Industrial Robots Industrial Robots Control Control Part 1 Control - PowerPoint PPT Presentation

Industrial Robots Industrial Robots Control Control – Part 1 Control Control Part 1 Part 1 Part 1

Introduction to robot control � The motion control problem motion control problem consists in the design of control algorithms for the robot actuators � In particular it consists in generating the time functions of the generalized actuating torques, such that the TCP motion li d i h h h TCP i follows a specified task specified task in the cartesian space, fulfilling the specifications on transient and steady state response specifications on transient and steady ‐ state response requirements Basilio Bona 2 ROBOTICA 03CFIOR

Tasks Two types of tasks T f t t tasks can be defined: k k b d fi d 1. Tasks that do not require an interaction with the environment ( free space motion ); the manipulator moves its TCP following ( f i ) h i l i TCP f ll i cartesian trajectories, with constraint on positions, velocities and accelerations due to the manipulator itself or the task accelerations due to the manipulator itself or the task requirements q t q t ( ) ( ) � Sometimes it is sufficient to move the joints from a specified value � Sometimes it is sufficient to move the joints from a specified value i 0 q t ( ) to another specified value without following a specific geometric i f path 2. Tasks that require and interaction with the environment, i.e., where the TCP shall move in some cartesian subspace while subject to forces or torques from the environment We will consider only the first type only the first type of task Basilio Bona 3 ROBOTICA 03CFIOR

Motion control � In particular the motion control problem motion control problem consists in generating the time functions of the generalized actuating torques, such that the TCP motion follows a specified task in the cartesian space, fulfilling the specifications on transient and steady ‐ state response requirements i � Control schemes can be developed for: � Joint space control p � Task space control considering that the task description is usually specified in the considering that the task description is usually specified in the task space, while control actions are defined in the joint space Basilio Bona 4 ROBOTICA 03CFIOR

Joint space control Th I The Inverse Kinematics block transforms the desired task space positions Ki ti bl k t f th d i d t k iti and velocities into desired joint space reference values. The Transducer measures the value of the joint quantities (angles The Transducer measures the value of the joint quantities (angles, displacements) and compares them with the desired ones, obtained, if necessary, from the desired cartesian quantities. The Controller uses the error to generate a (low power) signal for the Actuator that transforms it in a (high power) torque (via the Gearbox ) that moves the robot joints Basilio Bona 5 ROBOTICA 03CFIOR

Task space control p p d Controller Actuator Gearbox Robot Transducer Transducer In this case, the Transducer must measure the task space quantities in order to In this case, the Transducer must measure the task space quantities in order to compare them with desired ones. Usually this is not an easy task, since it requires environment ‐ aware sensors; y y , q ; the most used ones are digital camera sensors (vision ‐ based control) or other types of exteroceptive exteroceptive sensors (infra ‐ red, ultra ‐ sonic, ...). Otherwise one uses the direct kinematics to estimate the task space pose Torques are always applied to the joints, so Inverse Kinematics is hidden inside the Controller block Basilio Bona 6 ROBOTICA 03CFIOR

Joint space control architectures Two main joint space control architectures T i j i t joint space control architectures are possible j i t t t l l hit hit t t ibl Decentralized control or independent joint control : each i ‐ th joint motor has a p j j local controller that takes into account only local variables, i.e., the joint � q t ( ) q t ( ) position and velocity i i The control is of SISO type usually based on a P PD or PID architecture The control is of SISO type, usually based on a P, PD or PID architecture The controller is designed considering only an approximated model of the i ‐ th joint. This scheme is very common in industrial robots, due to its simplicity, modularity and robustness The classical PUMA robot architecture is shown in the following slide The classical PUMA robot architecture is shown in the following slide Centralized control : there is only one MIMO controller that generates a command vector for each joint motor; it is based on the complete model of the manipulator and takes into account the entire vector of measured positions and velocities and velocities Basilio Bona 7 ROBOTICA 03CFIOR

Decentralized control Decentralized Joint q t 1 ( ) joint 1 Control reference controller 1 q t q t 2 ( ) ( ) joint 2 joint 2 Task space Joint space reference controller 2 … q t 6 ( ) joint 6 reference controller 6 Basilio Bona 8 ROBOTICA 03CFIOR

Decentralized control Teach Teach Terminal Disk Other pendant PUMA Control μ G Amplifier D/ A Motor 1 DLV-11J Encoder T= 0.875 ms EPROM EPROM Reference Interface angles T= 28 ms RAM CPU μ G D/ A Amplifier Motor 6 Encoder T= 0.875 ms COMPUTER ROBOT CONTROL Basilio Bona 9 ROBOTICA 03CFIOR

Motor and gearbox model (rigid body assumptions) Gearbox Gearbox = Geartrain Geartrain N Friction r = Gearbox ′ ′ N N; ω τ , Inertia m r Robot τ m Friction ′ ′ ′ N ; ω τ , Inertia m r Motor ′ τ m ′ ′ τ ω τ ω Output pow er I nput pow er r m r m Basilio Bona 10 ROBOTICA 03CFIOR

Motor and gearbox model ω β m b τ = τ + + τ r m p Γ R L τ N N i i a a a a b b m a i e Γ ′ N v E m τ τ a ′ τ τ p m ′ ω β β m m m ′ ′ ′ τ = τ − τ r m p ′ ′ τ p Basilio Bona 11 ROBOTICA 03CFIOR

Losses in geared motor Motor Joint side side ′ ′ ω τ ω τ ω τ v i Ei a a a m r m m m r Armature Motor Joint Gearbox circuit inertia inertia d η + L i R i a a a a d t gearbox efficiency efficiency d voltage drop ′ ′ Γ ω + β ω d m m m m d t Γ Γ ω ω + + β ω β ω b m b m d t τ ′ p τ p Basilio Bona 12 ROBOTICA 03CFIOR

Gearbox model ρ ′ ′ = N ρ θ ρθ = = r ′ ′ ω ω τ τ ρ ρ N N ′ ′ ρ ω ρ ω = ρω ρω m r Joint side ρ η = 1 Ideal gearbox: θ Power in Power out GEARBOX GEARBOX θ ′ ′ ′ ω τ ′ ′ ω τ = ηω τ m r m r m r ρ ′ ′ Motor side M t id ′ ′ ω τ τ ′ τ τ = τ m r r r r r ′ ω ω = m m r Basilio Bona 13 ROBOTICA 03CFIOR

CC motor equations – 1 MOTOR SI DE d d = − − L i v R i E a a a a a d t φ φ = K i K i φ e ′ ′ = φ ω = ω E k K ′ ⇒ ′ ω ω ≈ ⇒ ≈ m m m m k k k k K K K K ′ ′ ω τ τ = φ = k i K i τ m a a ′ τ τ = i m a K τ �� � ′ ′ ′ ′ ′ ′ τ = Γ θ + β θ = Γ ω + β ω � p m m m m m m m m ′ ′ ′ τ = τ − τ r r m m p p Basilio Bona 14 ROBOTICA 03CFIOR

CC motor equations – 2 MOTOR SI DE GEARBOX SI DE 1 1 ′ ′ τ = τ r ′ = τ τ r r r r r ′ ′ = τ − τ r ( ) 1 ( m p = r τ + + τ ( ) ) ⎡ ⎡ ⎤ ⎤ ′ ′ ′ = τ − Γ ω − β ω � r ⎢ ⎥ m p ⎣ ⎦ m m m m m ⎡ ⎤ 1 ′ = τ − Γ ω − β ω � r ( r ) ( r ) ⎡ ⎤ ⎢ ⎥ = r τ τ + + Γ Γ ω ω + + β ω β ω � ⎣ ⎣ ⎦ ⎦ ⎢ ⎢ ⎥ ⎥ m m m m m m m m m m ⎣ ⎣ ⎦ ⎦ m b m b m ′ 2 ( = τ − Γ ω � + β ω r r ) ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ m m m m m 1 1 1 ⎟ ⎟ ⎜ ⎜ ⎢ ⎥ ′ ′ = τ + Γ ω + β β ω � ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎟ ⎟ ⎢ ⎢ ⎥ ⎥ ⎜ ⎜ ⎜ ⎜ ⎟ ⎟ ⎟ ⎟ m m b b m m b b m m r r r ⎝ ⎠ ⎝ ⎠ ⎣ ⎦ 1 1 ( ′ ′ = τ + Γ ω + β ω β � 2 ( ) ) m m b b m m b b m m r 2 r Basilio Bona 15 ROBOTICA 03CFIOR

Control equations �� + � � + � + + T = τ H q q ( ) C q q q ( , ) B q q ( ) g q ( ) J F e component-wise joint torques n n n ∑ ∑ ∑∑ ∑∑ + + + + β β + + + + τ = τ q q �� q q � � q q H ( ) ( ) q q h ( ( ) ) q q q q q q g g ( ( ) ) ij ij j j ijk ijk j j k k bi bi i i i i fi fi ri i = = = j 1 j 1 k 1 n n n ∑ ∑∑ �� + �� + � � + β � + + τ = τ q q q q H ( ) q H ( ) q h ( ) q q q g ( ) i i i ij j ijk j k bi i i fi r i ≠ = = j i j 1 k 1 Co o s & ce t Coriolis & centripetal peta Friction, gravity ct o , g a ty I Inertial torques ti l t torques & external torques Basilio Bona 16 ROBOTICA 03CFIOR