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Drake
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Drake
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There are many ways to model contact between rigid bodies. Drake uses an approach we call “compliant” contact. In compliant contact, nominally rigid bodies are allowed to penetrate slightly, as if the rigid body had a slightly deformable layer, but whose compression has no appreciable effect on the body’s mass properties. The contact force between two deformed bodies is distributed over a contact patch with an uneven pressure distribution over that patch. It is common in robotics to model that as a single point contact or a set of point contacts. Hydroelastic contact instead attempts to approximate the patch and pressure distribution to provide much richer and more realistic contact behavior. For a high-level overview, see this blog post.
Drake implements two models for resolving contact to forces: point contact and hydroelastic contact. See Appendix A: Compliant Contact Models for a fuller discussion of the theory and practice of contact models. For notes on implementation status, see Appendix B: Current state of implementation. Also see Appendix C: Examples and Tutorials.
It is relatively simple to enable a simulation to use hydroelastic contact. However, using it effectively requires some experience and consideration. This section details the mechanisms and choices involved in enabling hydroelastic contact and the next section helps guide you through some common tips, tricks, and traps.
Using hydroelastic contact requires two things:
Collision geometries for hydroelastic contact can be either "compliant-hydroelastic" with tetrahedral meshes describing an internal pressure field or "rigid-hydroelastic" with triangle surface meshes that are regarded as infinitely stiff. The figure below shows examples of a compliant hydroelastic box and a rigid hydroelastic box.
The figure below shows a contact surface between a compliant-hydroelastic cylinder and a compliant-hydroelastic sphere. The contact surface is internal to both solids and is defined as the surface where the two pressure fields are equal.
Pictured below, a rigid-hydroelastic cylindrical spatula handle is grasped by two hydroelastic-compliant ellipsoidal bubble grippers. The contact surface between the spatula handle's rigid-hydroelastic geometry and either gripper is on the surface of the rigid-hydroelastic geometry.
Because MultibodyPlant is responsible for computing the dynamics of the system (and the contact forces are part of that), the ability to enable/disable the hydroelastic contact model is part of MultibodyPlant’s API: drake::multibody::MultibodyPlant::set_contact_model().
There are three different options:
The default model is kHydroelasticWithFallback.
kPoint is the implementation of the point contact model (see Appendix A: Compliant Contact Models).
Models kHydroelastic and kHydroelasticWithFallback will both enable the hydroelastic contact. For forces to be created from hydroelastic contact, geometries need to have hydroelastic representations (see Creating hydroelastic representations of collision geometries).
kHydroelastic is a strict contact model that will attempt to create a hydroelastic contact surface whenever a geometry with a hydroelastic representation appears to be in contact (based on broad-phase bounding volume culling). With this contact model, the simulator will throw an exception if:
Collisions between two geometries where neither has a hydroelastic representation are simply ignored.
kHydroelasticWithFallback provides “fallback” behavior for when kHydroelastic would throw. When those scenarios are detected, it uses the point contact model between the colliding geometries so that the contact can be accounted for and produce contact forces. As the implementation evolves, more and more contact will be captured with hydroelastic contact and the circumstances in which the point-contact fallback is applied will decrease.
By default no geometry in drake::geometry::SceneGraph has a hydroelastic representation. So, enabling hydroelastic contact in MultibodyPlant, but forgetting to configure the geometries will lead to either simulation crashes or point contact-based forces.
In order for a mesh to be given a hydroelastic representation, it must be assigned certain properties. The exact properties it needs depends on the Shape type and whether it is rigid or compliant. Some properties can be defined, but if they are absent they’ll be provided by MultibodyPlant. First we’ll discuss each of the properties and then discuss how they can be specified.
SceneGraph.MultibodyPlant provides a default value of zero.Properties can be assigned to geometries inside a URDF or SDFormat file using some custom Drake XML tags. Alternatively, the properties can be assigned programmatically.
Drake has introduced a number of custom tags to provide a uniform language to specify hydroelastic properties in both URDF and SDFormat. The tag names are the same but the values are expressed differently (to align with the practices common to URDF and SDFormat). For example, consider a custom tag <drake:foo> that takes a single integer value. In an SDFormat file it would look like:
<drake:foo>17</drake:foo>
But in a URDF file it would look like this:
<drake:foo value=”17”/>
Both URDF and SDFormat files define a <collision> tag. This tag contains the tag for specifying the geometry type and associated properties. The hydroelastic properties can be specified as a child of the <collision> tag. Consider the following SDFormat example:
…
<collision name="body1_collision">
<geometry>
...
</geometry>
<drake:proximity_properties>
<drake:compliant_hydroelastic/>
<drake:mesh_resolution_hint>0.1</drake:mesh_resolution_hint>
<drake:hydroelastic_modulus>5e7</drake:hydroelastic_modulus>
<drake:hunt_crossley_dissipation>1.25</drake:hunt_crossley_dissipation>
</drake:proximity_properties>
</collision>
…
and the following equivalent URDF example:
…
<collision name="body1_collision">
<geometry>
...
</geometry>
<drake:proximity_properties>
<drake:compliant_hydroelastic/>
<drake:mesh_resolution_hint value="0.1"/>
<drake:hydroelastic_modulus value="5e7/>
<drake:hunt_crossley_dissipation value="1.25/>
</drake:proximity_properties>
</collision>
…
For a body, we’ve defined a collision geometry called “body1_collision”. Inside the <collision> tag (as a sibling to the <geometry> tag), we’ve introduced the Drake-specific <drake:proximity_properties> tag. In it we’ve defined the geometry to be compliant for hydroelastic contact and specified its resolution hint, its hydroelastic modulus, and its dissipation.
Let’s look at the specific tags:
Hydroelastic properties can be set to objects programmatically via the following APIs (see their documentation for further details):
Some extra notes:
AddContactMaterial() isn’t hydroelastic contact specific, but does provide a mechanism for setting the friction coefficients that hydroelastic and point contact models both use.
AddRigidHydroelasticProperties() is overloaded. One version accepts a value for resolution hint, one does not. When in doubt which to use, it is harmless to provide a resolution hint value that would be ignored for some geometries, but failing to provide one where necessary will cause the simulation to throw an exception. Note the special case for declaring a compliant half space – it takes the required slab thickness parameter in addition to the hydroelastic modulus value.
Start Meldis by:
$ bazel run //tools:meldis -- --open-window &
Run a simulation with hydroelastic contact model; for example,
$ bazel run //examples/hydroelastic/ball_plate:ball_plate_run_dynamics -- \ --mbp_dt=0.001 --x0=0.10 --z0=0.15 --vz=-7.0 \ --simulation_time=0.015 --simulator_publish_every_time_step
At the time of this writing, the Meldis view of this example looks like this:
In the above picture, we see two red force vectors acting at the centroids of the two contact surfaces and also the two blue moment vectors. One contact surface represents the ball pushing the dinner plate down. The other contact surface represents the rectangular floor pushing the dinner plate up. (Gravity forces are not shown, nor is the contact between the ball and the floor.) Notice that only approximately half of the bottom of the plate makes contact with the floor.
The Scene panel can toggle on/off many different aspects of the visualization using checkboxes, including: which contacts are shown, whether to view the illustration (visual) geometry and/or collision (proximity) geometry and/or the bodies' inertia, as well as sliders for controlling transparency to better view overlapping shapes.
When viewing collisions, note that red arrows indicate a hydroelastic contact, with an associated contact patch. Green arrows indicate point contact, which does not have any contact patch.
Here are various ways that hydroelastic contact may surprise you.
This is a random collection of things we can do to maximize the benefits of the hydroelastic contact model. Some of these tricks accommodate current implementation limitations, and some are to work within the theoretical framework.
Before we get into hydroelastic contact, it’s worth describing the compliant point contact model as a reference model. The point contact model defines the contact force by determining the minimum translational displacement (MTD). The minimum translational displacement is the smallest relative displacement between two volumes that will take them from intersecting to just touching. This quantity need not be unique (if two spheres have coincident centers, any direction will serve). Once we have this displacement, we get three quantities that we use to define the contact force:
This model is simple to implement and cheap to compute, but has some drawbacks.
Figure 1: Two intersections with significantly different intersecting volumes characterized with the same measure: d.
Figure 2: Modeling contact forces with point contact (considering the blue half space as rigid). (a) the actual intersection of the simulated bodies. (b) the conceptual deformation of the orange body creating a large area of contact. (c) how point contact sees the deformation: contact at a single point.
Hydroelastic contact was created to address some of the short-comings in point contact. In fact, one might argue that many of the strategies used to mitigate the shortcomings of point contact (such as using lots of points) push it closer and closer to hydroelastic contact.
Hydroelastic Contact is another compliant contact formulation. It was originally introduced by [Elandt 2019]. Modifications and further development of the model can be found in [Masterjohn 2022]. In Drake, we refer to this model as the “hydroelastic” model. It differs from point contact in how it characterizes the contact. Rather than a single point, it imagines an entire contact surface. This surface is an approximation of the contact surface as visualized in Figure 2(b).
When two objects come into contact, forces are produced due to deformation ("strain") of the objects at the contact interface. At first touch, there are no forces but as the objects are pressed further they deform to produce a region over which contact pressure is non-zero, causing equal-and-opposite forces to act on the objects. Calculating the actual deformations is expensive. Hydroelastic contact is based on the idea that for relatively small deformations we can approximate the resulting contact interface and pressure distribution without having to compute the actual deformations. We do that by precalculating a "pressure field" on the interior of compliant objects (see Figure 3). The pressure field approximates the pressure that would result from deforming the surface to some point within the field. A point on the surface (that is, no deformation) experiences zero pressure, but as it is pressed inward, it experiences an increase in pressure (up to a maximum pressure on the interior of the body). When two bodies are colliding, we look for a surface in the intersecting volume where the pressure on the surface is the same in each object; it’s an equilibrium surface (see Figure 4). There is pressure defined across the entire contact surface. It is integrated to define the resultant contact force and moment.
Figure 3: Three shapes and possible pressure fields in the interior of the object. Pressure is zero at the outer boundary, and maximum on the interior.
Figure 4: The equilibrium contact surface (pale green) between two bodies where the left-hand, yellow body has (a) less compliance, (b) equal compliance, and (c) greater compliance.
This equilibrium surface has important properties:
The theory operates on arbitrary geometries and pressure fields. In practice, we operate on discrete representations of both the geometry and the field.
Compliant objects are represented by tetrahedral meshes. The Drake data type is VolumeMesh. The pressure fields on those meshes are piecewise linear.
The resulting contact surface is likewise a discrete mesh. This mesh may be built of nothing but triangles or polygons. The choice of representation has various implications on the computation of contact forces (see below). The pressure on the contact surface is likewise a piecewise linear function.
We model perfectly rigid objects (objects with no compliance at all) as triangle surface meshes. They have no pressure field associated with them because any penetration from the surface instantaneously produces infinite pressure. When colliding a rigid object against a compliant object, the contact surface always follows the surface of the rigid object. Think of it as the compliant object doing 100% of the deformation, so it conforms to the shape of the rigid object.
Important points to note:
This section will be updated as the scope and feature set of hydroelastic contact is advanced. The main crux of this section is to clearly indicate what can and cannot be done with hydroelastic contact.
<drake:declare_convex/> tag under the <mesh> tag in either an SDFormat or URDF file.hunt_crossley_dissipation, for both point and hydroelastic contact. The SAP approximation parameter relaxation_time is ignored by these approximations.relaxation_time, for both point and hydroelastic contact. The Hunt-Crossley dissipation parameter is ignored by this approximation.hunt_crossley_dissipation (TAMSI, Similar and Lagged discrete approximations as well as continuous plant model) and relaxation_time (SAP approximation specific parameter) on the model, but the parameter may be ignored depending on your plant configuration. See the documentation for that in the MultibodyPlant documentation.Tutorial Hydroelastic Contact Basics with Jupyter Python notebook shows how to simulate hydroelastic contact for a compliant block dropped on a rigid rectangular plate. The below-left picture shows one frame of the block's contact with the contact force as a red arrow and the contact torque as a blue arrow. The below-right picture zooms into the hydroelastic contact surface showing pressure distribution.
