Optimization-based control for dual-arm manipulation
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1 Optimization-based control for dual-arm manipulation Yuquan Wang, Francisco Viña, Yiannis Karayiannidis, Christian Smith and Petter Ögren KTH, Center for Autonomous Systems (CAS) June 5, 2014 Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
2 Background Intuitive examples Background: Why constraint-based programming? Problem: Candidate solution: Trajectory planing Pan&brush trajectories e(t) Joint trajectories q(t) Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
3 Background Intuitive examples Background: Why constraint-based programming? Problem: Candidate solution: Trajectory planing Pan&brush trajectories e(t) Joint trajectories q(t) Drawbacks: Not reactive Hard to extend Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
4 Background Intuitive examples Background: Why constraint-based programming? Problem: Candidate solution: Trajectory planing Pan&brush trajectories e(t) Joint trajectories q(t) Drawbacks: Not reactive Hard to extend Alternative: Constraint-based programming Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
5 Background Intuitive examples How to use constraint-based programming? Example: Specifing constraints: Combining constraints. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
6 Background Intuitive examples How to use constraint-based programming? Example: Specifing constraints: Relative position Brush orientation Contact force Obstacle avoidance Singularity avoidance Combining constraints. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
7 Background Intuitive examples Build a monster from something simple Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
8 Background Intuitive examples Build a monster from something simple Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
9 Background Earlier works Seminal earlier works in constraint-based programming Additional tasks (Seraji 1989) User defined objective functions (Peng and Adachi 1993) Stack of Tasks (Mansard and Chaumette 2007) itasc (De Schutter 2007) Sub-tasks (Tatlicioglu 2008) Prioritizing linear equality and inequality systems (Kanoun 2009) Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
10 Dual arm manipulation Contributions Sample task Dual arm manipulation using constraint based programming Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
11 Contributions Theoretical improvements Our formulation of constraint-based programming Quadratic optimization problem: 2014 IFAC: Dual arm manipulation using constraint-based programming Syroco: A multi objective control approach to online dual arm manipulation. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
12 Contributions Theoretical improvements Our formulation of constraint-based programming Quadratic optimization problem: min u ḟ j (q(t), u, t) + u T Qu, j I matrix. Q is a diagonal positive definite Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
13 Contributions Theoretical improvements Our formulation of constraint-based programming Quadratic optimization problem: min u ḟ j (q(t), u, t) + u T Qu, j I (s.t.) ḟ m (q, u, t) b m, m I ie, where b m, b n are positive scalars and Q is a diagonal positive definite matrix. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
14 Contributions Theoretical improvements Our formulation of constraint-based programming Quadratic optimization problem: min u ḟ j (q(t), u, t) + u T Qu, j I (s.t.) ḟ m (q, u, t) b m, m I ie, ḟ n (q, u, t) = b n, n I e, where b m, b n are positive scalars and Q is a diagonal positive definite matrix. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
15 Contributions Theoretical improvements Explicitly parameterize the convergence of each constraint: ḟ m (q, t) b m, m I ie, ḟ n (q, t) = b n, n I e, Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
16 Contributions Theoretical improvements Explicitly parameterize the convergence of each constraint: ḟ m (q, t) k m e m, m I ie, ḟ n (q, t) = k n e n, n I e, Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
17 Contributions Theoretical improvements Explicitly parameterize the convergence of each constraint: ḟ m (q, t) k m (f m (q, t) b m ), m I ie, ḟ n (q, t) = k n (f n (q, t) b n ), n I e, Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
18 Contributions Theoretical improvements Time-forward terms: ḟ m (q, t) k m (f m (q, t) b m ), m I ie, ḟ n (q, t) = k n (f n (q, t) b n ), n I e, Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
19 Contributions Theoretical improvements Time-forward terms: f m (q, t) q q f n (q, t) q q k m (f m (q, t) b m ) fm(q,t) t, m I ie, = k n (f n (q, t) b n ) fn(q,t) t, n I e, Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
20 Contributions Theoretical improvements Prioritizing the constaints: min u ḟ j (q(t), u, t) + u T Qu, j I (s.t.) ḟ m (q, u, t) k m (f m (q, t) b m ), m I ie, ḟ n (q, u, t) = k n (f n (q, t) b n ), n I e, where k m, b m are positive scalars and Q is a diagonal positive definite matrix. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
21 Contributions Theoretical improvements Prioritizing the constaints: min u ḟ j (q(t), u, t) + u T Qu+µ T W µ, j I (s.t.) ḟ m (q, u, t)+µ m k m (f m (q, t) b m ), m I ie, ḟ n (q, u, t)+µ n = k n (f n (q, t) b n ), n I e, where k m, b m are positive scalars and Q, W are diagonal positive definite matries. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
22 Contributions Theoretical improvements Our formulation of constraint-based programming Advantages: Compact formulation of a QP including equalities and inequalities. Time feed-forward terms. Parameterize the convergence rate. Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
23 Contributions Validation through examples Circular trajectory in the pan cleaning task Different convergence rate in simulation: Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
24 Contributions Validation through examples Circular trajectory in the pan cleaning task Experiment on a dual-arm robot: Tool relative to frying pan Z [m] X [m] Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
25 Contributions Validation through examples Circular trajectory in the pan cleaning task Experiment with contact force control: 0.03 Tool relative to frying pan Z [m] X [m] Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
26 Performance indices Contributions Validation through examples Deviation[m] Radians Measure Measure Force [N] x 10 3 Deviation Tool Orientation Left and right arm singularity measures Obstacle avoidance along z axis Force along pan normal direction and the reference is 8N 10 5 bound: 1*cos(pi/8) bound: bound: 0.1 Reference Time [s] (for all the rows) Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
27 Future work Human robot co-manipulation Human robot co-manipulation Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
28 Future work Human robot co-manipulation { r R } Human { h} {} r { r L } Robot Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
29 Acknowledgement Acknowledgement and questions Acknowledgement: Swedish Foundation for Strategic Research (SSF) Swedish Research Council (VR) EU FP7 project RoboHow.Cog Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
30 Acknowledgement Acknowledgement and questions Acknowledgement: Swedish Foundation for Strategic Research (SSF) Swedish Research Council (VR) EU FP7 project RoboHow.Cog Questions? Yuquan Wang (KTH, CVAP) ICRA 2014 June 5, / 16
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