The Robustness of Tether Friction in Non-idealized Terrains

Abstract

Reduced traction limits the ability of mobile robotic systems to resist or apply large external loads, such as tugging a massive payload. One simple and versatile solution is to wrap a tether around naturally occurring objects to leverage the capstan effect and create exponentially-amplified holding forces. Experiments show that an idealized capstan model explains force amplification experienced on common irregular outdoor objects - trees, rocks, posts. Robust to variable environmental conditions, this exponential amplification method can harness single or multiple capstan objects, either in series or in parallel with a team of robots. This adaptability allows for a range of potential configurations especially useful for when objects cannot be fully encircled or gripped. These principles are demonstrated with mobile platforms to (1) control the lowering and arrest of a payload, (2) to achieve planar control of a payload, and (3) to act as an anchor point for a more massive platform to winch towards. We show the simple addition of a tether, wrapped around shallow stones in sand, amplifies holding force of a low-traction platform by up to 774x.

Figures (8)

• Figure 1: Capstan-enabled maneuvers Example exploitation of natural capstans for robotic missions on low-traction substrates are demonstrated. Capstan objects are shown utilized in single (top), serial (middle), and parallel (bottom) configurations. Robotic teamwork, target transport, and multi-millibot or swarm scaling modes, respectively, are all enabled through capstan amplification. Photo credits: (top) H.S. Stuart, (middle) R. Henrik Nilsson, CC BY-SA 4.0, (bottom) Jar.ciurus, CC BY-SA 3.0 PL.
• Figure 2: Comparison to robotic attachment methods. Comparison of properties of various attachment modes frequently used by robots. The simplified capstan effect amplifies tendon tension $T$ exponentially with wrap angle $\theta$ and friction coefficient $\mu$. Tension scales linearly with normal force $N$ and is independent of local radius $R$.
• Figure 3: Investigation of capstan effect across multiple capstans.(A1a-j) All tested permutations of wrap angles summing to 360, 720, and 900 degrees, corresponding to data in (C). (B) Experimental setup for laboratory capstan testing (C) Mean $A_F$ at slip produced as a function of number of capstans. Statistical significance is indicated with ** corresponding to p $<$ 0.005. (D1)$A_F$ for the various permutations of capstan material order presented in (D2). S and T abbreviate sandpaper and tape, their friction coefficients $\mu_S$ and $\mu_T$. * corresponds to p $<$ 0.05.
• Figure 4: Characterization of friction for various natural capstans.(A1) - (A6) Images of capstan objects, with friction coefficient fit to the means of 5 trials at each wrap angle. Wrapped tether location indicated with a dashed red line. Standard deviation is reported for multi-object data sets. Plots below each image show the measured mean and standard deviation tension amplification at each wrap angle with a dashed curve representing the fit $\mu$. (B1) Tension amplification measured across 10 redwoods and 5 different wrap angles, corresponding to 50 data points at each wrap angle, described by the box plots. The red shaded region indicates the 95% confidence interval on the friction coefficient fit to all data points. The lowest black line and gray region above indicates the lowest measured friction coefficient for wrap angles above 360 degrees. (B2) Plot of fit friction coefficient for each redwood as a function of tree circumference, with a fit line that indicates a weak positive correlation.
• Figure 5: Dynamic slipping of capstan-tether system.(A1) A tether wrapped around a redwood tree is manually pulled until slip and continued to be pulled for approximately 10 seconds. $A_F$ over time is plotted. (A2) Experimental setup for redwood tree snagging, including a weighted sled ($T_0$), handheld force gauge ($T$), and a 360 degree wrap of the tree. (B1) A tether wrapped around a rock is pulled for 12 seconds after initial slip and $A_F$ over time is plotted. (B2) Experimental setup for rock snagging data. (C1) Experimental setup for recording slip-stick and mounding phenomena, in which holding force is measured directly without capstan amplification. (C2) A sled is dragged across a heterogeneous and homogeneous substrate, experiencing variation in force required to promote motion. (C3) A sled dragged through one meter of MARS90 regolith simulant shows a gradual increase and subsequent leveling of force required to slip over time.