, to generate the grasp force. Based on the force model, safety indicators called “safety observers” are proposed to monitor system instability caused by sudden release of haptic stylus by a user during interactions with virtual objects. Experimental results show that the proposed models can effectively reduce the velocities of the haptic stylus and suppress jerking movement, and stabilize the haptics system even in presence of active forces. The proposed safety controllers can respond to the “safety observers” and generate appropriate damping forces to counteract the instability incurred, whereas traditional control methods fail to trigger a protection mechanism under the same situation. As prior knowledge of virtual environments and additional hardware sensors are not required, the proposed approaches have the potential to be widely adopted in haptics-enabled applications.

Appendix

Figure 16 depicts a two-port network-based passivity analysis, where the sign convention for all forces and velocities is defined when power enters the system ports. The system energy exchange is governed by the following equation [9],

$$ {\displaystyle \underset{0}{\overset{t}{\int }}}{F}_{hap}\left(\tau \right){V}_h\left(\tau \right)dt={E}_p+{E}_d-{E}_g, $$

(18)

where F _hap is the force generated by the haptic interface, V _h is the hand velocity, E _p is the energy that is stored in the haptic device, E _g is the energy generated by the “non-idealities” in the control loop, e.g., discretization, quantization, etc., and E _d is the energy dissipated by frictions. The excessive energy ΔE at time step n with a sampling time step ΔT in a discrete-time form is derived as,

$$ \varDelta E(n)={E}_d(n)-{E}_g(n)\approx \varDelta T{\displaystyle \sum_{i=1}^n}{F}_h(i)V(i)-{E}_p(n). $$

(19)

Fig. 16

Network representation of a haptics-enabled system for passivity analysis

Note that in above equation, assuming the stylus of the haptic interface is grasped by the user, the hand velocity V _h is approximated by the velocity of the haptic stylus V and the force produced by the haptic interface is replaced by the force F _h as defined by Eq. (4). When the user interacts with the virtual environment in the active regions, the amount of potential energy E _p that is converted to kinetic energy (E _k ) is η = E _k /E _p . The E _p is approximated by the kinetic energy as E _p  = E _k /η = mV ²/2η, where m is the physical inertia of the stylus. From Eq. (19), the Safety Observer (SO) E _so is defined by,

$$ {E}_{so}(n)=\varDelta E(n)\approx \varDelta T{\displaystyle \sum_{i=1}^n}{F}_h(i)V(i)- mV{(n)}^2/2\eta\ . $$

(20)