Control of redundant robots using learned models: an operational - PowerPoint PPT Presentation

Control of redundant robots using learned models: an operational space control approach Presented at the IEEE/RSJ International Conference on Intelligent Robots and Systems October 12, 2009 / St Louis - USA by Camille Salaün, Vincent Padois (vincent.padois@upmc.fr) , Olivier Sigaud Université Pierre et Marie Curie Institut des Systèmes Intelligents et de Robotique (CNRS UMR 7222) V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 1 / 14

Introduction Introduction ◮ Robotics applications: moving from the industrial domain to the service domain (e.g. [1]) Induces increasing complexity Robots : complex structures, more actuators, more sensors Unstructured / Unknown environments V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 2 / 14

Introduction Introduction ◮ Robotics applications: moving from the industrial domain to the service domain (e.g. [1]) Induces increasing complexity Robots : complex structures, more actuators, more sensors Unstructured / Unknown environments Robustness and adaptivity are required: learning is part of the solution V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 2 / 14

Introduction Introduction ◮ Robotics applications: moving from the industrial domain to the service domain (e.g. [1]) Induces increasing complexity Robots : complex structures, more actuators, more sensors Unstructured / Unknown environments Robustness and adaptivity are required: learning is part of the solution That does not mean throwing away model-based robotics control → it can provide a sound framework and a good starting point V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 2 / 14

Introduction Introduction ◮ Robotics applications: moving from the industrial domain to the service domain (e.g. [1]) Induces increasing complexity Robots : complex structures, more actuators, more sensors Unstructured / Unknown environments Robustness and adaptivity are required: learning is part of the solution That does not mean throwing away model-based robotics control → it can provide a sound framework and a good starting point General goal of this work Propose a methodology to combine learning methods and model-based control → The work in this paper illustrates a methodology to do so ֒ V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 2 / 14

Introduction Outline of this presentation Introduction 1 Background in Operational Space Control 2 Learning strategy and learning tools 3 Simulated experiments description 4 Results and Analysis 5 Conclusions and Perspectives 6 References 7 V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 3 / 14

Background in Operational Space Control Background in Operational Space Control ◮ Model-based control techniques are mostly based on the knowledge of the model(s) relating the joint space (dimension n ) to the task space (dimension m ) [2]. V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 4 / 14

Background in Operational Space Control Background in Operational Space Control ◮ Model-based control techniques are mostly based on the knowledge of the model(s) relating the joint space (dimension n ) to the task space (dimension m ) [2]. These mapping can be described at two different levels Geometric: ξ = h ( q ) → non-linear, hard to inverse Velocity kinematics: ˙ ξ = J ( q ) ˙ q V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 4 / 14

Background in Operational Space Control Background in Operational Space Control ◮ Model-based control techniques are mostly based on the knowledge of the model(s) relating the joint space (dimension n ) to the task space (dimension m ) [2]. These mapping can be described at two different levels Geometric: ξ = h ( q ) → non-linear, hard to inverse Velocity kinematics: ˙ ξ = J ( q ) ˙ q The relation between forces and accelerations is also important Dynamics in the joint space: Γ = A ( q ) ¨ q + b ( q , ˙ q ) + g ( q ) + ǫ ( q , ˙ q ) − Γ ext q ) + p ( q ) + ǫ ′ ( q , ˙ Dynamics in the task space: f = Λ ( q ) ¨ ξ + µ ( q , ˙ q ) − f ext [3] V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 4 / 14

Background in Operational Space Control Background in Operational Space Control ◮ Model-based control techniques are mostly based on the knowledge of the model(s) relating the joint space (dimension n ) to the task space (dimension m ) [2]. These mapping can be described at two different levels Geometric: ξ = h ( q ) → non-linear, hard to inverse Velocity kinematics: ˙ ξ = J ( q ) ˙ q The relation between forces and accelerations is also important Dynamics in the joint space: Γ = A ( q ) ¨ q + b ( q , ˙ q ) + g ( q ) + ǫ ( q , ˙ q ) − Γ ext q ) + p ( q ) + ǫ ′ ( q , ˙ Dynamics in the task space: f = Λ ( q ) ¨ ξ + µ ( q , ˙ q ) − f ext [3] Common approaches in model-based control often rely on: An error signal in the task space The inversion of the joint space to task mapping The use of the dynamics equation to compute the forces to apply to the robot V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 4 / 14

Background in Operational Space Control Background in Operational Space Control ◮ Model-based control techniques are mostly based on the knowledge of the model(s) relating the joint space (dimension n ) to the task space (dimension m ) [2]. These mapping can be described at two different levels Geometric: ξ = h ( q ) → non-linear, hard to inverse Velocity kinematics: ˙ ξ = J ( q ) ˙ q The relation between forces and accelerations is also important Dynamics in the joint space: Γ = A ( q ) ¨ q + b ( q , ˙ q ) + g ( q ) + ǫ ( q , ˙ q ) − Γ ext q ) + p ( q ) + ǫ ′ ( q , ˙ Dynamics in the task space: f = Λ ( q ) ¨ ξ + µ ( q , ˙ q ) − f ext [3] Common approaches in model-based control often rely on: An error signal in the task space The inversion of the joint space to task mapping The use of the dynamics equation to compute the forces to apply to the robot ◮ In this work we focus on the velocity kinematics level (dynamics is assumed to be known) V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 4 / 14

Background in Operational Space Control Inverse Velocity Kinematics ⋆ , compute the corresponding ˙ ◮ Problem : given a desired task space velocity ˙ ξ q V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 5 / 14

Background in Operational Space Control Inverse Velocity Kinematics ⋆ , compute the corresponding ˙ ◮ Problem : given a desired task space velocity ˙ ξ q Assuming singularity free configurations, the solution can be written as q = J ( q ) ♯ ˙ ⋆ ˙ ξ V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 5 / 14

Background in Operational Space Control Inverse Velocity Kinematics ⋆ , compute the corresponding ˙ ◮ Problem : given a desired task space velocity ˙ ξ q Assuming singularity free configurations, the solution can be written as q = J ( q ) ♯ ˙ ⋆ ˙ ξ 3 cases have to be distinguished V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 5 / 14

Background in Operational Space Control Inverse Velocity Kinematics ⋆ , compute the corresponding ˙ ◮ Problem : given a desired task space velocity ˙ ξ q Assuming singularity free configurations, the solution can be written as q = J ( q ) ♯ ˙ ⋆ ˙ ξ 3 cases have to be distinguished Fully constrained ( n = m ): one exact solution, J ( q ) ♯ = J ( q ) − 1 V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 5 / 14

Background in Operational Space Control Inverse Velocity Kinematics ⋆ , compute the corresponding ˙ ◮ Problem : given a desired task space velocity ˙ ξ q Assuming singularity free configurations, the solution can be written as q = J ( q ) ♯ ˙ ⋆ ˙ ξ 3 cases have to be distinguished Fully constrained ( n = m ): one exact solution, J ( q ) ♯ = J ( q ) − 1 Over constrained ( n < m ): no exact solution, minimum error if J ( q ) ♯ is a (weighted) pseudo-inverse [4, 5] V. Padois (UPMC-ISIR) Control of redundant robots using learned models ... IROS - 12/10/2009 - St Louis, USA 5 / 14