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<li><a class="el" href="#mbp_introspection">Introspection</a>: Perform introspection to find out what's in the MultibodyPlant.</li>
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<p><a class="anchor" id="model_instances"></a></p><h3>Model Instances</h3>
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<p>A MultiBodyPlant may contain multiple model instances. Each model instance corresponds to a set of bodies and their connections (joints). Model instances provide methods to get or set the state of the set of bodies (e.g., through <a class="el" href="#a61c4037d7f25d2e511f86e9102772290" title="Returns a const vector reference [q; v] to the generalized positions q and generalized velocities v i...">GetPositionsAndVelocities()</a> and <a class="el" href="#acdf6af4e5e5e71b55ea7ea3034ac5e90" title="Sets generalized positions q and generalized velocities v in a given Context from a given vector [q; ...">SetPositionsAndVelocities()</a>), connecting controllers (through <a class="el" href="#a3c6b13fba0889c4bb9a88610254a387b" title="Returns a constant reference to the output port for the multibody state x = [q, v] of the model.">get_state_output_port()</a> and <a class="el" href="#a69ef9262ffab02b34bdf20449aab7551" title="Returns a constant reference to the input port for external actuation for all actuated dofs.">get_actuation_input_port()</a>), and organizing duplicate models (read through a parser). In fact, many MultibodyPlant methods are overloaded to allow operating on the entire plant or just the subset corresponding to the model instance; for example, one <a class="el" href="#a15aab0eeb92b8e9f0a9bfcab8abaca69" title="Returns a const vector reference to the vector of generalized positions q in a given Context.">GetPositions()</a> method obtains the generalized positions for the entire plant while another <a class="el" href="#a15aab0eeb92b8e9f0a9bfcab8abaca69" title="Returns a const vector reference to the vector of generalized positions q in a given Context.">GetPositions()</a> method obtains the generalized positions for model instance.</p>
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<p>A <a class="el" href="classdrake_1_1multibody_1_1_multibody_plant.html" title="MultibodyPlant is a Drake system framework representation (see systems::System) for the model of a ph...">MultibodyPlant</a> may contain multiple model instances. Each model instance corresponds to a set of bodies and their connections (joints). Model instances provide methods to get or set the state of the set of bodies (e.g., through <a class="el" href="#a61c4037d7f25d2e511f86e9102772290" title="Returns a const vector reference [q; v] to the generalized positions q and generalized velocities v i...">GetPositionsAndVelocities()</a> and <a class="el" href="#acdf6af4e5e5e71b55ea7ea3034ac5e90" title="Sets generalized positions q and generalized velocities v in a given Context from a given vector [q; ...">SetPositionsAndVelocities()</a>), connecting controllers (through <a class="el" href="#a3c6b13fba0889c4bb9a88610254a387b" title="Returns a constant reference to the output port for the multibody state x = [q, v] of the model.">get_state_output_port()</a> and <a class="el" href="#a69ef9262ffab02b34bdf20449aab7551" title="Returns a constant reference to the input port for external actuation for all actuated dofs.">get_actuation_input_port()</a>), and organizing duplicate models (read through a parser). In fact, many MultibodyPlant methods are overloaded to allow operating on the entire plant or just the subset corresponding to the model instance; for example, one <a class="el" href="#a15aab0eeb92b8e9f0a9bfcab8abaca69" title="Returns a const vector reference to the vector of generalized positions q in a given Context.">GetPositions()</a> method obtains the generalized positions for the entire plant while another <a class="el" href="#a15aab0eeb92b8e9f0a9bfcab8abaca69" title="Returns a const vector reference to the vector of generalized positions q in a given Context.">GetPositions()</a> method obtains the generalized positions for model instance.</p>
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<p>Model instances are frequently defined through SDFormat files (using the <span class="tt">model</span> tag) and are automatically created when SDFormat files are parsed (by <a class="el" href="classdrake_1_1multibody_1_1_parser.html" title="Parses model description input into a MultibodyPlant and (optionally) a SceneGraph.">Parser</a>). There are two special <a class="el" href="namespacedrake_1_1multibody.html#af65439a17091283a89eb12f1955c6db0" title="Type used to identify model instances by index within a multibody plant.">multibody::ModelInstanceIndex</a> values. The world body is always <a class="el" href="namespacedrake_1_1multibody.html#af65439a17091283a89eb12f1955c6db0" title="Type used to identify model instances by index within a multibody plant.">multibody::ModelInstanceIndex</a> 0. <a class="el" href="namespacedrake_1_1multibody.html#af65439a17091283a89eb12f1955c6db0" title="Type used to identify model instances by index within a multibody plant.">multibody::ModelInstanceIndex</a> 1 is reserved for all elements with no explicit model instance and is generally only relevant for elements created programmatically (and only when a model instance is not explicitly specified). Note that <a class="el" href="classdrake_1_1multibody_1_1_parser.html" title="Parses model description input into a MultibodyPlant and (optionally) a SceneGraph.">Parser</a> creates model instances (resulting in a <a class="el" href="namespacedrake_1_1multibody.html#af65439a17091283a89eb12f1955c6db0" title="Type used to identify model instances by index within a multibody plant.">multibody::ModelInstanceIndex</a> ≥ 2) as needed.</p>
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<p>See <a class="el" href="#ac89140adb93cb9e507f71c30eb783198" title="Returns the number of model instances in the model.">num_model_instances()</a>, <a class="el" href="#aba2887f0ca1fbbdfb49cf6b0ee21e553" title="Returns the size of the generalized position vector q for this model.">num_positions()</a>, <a class="el" href="#ae0163ac0976659d811e3337647ff0313" title="Returns the size of the generalized velocity vector v for this model.">num_velocities()</a>, <a class="el" href="#ae3fc8de8de8eaf2d37a24c79d6be8e97" title="Returns the total number of actuated degrees of freedom.">num_actuated_dofs()</a>, <a class="el" href="#a4edf1daa65069a26255c903b02bce4c6" title="Creates a new model instance.">AddModelInstance()</a> <a class="el" href="#a61c4037d7f25d2e511f86e9102772290" title="Returns a const vector reference [q; v] to the generalized positions q and generalized velocities v i...">GetPositionsAndVelocities()</a>, <a class="el" href="#a15aab0eeb92b8e9f0a9bfcab8abaca69" title="Returns a const vector reference to the vector of generalized positions q in a given Context.">GetPositions()</a>, <a class="el" href="#a83faa6d43006794cd8f7ee6f851e1d09" title="Returns a const vector reference to the generalized velocities v in a given Context.">GetVelocities()</a>, <a class="el" href="#acdf6af4e5e5e71b55ea7ea3034ac5e90" title="Sets generalized positions q and generalized velocities v in a given Context from a given vector [q; ...">SetPositionsAndVelocities()</a>, <a class="el" href="#a40ecddd72c91e66ee38fe023bc58b3a0" title="Sets the generalized positions q in a given Context from a given vector.">SetPositions()</a>, <a class="el" href="#aa6864e2bce8855ab702b8ea1bb748f00" title="Sets the generalized velocities v in a given Context from a given vector.">SetVelocities()</a>, <a class="el" href="#a5d2ae02e64d4433eb7c5bbebd2a9dd0d" title="Returns a vector of generalized positions for model_instance from a vector q_array of generalized pos...">GetPositionsFromArray()</a>, <a class="el" href="#a52b25b565255d213a7f483b12f18ab68" title="Returns a vector of generalized velocities for model_instance from a vector v of generalized velociti...">GetVelocitiesFromArray()</a>, <a class="el" href="#ab264035a2e8c56b57bd80afb0b6ffb48" title="Sets the vector of generalized positions for model_instance in q using q_instance,...">SetPositionsInArray()</a>, <a class="el" href="#a89105b866dae232e6a9236d50f1fb08c" title="Sets the vector of generalized velocities for model_instance in v using v_instance,...">SetVelocitiesInArray()</a>, <a class="el" href="#a695e24adcadab868d6dd5a57f51953fd" title="Given actuation values u_instance for the actuators in model_instance, this function updates the actu...">SetActuationInArray()</a>, <a class="el" href="#ae12f32b40b7a41c3aa933ed74b2417fb">HasModelInstanceNamed()</a>, <a class="el" href="#a6967a3b13b5d006821d7590945a0c168" title="Returns the name of a model_instance.">GetModelInstanceName()</a>, <a class="el" href="#a3c6b13fba0889c4bb9a88610254a387b" title="Returns a constant reference to the output port for the multibody state x = [q, v] of the model.">get_state_output_port()</a>, <a class="el" href="#a69ef9262ffab02b34bdf20449aab7551" title="Returns a constant reference to the input port for external actuation for all actuated dofs.">get_actuation_input_port()</a>.</p>
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<p><a class="anchor" id="mbp_equations_of_motion"></a></p><h3>System dynamics</h3>

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<dd><a class="anchor" id="_deprecated000026"></a>Use fmt functions instead (e.g., fmt::format(), fmt::to_string(), fmt::print()). Refer to GitHub issue #17742 for more information. <br />
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<dt>Member <a class="el" href="namespacedrake.html#a24d3bbc3fbb363dfb7cdc7ff5c71c850">drake::operator&lt;&lt;</a> (std::ostream &amp;os, const typename <a class="el" href="classdrake_1_1_polynomial_1_1_monomial.html" title="An additive atom of a Polynomial: The product of any number of Terms and a coefficient.">Polynomial&lt; T &gt;::Monomial</a> &amp;m)</dt>
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<dt>Member <a class="el" href="namespacedrake.html#a6349afb82c0796366e318e99f25c3e5f">drake::operator&lt;&lt;</a> (std::ostream &amp;os, const <a class="el" href="classdrake_1_1_polynomial.html" title="A scalar multi-variate polynomial, modeled after the msspoly in spotless.">Polynomial&lt; T &gt;</a> &amp;poly)</dt>
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<dt>Member <a class="el" href="namespacedrake.html#a8db300eaec345b10d2e808b900239b8e">drake::operator&lt;&lt;</a> (std::ostream &amp;os, const Eigen::Matrix&lt; <a class="el" href="classdrake_1_1_polynomial.html" title="A scalar multi-variate polynomial, modeled after the msspoly in spotless.">Polynomial&lt; T &gt;</a>, Rows, Cols &gt; &amp;poly_mat)</dt>
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<dd><a class="anchor" id="_deprecated000007"></a>Wrap Eigen objects M with fmt_eigen() to format Eigen data into fmt strings e.g., fmt::to_string(fmt_eigen(M)), fmt::format(\M = {}\, fmt_eigen(M)). You'll need to #include \drake/common/fmt_eigen.h\ to access that function. Refer to GitHub issue #17742 for more information. <br />
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<dd><a class="anchor" id="_deprecated000008"></a>Wrap Eigen objects M with fmt_eigen() to format Eigen data into fmt strings e.g., fmt::to_string(fmt_eigen(M)), fmt::format(\M = {}\, fmt_eigen(M)). You'll need to #include \drake/common/fmt_eigen.h\ to access that function. Refer to GitHub issue #17742 for more information. <br />
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<dt>Member <a class="el" href="namespacedrake_1_1perception_1_1pc__flags.html#ad70a51f0c16bb5f6b6fc3e4a51b0529a">drake::perception::pc_flags::operator&lt;&lt;</a> (std::ostream &amp;os, const <a class="el" href="classdrake_1_1perception_1_1pc__flags_1_1_fields.html" title="Allows combination of BaseField and DescriptorType for a PointCloud.">Fields</a> &amp;rhs)</dt>
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<dt>Member <a class="el" href="namespacedrake_1_1symbolic.html#af69250c699b4b8cbcbb54d322570d175">drake::symbolic::operator&lt;&lt;</a> (std::ostream &amp;os, <a class="el" href="classdrake_1_1symbolic_1_1_variable.html#a5f787df9cdf370248382504196841479" title="Supported types of symbolic variables.">Variable::Type</a> type)</dt>
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<dt>Member <a class="el" href="namespacedrake_1_1symbolic.html#ad33e2289eb5f8ba9d8a286bd6e954001">drake::symbolic::operator&lt;&lt;</a> (std::ostream &amp;out, const <a class="el" href="classdrake_1_1symbolic_1_1_chebyshev_basis_element.html" title="ChebyshevBasisElement represents an element of Chebyshev polynomial basis, written as the product of ...">ChebyshevBasisElement</a> &amp;m)</dt>
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<dt>Member <a class="el" href="namespacedrake_1_1symbolic.html#ada77c9969b0422090c05636a895c0e8e">drake::symbolic::operator&lt;&lt;</a> (std::ostream &amp;out, const <a class="el" href="classdrake_1_1symbolic_1_1_monomial.html" title="Represents a monomial, a product of powers of variables with non-negative integer exponents.">Monomial</a> &amp;m)</dt>
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<dt>Member <a class="el" href="namespacedrake_1_1symbolic.html#ad33e2289eb5f8ba9d8a286bd6e954001">drake::symbolic::operator&lt;&lt;</a> (std::ostream &amp;out, const <a class="el" href="classdrake_1_1symbolic_1_1_chebyshev_basis_element.html" title="ChebyshevBasisElement represents an element of Chebyshev polynomial basis, written as the product of ...">ChebyshevBasisElement</a> &amp;m)</dt>
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<dd><a class="anchor" id="_deprecated000005"></a>Use fmt functions instead (e.g., fmt::format(), fmt::to_string(), fmt::print()). Refer to GitHub issue #17742 for more information. <br />
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<dt>Member <a class="el" href="namespacedrake_1_1symbolic.html#aebaa1c50ddcd18c8de9ba5ebc01f3989">drake::symbolic::operator&lt;&lt;</a> (std::ostream &amp;out, const <a class="el" href="classdrake_1_1symbolic_1_1_monomial_basis_element.html" title="MonomialBasisElement represents a monomial, a product of powers of variables with non-negative intege...">MonomialBasisElement</a> &amp;m)</dt>
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