Contact mode

• Also called: contact state
• Category: Planning & manipulation › Manipulation
• Tags: contact, manipulation, hybrid-dynamics, friction, planning

A discrete label stating which contacts in a robot-object system are active and whether each is sticking or sliding; each label corresponds to a different set of smooth dynamics.

Definition

In a system with frictional contact, each potential contact can be in one of several states: separated, with no force; sticking, in contact with no relative tangential motion; or sliding, in contact and moving tangentially, with the friction force on the boundary of the friction cone and opposing the motion. A contact mode assigns one of these states to every contact in the system. Within a fixed mode the equations of motion are smooth, because the active constraints and the form of the friction forces are known. At the boundaries between modes the dynamics change abruptly. Contact dynamics are therefore hybrid: smooth modes separated by guard surfaces, such as a contact gap reaching zero or a sticking contact's tangential force reaching the friction limit.

The number of modes grows exponentially with the number of contacts. With n contacts and three states each there are up to 3ⁿ combinations, and more in three dimensions where sliding can occur in different directions, although many are infeasible for a given geometry. This combinatorial structure is the main obstacle in planning contact-rich manipulation and locomotion. Methods differ in how they deal with it: enumerating feasible modes and planning a sequence through them; encoding mode choices with integer variables in mixed-integer programs; contact-implicit trajectory optimization, which represents contact with complementarity constraints so the optimizer chooses modes implicitly; and smoothing, which replaces the nonsmooth contact dynamics with a smooth approximation so that gradient-based methods can see beyond the current mode, as in the global planning paper on our site.

For quasi-static and quasi-dynamic manipulation, where inertial effects are small compared with contact and friction forces, mode enumeration is often tractable for a few contacts and gives an interpretable plan, for example: push the object while the finger sticks, let the finger slide to a new position, then pivot the object about one corner. Mode schedules are also central in legged locomotion, where the gait defines which feet are in contact over time, although there the sequence is often fixed in advance by a gait schedule instead of being searched.

Why it matters

Choosing which contacts to make and break, and whether they stick or slide, is the core decision in manipulation and locomotion. Contact modes explain why these problems are hard for smooth optimizers and how modern planners work around that.

Key applications

• Planning nonprehensile manipulation such as pushing, pivoting and toppling
• In-hand manipulation with sliding and rolling contacts
• Contact-implicit trajectory optimization for legged robots
• Gait and contact sequence planning
• Estimating contact state from force and tactile sensing

In practice

A team plans for a robot to push a box across a table and then rotate it upright against a wall. They model the finger-box contact, the box-table contact as corner points and the box-wall contact. For the pushing phase they choose a mode with the finger sticking on the box and the box sliding on the table; for the pivot they choose the box sticking at its corner against the wall, sliding on the table, with the finger sliding on the box face. Within each mode they solve for finger motions that keep all forces inside their friction cones. During execution they watch force readings and the tracked box pose to detect unplanned mode changes, such as the finger slipping, and replan when one occurs.

Common misconceptions

• A contact mode only says which contacts are touching — it also says whether each sticks or slides, which changes the dynamics as much as making or breaking contact
• Planners must enumerate every contact mode — contact-implicit optimization and smoothing avoid explicit enumeration, at the cost of weaker guarantees and local minima
• Contact modes are a modeling artifact — they reflect real physical changes; a gripper that slips has changed mode, and a controller that ignores this can fail

Who should know this

• Manipulation planning researchers
• Legged locomotion control engineers
• Physics simulation developers
• Tactile and force sensing engineers

Related technologies

• Linear Complementarity Problems
• Contact-Implicit Trajectory Optimization
• Quasi-Static Contact Models
• Drake
• MuJoCo

Related terms

• Hybrid system
• Friction Cone
• Mixed-Integer Programming
• Wrench
• Dexterous Manipulation
• Extrinsic dexterity

Related projects

• LeRobot: HuggingFace ML library for real-world robotics in PyTorch
• Isaac Lab: NVIDIA robot learning framework: one task API across Newton, PhysX and Isaac Sim
• NVIDIA Isaac GR00T: NVIDIA open foundation model for humanoid robot reasoning and skills
• OpenVLA: 7B-parameter Vision-Language-Action model for robotic manipulation
• Drake: MIT robotics toolbox for model-based dynamics, optimization, and control system design
• OpenArm: 7DOF humanoid arm for physical AI research in contact-rich environments