Temporal representation of loops. More...

#include <codac_TPlane.h>

Inheritance diagram for codac::TPlane:

[legend]

Collaboration diagram for codac::TPlane:

[legend]

Public Member Functions
	TPlane (const Interval &tdomain)
	Creates a 2d temporal space \([t_0,t_f]^2\).

	~TPlane ()
	TPlane destructor.

void	compute_loops (float precision, const TubeVector &p, const TubeVector &v)
	Computes the loops (detections and proofs) as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

void	compute_detections (float precision, const TubeVector &p)
	Computes this tplane as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) only.

void	compute_detections (float precision, const TubeVector &p, const TubeVector &v)
	Computes this tplane as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

void	compute_proofs (const TubeVector &p)
	Tries to prove the existence of loops in each detection set.

void	compute_proofs (const TubeVector &p, const TubeVector &v)
	Tries to prove the existence of loops in each detection set.

int	nb_loops_detections () const
	Returns the number of loop detections.

int	nb_loops_proofs () const
	Returns the number of proven loops.

const std::vector< ConnectedSubset > &	detected_loops_subsets () const
	Returns the set of detected loops.

const std::vector< IntervalVector >	detected_loops () const
	Returns the set of boxed detected loops.

const std::vector< ConnectedSubset > &	proven_loops_subsets () const
	Returns the set of proven loops.

const std::vector< IntervalVector >	proven_loops () const
	Returns the set of boxed proven loops.

Trajectory	traj_loops_summary () const
	Returns a temporal function of value 0 in case of no-detection, 1 in case of loop detection and 2 in case of loop proof.

void	compute_proofs (const std::function< IntervalVector(const IntervalVector &)> &f)
	Tries to prove the existence of loops in each detection set.

Public Member Functions inherited from codac::Paving
	Paving (const IntervalVector &box, SetValue value=SetValue::UNKNOWN)
	Creates a paving.

	~Paving ()
	Paving destructor.

Paving *	get_first_subpaving ()
	Points to the first subpaving of the binary tree implementing this paving set.

const Paving *	get_first_subpaving () const
	Points to the first subpaving of the binary tree implementing this paving set.

Paving *	get_second_subpaving ()
	Points to the second subpaving of the binary tree implementing this paving set.

const Paving *	get_second_subpaving () const
	Points to the second subpaving of the binary tree implementing this paving set.

Paving *	get_root ()
	Returns a pointer to the root of the paving structure.

const Paving *	get_root () const
	Returns a pointer to the root of the paving structure.

Paving *	get_first_leaf (SetValue val, bool without_flag=false)
	Points to the first leaf of the specified value.

const Paving *	get_first_leaf (SetValue val, bool without_flag=false) const
	Points to the first leaf of the paving structure.

void	bisect (float ratio=0.49)
	Bisects this paving into two subpavings with some ratio bisection.

bool	is_leaf () const
	Returns true if this paving is made of two subpavings.

bool	flag () const
	Tests whether this paving has been flagged or not.

void	set_flag () const
	Flags this paving and all its children.

void	reset_flags () const
	Removes the flags of this Paving and all its children.

void	reset_paving (SetValue value=SetValue::UNKNOWN)
	Same as building a new Paving object.

void	get_boxes (std::list< IntervalVector > &l_subpavings, SetValue val, SetValue neg_val=SetValue::DEFAULT) const
	Returns a set of boxes leaves of some value.

void	get_pavings_intersecting (SetValue val, const IntervalVector &box_to_intersect, std::vector< const Paving * > &v_subpavings, bool no_degenerated_intersection=false) const
	Returns a set of Paving leaves of some value and intersecting a given box.

void	get_neighbours (std::vector< const Paving * > &v_neighbours, SetValue val=SetValue::IN\|SetValue::OUT\|SetValue::UNKNOWN, bool without_flag=false) const
	Returns the neighbors (adjacent items) of this Paving, having some value.

std::vector< ConnectedSubset >	get_connected_subsets (bool sort_by_size=false, SetValue val=SetValue::UNKNOWN\|SetValue::IN) const
	Returns the set of connected subsets of this paving.

Public Member Functions inherited from codac::Set
	Set (const IntervalVector &box, SetValue value=SetValue::UNKNOWN)
	Creates a set.

	~Set ()
	Set destructor.

SetValue	value () const
	Returns the value of this set.

int	size () const
	Returns the dimension of the paving.

const IntervalVector &	box () const
	Returns the n-dimensional box representing this set.

void	set_value (SetValue value)
	Sets the integer value for this set.

Static Public Member Functions
static void	verbose (bool verbose=true)
	Enables verbose mode for displaying information related to loops computations.

Protected Member Functions
void	compute_detections (float precision, const TubeVector &p, const TubeVector &v, bool with_derivative, bool extract_subsets)
	Recursive computation of the tplane, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

Protected Attributes
float	m_precision = 0.
	precision of the SIVIA algorithm, used later on in traj_loops_summary()

std::vector< ConnectedSubset >	m_v_detected_loops
	set of loops detections

std::vector< ConnectedSubset >	m_v_proven_loops
	set of loops proofs

Protected Attributes inherited from codac::Set
SetValue	m_value
	integer value of this set

IntervalVector	m_box
	box representing this set

Additional Inherited Members
Public Attributes inherited from codac::Paving
bool	m_flag = false
	optional flag, can be used by search algorithms

Paving *	m_root = nullptr
	pointer to the root

Paving *	m_second_subpaving = nullptr
	tree structure

Detailed Description

Temporal representation of loops.

A t-plane is a 2d temporal space \([t_0,t_f]^2\) that may contain t-pairs corresponding to looped trajectories. Considering 2d trajectories \(\mathbf{p}(\cdot):[t_0,t_f]\to\mathbb{R}^2\), we temporally define the set of loops as: \(\mathbb{T}^*=\left\{(t_1,t_2)\in [t_0,t_f]^2 \mid \mathbf{p}(t_1)=\mathbf{p}(t_2) , t_1 < t_2 \right\}\)

This class allows to detect and prove loops considering uncertainties on \(\mathbf{p}(\cdot)\) or in cases where only the velocities \(\mathbf{v}(\cdot)\) of the robot are at hand.

This has been the object of the publications:

Loop detection of mobile robots using interval analysis
C. Aubry, R. Desmare, L. Jaulin
Automatica, 2013

Proving the existence of loops in robot trajectories
S. Rohou, P. Franek, C. Aubry, L. Jaulin
The International Journal of Robotics Research, 2018

Constructor & Destructor Documentation

◆ TPlane()

codac::TPlane::TPlane ( const Interval & tdomain )

Creates a 2d temporal space \([t_0,t_f]^2\).

Parameters

tdomain temporal domain \([t_0,t_f]\)

Member Function Documentation

◆ compute_loops()

void codac::TPlane::compute_loops	(	float	precision,
		const TubeVector &	p,
		const TubeVector &	v )

Computes the loops (detections and proofs) as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

Parameters

precision	precision \(\epsilon\) of the SIVIA approximation
p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions
v	2d TubeVector \([\mathbf{v}](\cdot)\) for velocities

◆ compute_detections() [1/3]

void codac::TPlane::compute_detections	(	float	precision,
		const TubeVector &	p )

Computes this tplane as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) only.

Parameters

precision	precision \(\epsilon\) of the SIVIA approximation
p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions

◆ compute_detections() [2/3]

void codac::TPlane::compute_detections	(	float	precision,
		const TubeVector &	p,
		const TubeVector &	v )

Computes this tplane as a subpaving, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

Parameters

precision	precision \(\epsilon\) of the SIVIA approximation
p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions
v	2d TubeVector \([\mathbf{v}](\cdot)\) for velocities

◆ compute_proofs() [1/3]

void codac::TPlane::compute_proofs ( const TubeVector & p )

Tries to prove the existence of loops in each detection set.

Note: The tplane must have been computed beforehand.

Parameters

p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions

◆ compute_proofs() [2/3]

void codac::TPlane::compute_proofs	(	const TubeVector &	p,
		const TubeVector &	v )

Tries to prove the existence of loops in each detection set.

Note: The tplane must have been computed beforehand.

Parameters

p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions
v	2d TubeVector \([\mathbf{v}](\cdot)\) for velocities

◆ nb_loops_detections()

int codac::TPlane::nb_loops_detections ( ) const

Returns the number of loop detections.

Note: The tplane must have been computed beforehand.

Returns: the number of connected subsets corresponding to feasible loops

◆ nb_loops_proofs()

int codac::TPlane::nb_loops_proofs ( ) const

Returns the number of proven loops.

Note: The tplane and the proofs must have been computed beforehand.

Returns: the number of connected subsets for which at least one loop has been verified

◆ detected_loops_subsets()

const std::vector< ConnectedSubset > & codac::TPlane::detected_loops_subsets ( ) const

Returns the set of detected loops.

Note: The tplane must have been computed beforehand.

Returns: the set of connected subsets corresponding to loop detections

◆ detected_loops()

const std::vector< IntervalVector > codac::TPlane::detected_loops ( ) const

Returns the set of boxed detected loops.

Note: The tplane must have been computed beforehand.

Returns: the set of boxes \([t_1]\times[t_2]\) corresponding to loop detections

◆ proven_loops_subsets()

const std::vector< ConnectedSubset > & codac::TPlane::proven_loops_subsets ( ) const

Returns the set of proven loops.

Note: The tplane and the proofs must have been computed beforehand.

Returns: the set of connected subsets corresponding to loops proofs

◆ proven_loops()

const std::vector< IntervalVector > codac::TPlane::proven_loops ( ) const

Returns the set of boxed proven loops.

Note: The tplane and the proofs must have been computed beforehand.

Returns: the set of boxes \([t_1]\times[t_2]\) corresponding to loops proofs

◆ traj_loops_summary()

Trajectory codac::TPlane::traj_loops_summary ( ) const

Returns a temporal function of value 0 in case of no-detection, 1 in case of loop detection and 2 in case of loop proof.

This method is useful when used together with colormaps for display purposes.

Returns: the corresponding temporal function (trajectory)

◆ verbose()

static void codac::TPlane::verbose ( bool verbose = true )

static

Enables verbose mode for displaying information related to loops computations.

Parameters

verbose boolean

◆ compute_proofs() [3/3]

void codac::TPlane::compute_proofs ( const std::function< IntervalVector(const IntervalVector &)> & f )

Tries to prove the existence of loops in each detection set.

Note: The tplane must have been computed beforehand.

Parameters

f	the inclusion function \([\mathbf{f}]:\mathbb{IR}^2\to\mathbb{IR}^2\)

◆ compute_detections() [3/3]

void codac::TPlane::compute_detections	(	float	precision,
		const TubeVector &	p,
		const TubeVector &	v,
		bool	with_derivative,
		bool	extract_subsets )

protected

Recursive computation of the tplane, from the tube of positions \([\mathbf{p}](\cdot)\) and the tube of velocities \([\mathbf{v}](\cdot)\).

Note: This method is used as recursive algorithm.

Parameters

precision	precision \(\epsilon\) of the SIVIA approximation
p	2d TubeVector \([\mathbf{p}](\cdot)\) for positions
v	2d TubeVector \([\mathbf{v}](\cdot)\) for velocities
with_derivative	if `true`, the loop detection is made with derivative tubes given in arguments
extract_subsets	if `true`, a set of ConnectedSubset objects will be computed from this Paving

The documentation for this class was generated from the following file:

/home/simon/codac/src/robotics/loops/codac_TPlane.h

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ TPlane()

Member Function Documentation

◆ compute_loops()

◆ compute_detections() [1/3]

◆ compute_detections() [2/3]

◆ compute_proofs() [1/3]

◆ compute_proofs() [2/3]

◆ nb_loops_detections()

◆ nb_loops_proofs()

◆ detected_loops_subsets()

◆ detected_loops()

◆ proven_loops_subsets()

◆ proven_loops()

◆ traj_loops_summary()

◆ verbose()

◆ compute_proofs() [3/3]

◆ compute_detections() [3/3]