This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as a kinematic boundary following problem, in which the object boundary acts as the arm's 'shadow curve'. This formulation leads to a set of reduced kinematic equations expressed in terms of relative geometric shape variables, with the arm curvature serving as the control input. An optimal control problem is formulated to determine feasible arm shapes that achieve optimal grasping configurations, and its solution is obtained using Pontryagin's Maximum Principle. Based on the resulting optimal grasp kinematics, a class of continuum grasp quality metrics is proposed using the algebraic properties of the associated continuum grasp map. Feedback control aspects in the dynamic setting are also discussed. The proposed methodology is illustrated through systematic numerical simulations.
Figures & tables
Fig. 1: (a) Schematic of a continuum arm grasping a planar object with smooth boundary. The boundary of the object γ is parameterized by its arclength so . The arm is described by the position of its centerline r(s)∈\mathdsR2 where s∈[0,L] is the arclength of the centerline. The proposed control is given by the contact vector ρ(s) and the contact angle α(s) defined in ( 4 ). (b) An illustration showing the arm: i. approaching the target when 0<α<π/2 ; ii. departing the target when π/2<α<π .
Fig. 2: Optimal grasping configurations obtained by solving the optimal control problem ( 9 ). The problem is solved for three different smooth boundary objects: (a) circle, (b) ellipse and (c) deformed circle. A rendering of the arm grasping each object is shown at the top of each column. Below this, ρ(s)/ρd (solid blue line) and α(s) (solid orange line) are plotted against the normalized arc length s/L , with their expected convergence values indicated by blue and orange dashed lines, respectively. The arm curvature κ(s) (solid blue line) and object curvature κo(s) (dashed black line) are shown in the bottom plots.
Fig. 3: Grasp quality maps for the metrics Q1 , Q2 and Q3 for the circular, elliptical, and deformed circular objects. The quality values are normalized by the maximum quality for each object, where darker regions denote higher quality. The purple point indicates the optimal starting location, and the corresponding arm configuration is shown as a purple dashed curve.
Fig. 4: Dynamic simulation results for a soft arm grasping a fixed circular object. The top section shows six time instances of the arm in transparent purple. The bottom section shows a series of time snapshots of ρ/ρd and α in blue. The black dashed lines represent the theoretical static solutions, corresponding to the curvature ( 20 ). Black arrows illustrate the time progression of ρ/ρd and α .
Continuum manipulators provide dexterous motion in confined spaces, but structural compliance, hysteresis, and load-dependent deformation leave residual position and orientation errors that can undermine reliable contact with rigid grippers. To address this limitation, this paper presents a lightweight support-enhanced granular-jamming gripper tailored to a continuum manipulator. The gripper maintains compliance before jamming while establishing a direct load path to the continuum manipulator tip after jamming. To improve its grasping performance, we systematically designed membrane materials, particles, filling ratios, and the internal support structure, and further identify geometry-dependent grasp boundaries with respect to contact offset and object shape. Building on these results, we construct a physical manipulation system integrating the continuum manipulator, granular-jamming gripper, visual feedback, tendon actuation, and pneumatic control. We then train a reinforcement-learning-based reaching controller in a randomized simulation and deploy it on the physical system, demonstrating how positioning control and contact level mechanical adaptation can complement each other in a modular grasp-and-release task. By introducing an adaptive structure that relaxes the need for highly accurate modeling and positioning control, this work explores a design paradigm that integrates physical and embodied intelligence.
Mainstream plan-then-track approaches to multifingered grasp execution entail selecting a grasp, planning a collision-free trajectory, and tracking the resulting trajectory via a feedback controller. Pose-estimation error during execution or scene motion can invalidate this open-loop commitment and trigger replanning. We thus present Grasp Distance Fields (GDFs), smooth softmin distances to finite sets of arm-hand grasp configurations. Using their negative gradients as feedback, we jointly select and execute grasps without planning a trajectory. A CBF-CLF quadratic program (QP) enforces self-collision, workspace, object, and obstacle-clearance constraints, while its CLF slack quantifies obstruction of task progress. We bound the softmin approximation error by logN/ρ and prove forward invariance of the filtered safe set. To handle changes in contact topology, we combine a hysteretic contact-mode transition with a wrench-quality CBF that limits degradation of the realized force-closure margin relative to hold onset. Using our method, a fixed-base manipulator and a Unitree G1 equipped with the same underactuated hand grasp and lift 46 of 50 test objects amid clutter and moving obstacles. The realized grasps also retain a median 94% of their synthesized quality margin, and each QP solve requires 0.09 ms within a 20 ms control interval. Project page: www.clintonenwerem.com/gdf.
Clinton Enwerem, John S. Baras, Calin Belta
Department of Electrical and Computer Engineering and the Institute for Systems Research (ISR), University of Maryland, College Park, MD, USA
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