Mod´ elisation et identification d’un bras manipulateur sous-marin actionn´ e de mani` ere h´ et´ erog` ene Ifremer Universit´ e de Montpellier cois Leborne 1,2 , Vincent Creuze 1 , Ahmed Chemori 1 , Lorenzo Brignone 2 Fran¸ 1 LIRMM (Universit´ e de Montpellier / CNRS) 2 Ifremer Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 1 / 24
Outline 1 Context HROV Ariane Objectives of the project 2 Modeling of Ariane’s manipulator arms Description of the actuators of Ariane’s manipulator arms Derivation of the model of the actuators 3 Identification and validation Derivation of the dynamic identification model Experimental validation 4 Grasping tools Motivations and design First results 5 Conclusion and future work Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 2 / 24
Context HROV Ariane HROV Ariane ’s missions Some missions and challenges: Seabed core sampling Storage of a sample Collect of a gorgonian control vertical and avoid collisions avoid collisions horizontal forces don’t mix different control of the grip keep the coring tool samples together strength vertical Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 3 / 24
Context HROV Ariane The manipulator arms of Ariane Control modes : human given speed reference, in cartesian or joint space State of the manipulator arms : given by position sensors (count of the steps of the motor) Speed of the joints : up to 15 deg/s Tasks example Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 4 / 24
Context Objectives of the project Objectives of the project Objectives automation of recurrent tasks seabed coring storage of samples in the basket dual-arm manipulation of cumbersome samples Steps 1 dynamic modeling of the manipulator arms, including the actuators dynamics 2 identification of the dynamic parameters of the models 3 determination of dual-arm manipulation strategies adapted to underwater manipulation Focus of this presentation The dynamic modeling of the arms of Ariane with an emphasis placed upon their actuators, and the identification of the parameters of their models. Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 5 / 24
Modeling of Ariane’s manipulator arms 1 Context HROV Ariane Objectives of the project 2 Modeling of Ariane’s manipulator arms Description of the actuators of Ariane’s manipulator arms Derivation of the model of the actuators 3 Identification and validation Derivation of the dynamic identification model Experimental validation 4 Grasping tools Motivations and design First results 5 Conclusion and future work Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 6 / 24
Modeling of Ariane’s manipulator arms Description of the actuators of Ariane’s manipulator arms Description of the actuators of Ariane ’s manipulator arms Drawing of a revolute joint actuated by a linear actuator Motivations non-linear transformation of the rotation of the motor into the ro- tation of the joint The revolute joints actuated by linear actuators of the 6-DOF manipulator arm. the inertia and mass of the actu- ators cannot be neglected Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 7 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Kinematic modeling of a revolute joint actuated by a linear actuator Linear actuator’s length q p = q p max − q p min q m + q p min (1) q m max − q m min Inner joint’s coordinate � � l 2 1 + l 2 2 − q 2 Drawing of a revolute joint p q j = arccos (2) actuated by a linear actu- 2 l 1 l 2 ator Modified Denavit-Hartenberg joint’s coordinate q = rev q j + offset (3) Parameters of the model l 1 , l 2 lengths measured on the actuator q p max , q p min lengths measured on the actuator q m max , q m min values read by the motor drives at Ratio ˙ q/ ˙ q m against the each joint limit motor’s coordinate rev − 1 or 1 offset measured by placing the joint in particular positions Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 8 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Optimization of the actuators parameters 1/2 Acquisition of a ground truth for optimizing the actuators parameters: 1 a fiducial marker is fixed to the arm, in the field of view of a calibrated camera 2 the pose of the marker is estimated using ArUco 1 3 the motor coordinates and the poses of the marker are recorded while one joint of the arm moves The setup used to acquire the data required for from one limit to the other one the optimization of the actuators’ parameters We define and solve the following optimization problem: � N � � 1 � 2 � � ˙ � ⊤ � � minimize ˆ q X ( i ) − ˙ q ( i ) , X = l 1 , l 2 , q p min , q p max N X i =1 1 S. Garrido-Jurado and R. Mu˜ noz-Salinas and F.J. Madrid-Cuevas and M.J. Mar´ ın-Jim´ enez, Automatic generation and detection of highly reliable fiducial markers under occlusion Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 9 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Optimization of the actuators parameters 2/2 This allows to refine the value of l 1 , l 2 , q p min , and q p max ; and thus to improve to estimation of the joint coordinates only based on the count of the motors steps: Raw RMSE Optimized RMSE Improvement 0.0983 rad 0.0235 rad 76.1 % Joint coordinate estimation based on mea- Error of the joint coordinate estimation sured (blue) and optimized (red) model pa- based on measured (blue) and optimized rameters (red) model parameters Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 10 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Dynamic modeling of a revolute joint actuated by a linear actuator Equation of the gear motor: τ m = k T i − r 2 � � J m ¨ q m + f v m ˙ q m + f s m sign( ˙ q m ) (4) Equation of the ball-screw: F BS = 2 π p τ m − I BS ¨ q p − f v BS ˙ q p − f s BS sign( ˙ q p ) (5) Equation of the lever: τ l = l 2 sin ( α ) F BS (6) Which gives the equation of the whole actuator: τ l = k L ( q ) i − m L,eq ( q, ¨ q ) − f L,eq ( q, ˙ q ) (7) Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 11 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Dynamic modeling of the whole manipulator arm Equation of a directly actuated revolute joint: τ D = k T i − r 2 � � J m ¨ q m + f v m ˙ q m + f s m sign( ˙ q m ) (8) Equation of a revolute joint actuated by a linear actuator (levered): τ L = k L ( q ) i − m L,eq ( q, ¨ q ) − f L,eq ( q, ˙ q ) (9) It results in the following multidimensional model of all the actuators of an arm: τ = K ( q ) i − M actuators ( q ) ¨ q − N actuators ( q , ˙ q ) (10) where k T,j if joint j is direct K j,j ( q ) = (11) k L,j ( q ) if joint j is levered Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 12 / 24
Modeling of Ariane’s manipulator arms Derivation of the model of the actuators Dynamic models of the full manipulator arms The classical model of a manipulator arm is: τ = M ( q ) ¨ q + N ( q , ˙ q ) (12) and the expression of the torque is given by: τ = K ( q ) i − M actuators ( q ) ¨ q − N actuators ( q , ˙ q ) (13) So by mixing (12) and (13), we obtain: K ( q ) i = M ⋆ ( q ) ¨ q + N ⋆ ( q , ˙ q ) (14) with the following definitions: M ⋆ ( q ) = M ( q ) + M actuators ( q ) (15) N ⋆ ( q , ˙ q ) = N ( q , ˙ q ) + N actuators ( q , ˙ q ) Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 13 / 24
Identification and validation Derivation of the dynamic identification model Identification of the parameters of the 4-DOF arm of Ariane The dynamic model of the arm is lin- ear in its dynamic parameters, so we define: Φ ⋆ = K − 1 ( q ) [ Φ , Φ actuators ] (16) � T θ ⋆ = � θ T , θ T actuators to express the dynamic identification A reference excitation trajectory for the identification of the model model of the system as: Φ ⋆ ( q , ˙ q ) θ ⋆ = i q , ¨ (17) We finally estimate the dynamic pa- Φ ⋆ � � q (0) , ˙ q (0) , ¨ q (0) rameters by solving the overdeter- mined system created using the ob- . . F = . jects defined in (19): (19) Φ ⋆ � q ( N ) , ˙ q ( N ) , ¨ q ( N ) � θ ⋆ = F + ( q , ˙ ˆ q , ¨ q ) b (18) � T b = � i (0) · · · i ( N ) Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 14 / 24
Identification and validation Experimental validation Experimental validation of the model The real current (solid gray line) is compared to the estimated input current, without (blue dashed line) and with (red solid line) actuators’ dynamics, obtained as: ˆ q ) ˆ θ ⋆ b = F ( q , ˙ q , ¨ (20) We also compute the root mean square error of the estimation in both cases: � RMSE( ˆ E(( ˆ b − b ) 2 ) b ) = (21) Joint 1 � % � Joint 2 � % � Joint 3 � % � without actuators dynamics 0.129 0.154 0.152 with actuators dynamics 0.117 0.128 0.122 improvement (percent) 9.80 16.8 19.9 Fran¸ cois Leborne R´ eunion d’´ equipe ICAR 22 mars 2018 15 / 24
Recommend
More recommend
