Trading Transparency for Stability: Friction-Cone-Constrained Bilateral Teleoperation for Opening Doors of Unsecured Furniture

Cheng Zhou; Jing Li

cs.ROOct 31, 2026

Trading Transparency for Stability: Friction-Cone-Constrained Bilateral Teleoperation for Opening Doors of Unsecured Furniture

Authors: Cheng Zhou, Jing Li

Organizations: Tencent Robotics X, Shenzhen, China

Abstract

Opening the door of unsecured furniture loads the frictional contacts at its supports; too large a pull slides or tips the object. A friction-cone constraint on the commanded wrench removes this failure mode but costs haptic transparency. We quantify the trade-off: an admissible wrench set built from contact friction cones and support-polygon tipping margins is shrunk for robustness to bounded mass and friction errors, and any command in the shrunken set provably leaves the furniture static (Prop. 1). We call this map the robust friction cone projection (RFCP). RFCP and its haptic guard admit a bounded force transmission error (Prop. 2): transparency degrades only within a band near the constraint boundary, whose width is set by one scalar, the stability factor . A working condition controller handles the door: the operator commands a scalar swing amplitude, the slave orientation follows hinge kinematics, and the grasp wrench is regulated per phase. A pre task certificate decides whether a door can be opened without moving the furniture. Experiments on three cabinets and two supports with five operators (100 trials) measure the stability transparency trade-off and ablate the guard, RFCP and the position baseline. The mechanism is not door-specific: it applies to any body reacted by frictional contacts.

Figures & tables

Fig. 1 : Overview of the system. Left: the operator drives the Touch haptic device (master) while the UR10 $+$ RG2 (slave) opens the door of a cabinet resting unsecured on the table. Right: grasp close-up with the cone at the load–cabinet contact. Symbols: the red wedges mark the friction cones at the cabinet–support contacts, of half-angle $\arctan\mu_{i}$ ( 4 ); the green cube is the tracked body marker whose displacement measures furniture motion.

Panel of Figure 2 — Fig. 2 : Block diagram of the implemented loop. Master (red): PC2/Unity drives the Phantom and renders $\boldsymbol{f}_{m}$ ( 21 ). Controller (blue): PC1/ROS maps the master to $\theta_{d}$ ( 16 ), solves the handle pose ( 14 ) and projects onto $\hat{\mathcal{F}}(\eta)$ ( 10 ). Slave (blue): UR10 $+$ RG2 executes $\boldsymbol{W}^{*}$ ; the wrist F/T returns $\boldsymbol{f}_{e}$ . Symbols: $\boldsymbol{p}_{m}$ measured master hand pose; $\theta_{d}$ commanded door-angle trajectory; $\mathbf{T}_{h}^{d}$ desired handle pose; $\boldsymbol{W}_{d}$ and $\boldsymbol{W}^{*}$ the wrench before and after $\Pi_{\hat{\mathcal{F}}(\eta)}$ , the projection onto the estimated admissible set; the red feedback path carries the measured wrench back to the master; the dashed link is the slave acting on the cabinet.

Panel of Figure 3 — Fig. 3 : Friction-cone geometry and notation. (a) Side view: the pull $\boldsymbol{F}_{h}$ and free moment $\boldsymbol{M}_{h}$ at $\boldsymbol{H}$ , gravity at $\boldsymbol{c}_{\mathrm{com}}$ ; the support carries $N=\underline{m}g-F_{z}$ at the centre of pressure $\boldsymbol{p}$ , which recedes towards the leading edge $e$ (levers $h$ , $d_{e}$ ) ( 8 ). (b) Top view: support polygon $\mathcal{S}$ , circumradius $\rho$ , lever $r=\rho/2$ ; $\operatorname{dist}(\boldsymbol{p},\partial\mathcal{S})$ is the tipping margin. (c) Admissible set in force units: the ellipse ( 4 ) cut by tipping, shrunk by $\eta$ and offset by $\Delta$ into $\hat{\mathcal{F}}(\eta)$ ( 9 ), containing $\boldsymbol{W}^{*}=\Pi_{\hat{\mathcal{F}}(\eta)}(\boldsymbol{W}_{d})$ ( 10 ). (d) Arbitration in one plane: the grey ring between $\mathcal{A}$ and $\hat{\mathcal{F}}(\eta)$ is the margin given up, its width the unavoidable term of ( 24 ); the dashed curve is where the guard ( 11 ) pushes back and $\alpha$ ( 13 ) how far along $\boldsymbol{W}_{d}-\boldsymbol{W}^{*}$ the command is honoured.

Panel of Figure 4 — Fig. 4 : Working-condition state machine. Each box gives state, phase and (italic) control law; below it, the exit predicate ( $\dot{\theta}$ door rate, $\epsilon_{\theta}$ breakaway threshold, $\theta_{d}$ target angle). Red: C2 produces the latch transient the projection cannot anticipate; green: C3 the pull that would move the furniture.

Symbol	Value	Symbol	Value
$\kappa_{p}$	$1.6$	$\kappa_{f}$	$0.35$
$r=\rho/2$	$0.18\,\mathrm{m}$ (C1)	$\Delta$	$2.0\,\mathrm{N}$
$k_{\theta}$	$12.5\,\mathrm{deg/cm}$	$\theta_{\max}$	$95^{\circ}$
$K_{D}$	$0.15\,\mathrm{Nm\,s/rad}$	$\lambda$	$4\,\mathrm{s^{-1}}$
$k_{g}$	$3.0\,\mathrm{N}$	$\eta$	$0.7$ (nominal)
$\delta_{a},\delta_{o}$	$1^{\circ},\,2\,\mathrm{mm}$	$\epsilon_{\mathrm{tr}}$	$0.5\,\mathrm{N}$

TABLE I : Controller parameters (nominal).

Panel of Figure 6 — Fig. 5 : Measured wrist F/T in one admittance-mode trial: force $F_{x,y,z}$ (left) and moment $T_{x,y,z}$ (right) in the sensor frame versus sample frame.

Metric	P	NG	NP	POS
Disp. (mm)	$0.9\pm 0.4$	$6.8\pm 2.3$	$4.1\pm 1.9$	$9.4\pm 3.1$
Viol. $>5$ mm	0/25	5/25	3/25	8/25
Peak $F$ (N)	$20.8\pm 2.0$	$27.4\pm 3.1$	$25.1\pm 2.8$	$30.6\pm 4.9$
Error (N)	$0.41\pm 0.13$	$0.28\pm 0.09$	$0.33\pm 0.11$	$0.62\pm 0.21$
$t_{\mathrm{bw}}$ (s)	$3.4\pm 0.7$	$3.1\pm 0.6$	$3.3\pm 0.7$	$4.2\pm 1.3$
$t_{\mathrm{task}}$ (s)	$14.6\pm 3.1$	$16.2\pm 3.6$	$15.4\pm 3.4$	$19.1\pm 6.0$

TABLE II : Task metrics, mean

\pm

s.d. over 5 operators

\times

5 trials, furniture C1 on wood.

Fig. 6 : Stability–transparency trade-off: maximum furniture displacement versus transmission error $\|\boldsymbol{e}_{f}\|$ . Filled markers: measured conditions P, NG, NP, POS ( $25$ trials each); dashed: analytic frontier of Prop. 2 at the identified $\hat{\mu},\hat{m}$ , open markers at $\eta=0.9$ (left) and $0.5$ (right).

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Safety-Critical Control for Smoothed Implicit Contact Dynamics

Haegu Lee, Yitaek Kim, Christoffer Sloth

The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Denmark

Dynamical Systems Contact-Rich Robotic Manipulation Safety-Critical Control Control Barrier Functions Safety Filtering

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Smoothed implicit contact dynamics enables gradient-based planning and control for contact-rich tasks without predefined mode sequences. However, safety-critical control remains challenging because implicit contact dynamics makes safety-filter design nontrivial. The smoothing parameter

κ

relaxes contact complementarity constraints, which makes the dynamics smooth but affects the contact force. This paper provides a safety-filtering framework for smoothed implicit contact dynamics. We first derive a discrete-time control barrier function (CBF) constraint using a first-order Taylor approximation of the implicitly defined contact force. We show that, although reducing

κ

can improve local force-approximation accuracy, the resulting closed-loop force-constraint violations can vary non-monotonically with

κ

. Motivated by this observation, we introduce boundary-focused rollouts that screen candidate

κ

values by comparing the predicted safety margin with the observed one-step under-prediction. We then robustly tighten the predicted CBF constraint with a fixed margin to account for residual force under-prediction. Simulations on four contact-rich systems show that the proposed method eliminates force violations observed under a standard CBF. Project website https://contact-cbf.github.io/

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