Optimal Prioritized Dissipation and Closed-Form Damping Limitation under Actuator Constraints for Haptic Interfaces

Abstract

In haptics, guaranteeing stability is essential to ensure safe interaction with remote or virtual environments. One of the most relevant methods at the state-of-the-art is the Time Domain Passivity Approach (TDPA). However, its high conservatism leads to a significant degradation of transparency. Moreover, the stabilizing action may conflict with the device's physical limitations. State-of-the-art solutions have attempted to address these actuator limits, but they still fail to account simultaneously for the power limits of each actuator while maximizing transparency. This work proposes a new damping limitation method based on prioritized dissipation actions. It prioritizes an optimal dissipation direction that minimizes actuator load, while any excess dissipation is allocated to the orthogonal hyperplane. The solution provides a closed-form formulation and is robust in multi-DoF scenarios, even in the presence of actuator and motion anisotropies. The method is experimentally validated using a parallel haptic interface interacting with a virtual environment and tested under different operating conditions.

Figures (11)

• Figure 1: Block representation of an impedance-based haptic interface interacting with a virtual environment. The human operator is supposed to be passive, while the virtual environment is simulated to behave actively according to ryu2004sampled. The PC is included to make the entire system passive.
• Figure 2: Application of strategy porcini2023actuator with anisotropic velocities. On the first row joints' velocity are shown, where $\dot{q}_1$ is always greater than the others during the dissipation. On the second row the limitation in norm of the torques is verified. On the last row the dissipation torque at joint 1 is demonstrated to violate the physical limits.
• Figure 3: Application of strategy porcini2023actuator with anisotropic actuator limits. On the first row, the limitation in the norm of the torques is satisfied. On the second row, the torque at joint 2 – which was constrained to one third of its maximum possibilities – is shown to not satisfy the physical limits.
• Figure 4: Representation of the ($f_x$,$f_y$) plan. The square highlights the physical capabilities of the system, i.e. references provided to the actuators are realizable if contained in the square. $\mathbf{\hat{f}}$ is the reference force, $\mathbf{d}_A$ is the desired dissipation vector which generates, together with $\mathbf{\hat{f}}$, the commanded force $\mathbf{f}_{cmd,A}$ while $\mathbf{d}_B$ is the limited dissipation vector which generates $\mathbf{f}_{cmd,B}$. Since $\mathbf{f}_{cmd,A}$ is already realizable by the actuators, it should not be necessary to limit the dissipation $\mathbf{d}_A$, but this fact is not taken into account in porcini2023actuator.
• Figure 5: Rendered and dissipated fed back force, respectively $\hat{f}$ and $f_{cmd}$, along the virtual wall axis by using strategy in preusche2003time. According to the position of the wall, positive forces are repulsive, while negative are attractive.