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ROBOT CONTROL. T. Bajd and M. Mihelj. Robot control. Robot control deals with computation of the forces or torques which must be generated by the actuators in order to successfully accomplish the robot task. The robot task can be

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## ROBOT CONTROL

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**ROBOT CONTROL**T. Bajd and M. Mihelj**Robot control**• Robot control deals with computation of the forces or torques which must be generated by the actuators in order to successfully accomplish the robot task. • The robot task can be • execution of the motion in a free space, where position control is performed, or • in contact with the environment, where control of the contact force is required. • The choice of the control method depends on • the robot task, • the mechanical structure of the robot mechanism. • Robot control usually takes place in the world coordinate frame, which is defined by the user and is called also the coordinate frame of the robot task.**General control approach**End-effector pose Position Orientation RPY notation of the orientation**PD position control**• Control loop is closed separately for each particular degree of freedom • Less suitable for robotic systems characterized by nonlinear and time varying behavior • Position error computation • Reference positions • Measured robot joint positions • Position error**PD position control**• Control law; computation of control variable (torque, velocity) • Actuation of robot motors is proportional to the error • Velocity feedback loop introduces damping into the system • Velocity error can be introduced into the control law (faster system response) • leading to**PD positioncontrol with gravity compensation**• Robot inverse dynamic model • In static conditions can be simplified to • Estimated gravity term part of the control law**Robot dynamic model**• Robot inverse dynamic model • Robot forward dynamic model • Define new variable • leading to**Inverse dynamics control**• Assume that the robot dynamic model is known • inertial matrix is anapproximation of real values , • represents an approximation of • Consider the following control law • where input y will be defined later.**Inverse dynamics control block scheme**y represents computed acceleration in joint space**PD position control**• position error • velocity error • control law • error dynamics**Robot control in external coordinates**• Definition of pose error • Control based on the transposed Jacobian matrix • Control based on the inverse Jacobian matrix**Manipulator Jacobian matrix**• End-effector position • Differential kinematics Jacobianmatrix**Manipulator Jacobian matrix**• Jacobian matrix**Inverse Jacobian matrix**• Inverse velocity relation • For a square matrix of dimension two • Inverse velocity relation • Inverse Jacobian matrix equals**Transposed Jacobian matrix**• Robot in contact with the environment (contact force f) • Find resulting joint torques • In matrix form**Transposed Jacobian matrix**• Velocity relation • Force/torque relation • Transposed matrix • Force/torque relation TransposedJacobianmatrix**Transposed Jacobian matrix based Control**• Pose error in external coordinates • Control law formulation (control variable in external coordinates) • Control variable in joint space**Inverse Jacobian matrix based Control**• Velocity relation • Relation for small displacements • Relation for small pose errors • Control law in joint space**PD position control with gravity compensation in external**coordinates • Control law**Inverse dynamics control in external coordinates**• Inverse dynamics • Velocity relation • Acceleration relation • Computed acceleration for external coordinates control**Inverse dynamics control in external coordinates**• Pose error • Velocity error • Acceleration error • Error dynamics • Control law**Inverse dynamics control in external coordinates – block**scheme**Control of contact force with environment**• control of end-effector desired pose while the robot is in contact with the environment • case of robot assembly (inserting a peg into a hole) • robot movement assures minimal contact force during action • robot end-effector exerts a predetermined force on the environment • case of machining parts with robot (grinding) • robot movement depends on the difference between the desired and the actual contact force.**Robot dynamics with contact**• Dynamic model with contact force • Define new variable • leading to result of interaction with the environment**Inverse dynamics control with contact**• Inverse dynamics with contact • Forward dynamics with contact • Control law**Force control**• Force control is based on position control • Reference values for acceleration, velocity and pose are computed from force error**Force control**• Force error • Predefined manipulator behavior via inertia and damping matrices and • Reference trajectory**Parallel composition**• Parallel composition assumes force control in certain direction and pose control in other directions

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