Effect of Virtual Mass and Time Delay on the Stability of Haptic Rendering
Ahmad Mashayekhi, Mehdi Shakeri, Amin Khorasani, Tom Verstraten
AI summary
Problem
Haptic rendering struggles to balance transparency and stability when simulating virtual environments with time delays. Prior studies lacked closed-form stability predictions for virtual mass and damping, relying instead on zero-delay assumptions or trial-and-error methods.
Approach
The authors derive closed-form stability boundary equations for a one-degree-of-freedom haptic device interacting with a mass-spring-damper virtual environment, explicitly modeling constant time delay, virtual mass, and virtual damping.
Key results
- Maximum renderable virtual mass is twice the physical HD mass
- Closed-form equations predict stability boundaries for arbitrary time delays and damping
- Virtual mass tuning theoretically boosts renderable stiffness by up to 5.8×
- Nonzero minimum virtual spring stiffness required for stability in certain cases
Why it matters
Provides haptic system designers with explicit mathematical tools to predict and maximize rendering performance despite unavoidable control delays.
Abstract
Virtual mass simulation is one of the recent topics Q2 4 in the field of haptic devices (HDs), which can alter the apparent 5 mass of the HD. Simulating negative values of virtual mass leads to 6 a decrease in the apparent effective mass, improving transparency 7 but weakening stability. Positive virtual mass rendering increases 8 the apparent mass, reduces transparency, and enhances stability. 9 This paper analyzes the stability of a haptic device while simulating 10 a virtual environment consisting of a mass, spring, and damper 11 in the presence of a constant time delay. The results are closed- 12 form equations that can predict the stability boundary for small 13 and even large values of virtual damping and time delay. These 14 closed-form equations demonstrate that the maximum renderable 15 virtual mass is twice the physical mass of the HD, and the minimum 16 value equals its negative; both occur in the case of zero time delay. 17 Increasing the time delay reduces both the minimum and maximum 18 values of the renderable virtual mass. The study also shows that 19 using virtual mass can improve the maximum value of a renderable 20 virtual spring. The equations show that, in the absence of delay, 21 properly tuning the virtual mass and virtual damping can enlarge 22 the maximum renderable stiffness by up to 5.8 times in theory. In 23 the experiments under time delay, the stiffness increased by a factor 24 of 3.5, compared to the theoretical prediction of 4.1 times. The 25 results further reveal situations where a nonzero minimum stiffness 26 is required for stability. All findings are validated via simulations 27 and experiments on a dedicated test bed. 28