Push, Press, Slide: Mode-Aware Planar Contact Manipulation via Reduced-Order Models

A single arm uses press-and-slide to transport an object, then leverages it as a tool to reposition a second object.

OVERVIEW

Abstract - Non-prehensile planar manipulation, including pushing and press-and-slide, is critical for diverse robotic tasks, but notoriously challenging due to hybrid contact mechanics, under-actuation, and asymmetric friction limits that traditionally necessitate computationally expensive iterative control. In this paper, we propose a mode-aware framework for planar manipulation with one or two robotic arms based on contact topology selection and reduced-order kinematic modeling. Our core insight is that complex wrench-twist limit surface mechanics can be abstracted into a discrete library of physically intuitive models. We systematically map various single-arm and bimanual contact topologies to simple non-holonomic formulations, e.g. unicycle for simplified press-and-slide motion. By anchoring trajectory generation to these reduced-order models, our framework computes the required object wrench and distributes feasible, friction-bounded contact forces via a direct algebraic allocator. We incorporate manipulator kinematics to ensure long-horizon feasibility and demonstrate our fast, optimization-free approach in simulation across diverse single-arm and bimanual manipulation tasks.

Top press-and-slide motion admits a planar force-invariant, body-fixed tracking point. This geometric point remains kinematically valid for all applied planar forces within the 2D friction circle; and acts like a virtual axle, allowing motion planning as a unicycle, car, or forklift.

Mode 1: Single-Arm Rear Pushing (ROM: Dubins Bicycle)

Single-arm rear pushing can be kinematically modeled as a car. By planning in this reduced-order model, the object is effectively driven like a rear-wheel steering vehicle using a standard Stanley controller.

Mode 2: Single-Arm Top Press-and-Slide (ROM: Unicycle)

Top press-and-slide motion admits a force-invariant, body-fixed tracking point, allowing the object to be modeled and controlled strictly as a unicycle. Here, the object is controlled via Samson's method, successfully navigating paths by pushing and pulling.

Because this unique planning point permits the object to be abstracted as an omnidirectional unicycle, car, or forklift, we can seamlessly apply advanced trajectory methods like Guiding Vector Field (GVF) path following.

Mode 3: Dual-Arm Rear Pushing (ROM: Bicycle / Diff. Drive)

Dual-arm rear pushing can be modeled as either an equivalent bicycle (when both arms can generate bidirectional torques) or a differential drive. In the bicycle model, arms cooperatively apply aligned forces, whereas in the differential drive model, control is achieved purely through longitudinal force differentials.

Mode 4: Orthogonal Bimanual Pushing (ROM: Quasi-Holonomic)

In perpendicular bimanual pushing, no single invariant planning point exists. Instead, the system possesses distinct CW and CCW pseudo-unicycle points (two close and two far away from the center of mass), which define a continuous unicycle control region. This topology permits holonomic curve tracking without rotation, and if turning is needed, the closest unicycle points yield the tightest radius.

Mode 5: Dual-Arm Top Press-and-Slide

Dual-arm top press-and-slide enables dynamic control over the center of pressure, allowing for exceptionally tight pivot-and-move maneuvers. Furthermore, shifting the center of pressure toward the turning arm grants it greater force authority, ensuring forward velocity is maintained even during aggressive rotations.

EXPERIMENTS AND RESULTS

Single-Arm Planar Pushing

A 15x15x15 cm cubic object is controlled using the equivalent car model. To ensure feasibility over long-horizon motions, manipulator kinematics are directly integrated into the optimization problem. Introducing a lightweight arm tracking term yields faster convergence and significantly reduces both positional and rotational tracking errors.

Press-and-Slide

A 60x20x10 cm box is driven to its target pose using a simple controller applying constant longitudinal force and proportional lateral force to track a virtual target. Empirical data confirms the theoretical unicycle point remains stable, bounded between 0.15–0.25 m from the CoM, varying only slightly due to contact patch shifts.