Guaranteed coverage assessment of a robotic survey with uncertain - PowerPoint PPT Presentation

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Guaranteed coverage assessment of a robotic survey with uncertain trajectory Vincent Drevelle Université de Rennes 1, IRISA, INRIA Rennes-Bretagne Atlantique, Lagadic Project (France) SWIM 2015, June 8 th , Prague V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 1 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Characterization of the Explored area Mission of the robot Explore a given zone, and ensure that it has been entirely covered by its sensor: mapping, mine hunting, search, ... tool: lawn-mowing, cleaning, ... V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 2 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Characterization of the Explored area Mission of the robot Explore a given zone, and ensure that it has been entirely covered by its sensor: mapping, mine hunting, search, ... tool: lawn-mowing, cleaning, ... Computing the area explored by the robot, prior to processing sensor data enables to assess mission before long transfer and processing time of sensor data focus first data processing on problematic parts of the mission plan a new mission to fill the gaps V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 2 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Characterization of the Explored area Mission of the robot Explore a given zone, and ensure that it has been entirely covered mapping, mine hunting, search, ... lawn-mowing, cleaning Robot positioning is uncertain Characterize the explored area w.r.t localization uncertainty V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 3 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Guaranteed Characterization of the Explored area Mission of the robot Explore a given zone, and ensure that it has been entirely covered mapping, mine hunting, search, ... lawn-mowing, cleaning Robot positioning is uncertain Characterize the explored area w.r.t localization uncertainty Use interval analysis to compute a guaranteed bracketing of the area explored by the robot V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 3 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Outline Problem statement 1 Explored area Characterization of the explored area in presence of uncertainties 2 Explored area with an uncertain trajectory Explored area characterization by Set Inversion Application 3 Underwater exploration simulation Guaranteed explored area computation Taking robot evolution into account 4 Improve guaranteed explored area computation V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 4 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area Outline Problem statement 1 Explored area Characterization of the explored area in presence of uncertainties 2 Explored area with an uncertain trajectory Explored area characterization by Set Inversion Application 3 Underwater exploration simulation Guaranteed explored area computation Taking robot evolution into account 4 Improve guaranteed explored area computation V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 5 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area Exploration robot � ˙ evolution x ( t ) = f ( x ( t ) , u ( t )) y ( t ) = g ( x ( t )) observation V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 6 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area Visible area The visible area at time t is represented by the set-valued function � � z ∈ R 2 : v ( z , x ( t )) ≤ 0 V ( t ) = where v ( z , x ( t )) is the visibility function  evolution x ( t ) ˙ = f ( x ( t ) , u ( t ))  y ( t ) = g ( x ( t )) observation � �  z ∈ R 2 : v ( z , x ( t )) ≤ 0 V ( t ) = visible area V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 7 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area Explored area The explored area is the union of the visible areas over the whole trajectory  evolution f ( x ( t ) , u ( t )) ˙ x ( t ) =    observation y ( t ) = g ( x ( t )) z ∈ R 2 : v ( z , x ( t )) ≤ 0 � � V ( t ) =  visible area  M ( t ) = � τ∈ [ 0 , t ] V ( τ )  explored area V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 8 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Outline Problem statement 1 Explored area Characterization of the explored area in presence of uncertainties 2 Explored area with an uncertain trajectory Explored area characterization by Set Inversion Application 3 Underwater exploration simulation Guaranteed explored area computation Taking robot evolution into account 4 Improve guaranteed explored area computation V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 9 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Explored area with an uncertain trajectory  uncertain trajectory x ( t ) ∈ [ x ]( t )  z ∈ R 2 : v ( z , x ( t )) ≤ 0 � � V ( t ) = visibility M ( t ) = � τ∈ [ 0 , t ] V ( τ )  explored map V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 10 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Bracketing of the visible area: guaranteed and possible Guaranteed visible area V ∀ : set of points that have necessarily been observed, regardless of the state uncertainty � � z ∈ R 2 : ∀ x ( t ) ∈ [ x ]( t ) , v ( z , x ( t )) ≤ 0 V ∀ [ x ] ( t ) = (1) Possible visible area V ∃ : set of points that may have been in the robot’s field of view: � � z ∈ R 2 : ∃ x ( t ) ∈ [ x ]( t ) , v ( z , x ( t )) ≤ 0 V ∃ [ x ] ( t ) = (2) V ∀ [ x ] ( t ) and V ∃ [ x ] ( t ) form a bracketing of the actual visible area V ( t ) : ∀ t ∈ [ t ] , V ∀ [ x ] ( t ) ⊂ V ( t ) ⊂ V ∃ [ x ] ( t ) V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 11 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Guaranteed visible area depends on position accuracy Robot is located inside a box. It observes a circular region: v ( z , x ) = � z − x � 2 − r 2 Position uncertainty box [ x ] V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 12 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Guaranteed visible area depends on position accuracy Robot is located inside a box. It observes a circular region: v ( z , x ) = � z − x � 2 − r 2 Guaranteed visible area V ∀ Possible visible area V ∃ Position uncertainty box [ x ] V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 12 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area with an uncertain trajectory Guaranteed and possible explored area Guaranteed explored area M ∀ : union of all the guaranteed visible areas during the mission M ∀ � V ∀ [ x ] = [ x ] ( t ) , (3) t ∈ [ t ] Possible explored area M ∃ : union of all the possible visible areas over time � M ∃ V ∃ [ x ] = [ x ] ( t ) . (4) t ∈ [ t ] A bracketing of the actual explored area M is given by M ∀ [ x ] ⊂ M ⊂ M ∃ [ x ] . V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 13 / 33

Introduction Problem statement Uncertain explored area Application Taking robot evolution into account Summary Explored area characterization by Set Inversion Outline Problem statement 1 Explored area Characterization of the explored area in presence of uncertainties 2 Explored area with an uncertain trajectory Explored area characterization by Set Inversion Application 3 Underwater exploration simulation Guaranteed explored area computation Taking robot evolution into account 4 Improve guaranteed explored area computation V. Drevelle (IRISA) Guaranteed coverage assessment... SWIM 2015 Prague 14 / 33