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 arctanμi ( 4 ); the green cube is the tracked body marker whose displacement measures furniture motion.
Fig. 2 : Block diagram of the implemented loop. Master (red): PC2/Unity drives the Phantom and renders fm ( 21 ). Controller (blue): PC1/ROS maps the master to θd ( 16 ), solves the handle pose ( 14 ) and projects onto F^(η) ( 10 ). Slave (blue): UR10 + RG2 executes W∗ ; the wrist F/T returns fe . Symbols: pm measured master hand pose; θd commanded door-angle trajectory; Thd desired handle pose; Wd and W∗ the wrench before and after ΠF^(η) , 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.
Fig. 3 : Friction-cone geometry and notation. (a) Side view: the pull Fh and free moment Mh at H , gravity at ccom ; the support carries N=mg−Fz at the centre of pressure p , which recedes towards the leading edge e (levers h , de ) ( 8 ). (b) Top view: support polygon S , circumradius ρ , lever r=ρ/2 ; dist(p,∂S) is the tipping margin. (c) Admissible set in force units: the ellipse ( 4 ) cut by tipping, shrunk by η and offset by Δ into F^(η) ( 9 ), containing W∗=ΠF^(η)(Wd) ( 10 ). (d) Arbitration in one plane: the grey ring between A and F^(η) is the margin given up, its width the unavoidable term of ( 24 ); the dashed curve is where the guard ( 11 ) pushes back and α ( 13 ) how far along Wd−W∗ the command is honoured.
Fig. 4 : Working-condition state machine. Each box gives state, phase and (italic) control law; below it, the exit predicate ( θ˙ door rate, ϵθ breakaway threshold, θd 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
κp
1.6
κf
0.35
r=ρ/2
0.18m (C1)
Δ
2.0N
kθ
12.5deg/cm
θmax
95∘
KD
0.15Nms/rad
λ
4s−1
kg
3.0N
η
0.7 (nominal)
δa,δo
1∘,2mm
ϵtr
0.5N
TABLE I : Controller parameters (nominal).
Fig. 5 : Measured wrist F/T in one admittance-mode trial: force Fx,y,z (left) and moment Tx,y,z (right) in the sensor frame versus sample frame.
Metric
P
NG
NP
POS
Disp. (mm)
0.9±0.4
6.8±2.3
4.1±1.9
9.4±3.1
Viol. >5 mm
0/25
5/25
3/25
8/25
Peak F (N)
20.8±2.0
27.4±3.1
25.1±2.8
30.6±4.9
Error (N)
0.41±0.13
0.28±0.09
0.33±0.11
0.62±0.21
tbw (s)
3.4±0.7
3.1±0.6
3.3±0.7
4.2±1.3
ttask (s)
14.6±3.1
16.2±3.6
15.4±3.4
19.1±6.0
TABLE II : Task metrics, mean ± s.d. over 5 operators × 5 trials, furniture C1 on wood.
Fig. 6 : Stability–transparency trade-off: maximum furniture displacement versus transmission error ∥ef∥ . Filled markers: measured conditions P, NG, NP, POS ( 25 trials each); dashed: analytic frontier of Prop. 2 at the identified μ^,m^ , open markers at η=0.9 (left) and 0.5 (right).
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/
Haegu Lee, Yitaek Kim, Christoffer Sloth
The Maersk Mc-Kinney Moller Institute, University of Southern Denmark, Denmark
Maintaining contact in non-prehensile manipulation requires more than nominal friction cone feasibility: a force barely inside the cone and one well inside it are both feasible, but they provide different margins against slip and contact loss. This paper uses signed friction distance to measure friction margin in force space and derives a task-adaptive margin from the force correction needed to balance pivot moment deviations in bimanual tilting. The resulting contact margins are embedded in a sequence of second-order cone programs (SOCPs), each giving a globally optimal contact force solution at a tilt angle. The optimizer balances the object about an environmental pivot while keeping robot and pivot contact forces away from the nominal friction boundary. Optimizer-level results show interpretable force redistribution and adaptation to object property changes. Real-world experiments demonstrate successful execution under object property variations and model mismatch, while fixed margin and no-margin comparisons illustrate the importance of adapting the margin to task demand. These results support signed friction distance margins as a force planning mechanism for maintaining contact in bimanual non-prehensile manipulation. Project page: https://keeping-contact.github.io/
Qian Ying Lee, Lin Yang, Domenico Campolo
School of Mechanical and Aerospace Engineering, Nanyang Technological University (NTU), Singapore. · R3 Institute (R3I) Singapore, Nanyang Technological University (NTU), Singapore
Multi-fingered hands offer great potential for compliant and robust grasping of unknown objects, yet their high-dimensional force control presents a significant challenge. This work addresses two key problems: (1) distributing forces across multiple contacts to counteract an object's weight, and (2) preventing rotational slip caused by gravitational torque when a grasp is distant from the object's center of mass. We address these challenges via tactile feedback and a Second-Order Cone Programming (SOCP)-based controller, without explicit torque modeling or slip detection. Our key insights are (1) rotational slip inevitably induces translational slip at some contact points for a multi-fingered grasp, and (2) the ratio of tangential to normal force at each contact is an effective early stability indicator. By actively constraining this ratio for each finger below the estimated friction coefficient, our controller maintains grasp stability against both translational and rotational slip. Real-world experiments on 12 diverse objects demonstrate the robustness and compliance of our approach.
Yubin Ke, Jiayi Chen, Hang Lv +2
Peking University · Galbot · Beijing Academy of Artificial Intelligence