通常情况下，外力是使用六轴力/扭矩传感器测量的，该传感器测量施加在末端执行器上的任何力，大多数市面上的力/扭矩传感器都是由应变计制成的。

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机器人动力学包含计算和显示欧拉拉格朗日动力学所需的所有函数，下面以一些例子来进行机器人动力学建模！

Matlab常用的程序如下：

其中，动力学函数具体如下：

function qddot = forwardDynamics(obj, varargin)
        %forwardDynamics Compute resultant joint acceleration given joint torques and states
        %   QDDOT = forwardDynamics(ROBOT) computes the resultant joint
        %   accelerations due to gravity when ROBOT is at its home
        %   configuration, with zero joint velocities and no external
        %   forces.
        %
        %   QDDOT = forwardDynamics(ROBOT, Q) computes the resultant
        %   joint accelerations due to gravity when ROBOT is at joint
        %   configuration Q, with zero joint velocities and no external
        %   forces.
        %
        %   QDDOT = forwardDynamics(ROBOT, Q, QDOT) computes the joint
        %   accelerations resulted from gravity and joint velocities
        %   QDOT when ROBOT is at Joint configuration Q. (Set Q = [] if
        %   the joint configuration is home configuration.)
        %
        %   QDDOT = forwardDynamics(ROBOT, Q, QDOT, TAU) computes the
        %   joint accelerations due to gravity, joint velocities QDOT
        %   and joint torques TAU when ROBOT is at joint configuration Q.
        %   (Set QDOT = [] to indicate zero joint velocities.)
        %
        %   QDDOT = forwardDynamics(ROBOT, Q, QDOT, TAU, FEXT) computes
        %   the joint accelerations due to gravity, joint velocities
        %   QDOT, torques applied to the joints TAU, and external forces
        %   applied to each body FEXT, when ROBOT is at configuration Q.
        %   (Set TAU = [] to indicate zero joint torques.)
        %
        %   If ROBOT's DataFormat property is set to 'column', the
        %   input variables must be formatted as
        %   - Joint configuration, Q - pNum-by-1 vector
        %   - Joint velocities, QDOT - vNum-by-1 vector
        %   - Joint torques, TAU - vNum-by-1 vector
        %   - External forces, FEXT - 6-by-NB matrix
        %
        %   where:
        %   - pNum is the position number of ROBOT
        %   - vNum is the velocity number of ROBOT (degrees of freedom)
        %   - NB is the number of bodies in ROBOT
        %   - Each column of FEXT represents a wrench
        %     -- top 3 elements: moment
        %     -- bottom 3 elements: linear force
        %
        %   If the DataFormat property of ROBOT is set to 'row', then
        %   all the vectors/matrices above need to be transposed.
        %
        %   The returned joint accelerations QDDOT is either a vNum-by-1
        %   or an 1-by-vNum vector, depending on the DataFormat property.
        %
        %   Examples:
        %       % Load example robot
        %       load exampleRobots.mat
        %
        %       % Set lbr robot dynamics input data format to 'row'
        %       lbr.DataFormat = 'row';
        %
        %       % Set the gravity
        %       lbr.Gravity = [0 0 -9.81];
        %
        %       % Get the home configuration for lbr
        %       q = lbr.homeConfiguration
        %
        %       % The end-effector (body 'tool0') experiences a wrench.
        %       % Use the 2 lines below to generate the corresponding
        %       % external force matrix, fext. Note that if the external
        %       % wrench is specified in the body 'tool0' frame, the
        %       % joint configuration, q, must be specified as the fourth
        %       % input argument for externalForce method.
        %       wrench = [0 0 0.5 0 0 0.3];
        %       fext = externalForce(lbr, 'tool0', wrench, q)
        %
        %       % Compute the resultant joint acceleration due to gravity
        %       % with the external force applied to the end-effector when
        %       % lbr is at its home configuration.
        %       qddot = forwardDynamics(lbr, q, [], [], fext);
        %
        %   See also inverseDynamics, externalForce

            narginchk(1,5);
            [q, qdot, tau, fext] = validateDynamicsFunctionInputs(obj.TreeInternal, false, varargin{:});
            qddot = robotics.manip.internal.RigidBodyTreeDynamics.forwardDynamicsCRB(obj.TreeInternal, q, qdot, tau, fext);
            qddot = resultPostProcess(obj.TreeInternal, qddot);
        end

我们可以通过上述的动力学函数进行正向动力学求解！！！

那么，逆向动力学的使用语法如下：

则，inverseDynamicsd  的具体函数如下：

function tau = inverseDynamics(obj, varargin)
        %inverseDynamics Compute required joint torques for desired motion.
        %   TAU = inverseDynamics(ROBOT) computes joint torques TAU
        %   required for ROBOT to statically hold its home
        %   configuration with no external forces applied.
        %
        %   TAU = inverseDynamics(ROBOT, Q) computes the required joint
        %   torques for ROBOT to statically hold the given
        %   configuration Q with no external forces applied.
        %
        %   TAU = inverseDynamics(ROBOT, Q, QDOT) computes the joint
        %   torques required for ROBOT given the joint configuration Q
        %   and joint velocities QDOT while assuming zero joint accelerations
        %   and no external forces. (Set Q = [] if the desired joint
        %   configuration is home configuration.)
        %
        %   TAU = inverseDynamics(ROBOT, Q, QDOT, QDDOT) computes the
        %   joint torques required for ROBOT given the joint
        %   configuration Q, joint velocities QDOT and joint accelerations
        %   QDDOT while assuming no external forces are applied. (Set
        %   QDOT = [] to indicate zero joint velocities.)
        %
        %   TAU = inverseDynamics(ROBOT, Q, QDOT, QDDOT, FEXT) computes
        %   the joint torques required for ROBOT given the joint
        %   configuration Q, joint velocities QDOT, joint accelerations
        %   QDDOT and the external forces FEXT. (Set QDDOT = [] to
        %   indicate zero joint accelerations.)
        %
        %   If ROBOT's DataFormat property is set to 'column', the
        %   input variables must be formatted as
        %   - Joint configuration, Q - pNum-by-1 vector
        %   - Joint velocities, QDOT - vNum-by-1 vector
        %   - Joint accelerations, QDDOT - vNum-by-1 vector
        %   - External forces, FEXT - 6-by-NB matrix
        %
        %   where:
        %   - pNum is the position number of ROBOT
        %   - vNum is the velocity number of ROBOT (degrees of freedom)
        %   - NB is the number of bodies in ROBOT
        %   - Each column of FEXT represents a wrench
        %     -- top 3 elements: moment
        %     -- bottom 3 elements: linear force
        %
        %   If the DataFormat property of ROBOT is set to 'row', then
        %   all the vectors/matrices above need to be transposed.
        %
        %   The returned joint torques TAU is either a vNum-by-1 or an
        %   1-by-vNum vector, depending on the DataFormat property.
        %
        %   Examples:
        %       % Load example robot
        %       load exampleRobots.mat
        %
        %       % Set lbr robot dynamics input data format to 'column'
        %       lbr.DataFormat = 'column';
        %
        %       % Generate a random configuration for lbr
        %       q = lbr.randomConfiguration
        %
        %       % Compute the required joint torques for lbr to
        %       % statically hold that configuration
        %       tau = inverseDynamics(lbr, q);
        %
        %   See also forwardDynamics, externalForce

            narginchk(1,5);
            [q, qdot, qddot, fext] = validateDynamicsFunctionInputs(obj.TreeInternal, true, varargin{:});
            tau = robotics.manip.internal.RigidBodyTreeDynamics.inverseDynamics(obj.TreeInternal, q, qdot, qddot, fext);
            tau = resultPostProcess(obj.TreeInternal, tau);
        end

通过利用正向动力学和逆向动力学就可以实现所需的动态计算！！！