ompl::base::TangentBundleStateSpace Class Reference

ConstrainedStateSpace encapsulating a planner-agnostic lazy atlas algorithm for planning on a constraint manifold. More...

#include <ompl/base/spaces/constraint/TangentBundleStateSpace.h>

Inheritance diagram for ompl::base::TangentBundleStateSpace:

Public Member Functions

 TangentBundleStateSpace (const StateSpacePtr &ambientSpace, const ConstraintPtr &constraint)
 
void sanityChecks () const override
 Do sanity checks, minus geodesic constraint satisfiability (as this is a lazy method).
 
bool discreteGeodesic (const State *from, const State *to, bool interpolate=false, std::vector< State *> *geodesic=nullptr) const override
 Traverse the manifold from from toward to. Returns true if we reached to, and false if we stopped early for any reason, such as a collision or traveling too far. No collision checking is performed if interpolate is true. If geodesic is not nullptr, the sequence of intermediates is saved to it, including a copy of from, as well as the final state, which is a copy of to if we reached to. Caller is responsible for freeing states returned in geodesic.
 
StategeodesicInterpolate (const std::vector< State *> &geodesic, double t) const override
 Like interpolate(...), but interpolates between intermediate states already supplied in stateList from a previous call to discreteGeodesic(..., geodesic). The from and to states are the first and last elements stateList. Returns a pointer to a state in geodesic. As TangentBundleStateSpace employs a lazy approach to manifold traversal, additional fix-up is required to generate a state that satisfies constraints.
 
bool project (State *state) const
 Reproject a state onto the surface of the manifold. Returns true if projection was successful, and the new state is valid.
 
- Public Member Functions inherited from ompl::base::AtlasStateSpace
 AtlasStateSpace (const StateSpacePtr &ambientSpace, const ConstraintPtr &constraint, bool separate=true)
 Construct an atlas with the specified dimensions. More...
 
 ~AtlasStateSpace () override
 Destructor.
 
void clear () override
 Reset the space (except for anchor charts).
 
StateSamplerPtr allocDefaultStateSampler () const override
 Allocate the default state sampler for this space.
 
StateSamplerPtr allocStateSampler () const override
 Allocate the previously set state sampler for this space.
 
void copyState (State *destination, const State *source) const override
 Copy a state to another. The memory of source and destination should NOT overlap. More...
 
StateallocState () const override
 Allocate a new state in this space.
 
void setEpsilon (double epsilon)
 Set epsilon, the maximum permissible distance between a point in the validity region of a chart and its projection onto the manifold. Default 0.1.
 
void setRho (double rho)
 Set rho, the maximum radius for which a chart is valid. Default 0.1.
 
void setAlpha (double alpha)
 Set alpha, the maximum permissible angle between the chart and the manifold inside the validity region of the chart. Must be within the range (0, pi/2). Default pi/16.
 
void setExploration (double exploration)
 Set the exploration parameter, which tunes the balance of refinement (sampling within known regions) and exploration (sampling on the frontier). Valid values are in the range [0,1), where 0 is all refinement, and 1 is all exploration. Default 0.5.
 
void setMaxChartsPerExtension (unsigned int charts)
 Sometimes manifold traversal creates many charts. This parameter limits the number of charts that can be created during one traversal. Default 200.
 
void setBiasFunction (const AtlasChartBiasFunction &biasFunction)
 Sets bias function for sampling.
 
void setSeparated (bool separate)
 Sets whether the atlas should separate charts or not.
 
void setBackoff (double backoff)
 Sets the backoff factor in manifold traversal factor.
 
double getEpsilon () const
 Get epsilon.
 
double getRho () const
 Get rho.
 
double getAlpha () const
 Get alpha.
 
double getExploration () const
 Get the exploration parameter.
 
double getRho_s () const
 Get the sampling radius.
 
unsigned int getMaxChartsPerExtension () const
 Get the maximum number of charts to create in one pass.
 
bool isSeparated () const
 Returns whether the atlas is separating charts or not.
 
std::size_t getChartCount () const
 Return the number of charts currently in the atlas.
 
double getBackoff () const
 Returns the current backoff factor used in manifold traversal.
 
AtlasChartnewChart (const StateType *state) const
 Create a new chart for the atlas, centered at xorigin, which should be on the manifold. Returns nullptr upon failure.
 
AtlasChartsampleChart () const
 Pick a chart at random.
 
AtlasChartowningChart (const StateType *state) const
 Find the chart to which x belongs. Returns nullptr if no chart found. Assumes x is already on the manifold.
 
AtlasChartgetChart (const StateType *state, bool force=false, bool *created=nullptr) const
 Wrapper to return chart state belongs to. Will attempt to initialize new chart if state does not belong to one. If force is true, this routine will reinitialize the chart that the state should be on. If created is not null, it will be set to true if a new chart is created.
 
AtlasChartanchorChart (const State *state) const
 Wrapper for newChart(). Charts created this way will persist through calls to clear(). More...
 
double estimateFrontierPercent () const
 Estimate what percentage of atlas charts do not have fully formed polytope boundaries, and are therefore on the frontier.
 
void printPLY (std::ostream &out) const
 Write a mesh representation of the atlas to a stream.
 
- Public Member Functions inherited from ompl::base::ConstrainedStateSpace
 ConstrainedStateSpace (const StateSpacePtr &ambientSpace, const ConstraintPtr &constraint)
 Construct a constrained space from an ambientSpace and a constraint.
 
bool isMetricSpace () const override
 Returns false as the implicit constrained configuration space defined by the constraint is not metric with respect to the ambient configuration space's metric.
 
void setSpaceInformation (SpaceInformation *si)
 Sets the space information for this state space. Required for collision checking in manifold traversal.
 
void setup () override
 Final setup for the space.
 
StateallocState () const override
 Allocate a new state in this space.
 
void constrainedSanityChecks (unsigned int flags) const
 Do some sanity checks relating to discrete geodesic computation and constraint satisfaction. See SanityChecks flags.
 
virtual unsigned int validSegmentCount (const State *s1, const State *s2) const override
 Return the valid segment count on the manifold, as valid segment count is determined by delta_ and lambda_.
 
void interpolate (const State *from, const State *to, double t, State *state) const override
 Find a state between from and to around time t, where t = 0 is from, and t = 1 is the final state reached by discreteGeodesic(from, to, true, ...), which may not be to. State returned in state.
 
void setDelta (const double delta)
 Set delta, the step size for traversing the manifold and collision checking. Default defined by ompl::magic::CONSTRAINED_STATE_SPACE_DELTA.
 
void setLambda (double lambda)
 Set lambda, where lambda * distance(x, y) is the maximum length of the geodesic x to y. Additionally, lambda * delta is the greatest distance a point can diverge from its previous step, to preserve continuity. Must be greater than 1.
 
double getDelta () const
 Get delta, the step size across the manifold.
 
double getLambda () const
 Get lambda (see setLambda()).
 
unsigned int getAmbientDimension () const
 Returns the dimension of the ambient space.
 
unsigned int getManifoldDimension () const
 Returns the dimension of the manifold.
 
const ConstraintPtr getConstraint () const
 Returns the constraint that defines the underlying manifold.
 
- Public Member Functions inherited from ompl::base::WrapperStateSpace
 WrapperStateSpace (const StateSpacePtr &space)
 
bool isCompound () const override
 Check if the state space is compound.
 
bool isDiscrete () const override
 Check if the set of states is discrete. More...
 
bool isHybrid () const override
 Check if this is a hybrid state space (i.e., both discrete and continuous components exist)
 
bool isMetricSpace () const override
 Return true if the distance function associated with the space is a metric.
 
bool hasSymmetricDistance () const override
 Check if the distance function on this state space is symmetric, i.e. distance(s1,s2) = distance(s2,s1). Default implementation returns true.
 
bool hasSymmetricInterpolate () const override
 Check if the interpolation function on this state space is symmetric, i.e. interpolate(from, to, t, state) = interpolate(to, from, 1-t, state). Default implementation returns true.
 
const std::string & getName () const
 
void setName (const std::string &name)
 
int getType () const
 
bool includes (const StateSpacePtr &other) const
 
bool includes (const StateSpace *other) const
 
bool covers (const StateSpacePtr &other) const
 
bool covers (const StateSpace *other) const
 
ParamSetparams ()
 
const ParamSetparams () const
 Get the parameters for this space.
 
double getLongestValidSegmentFraction () const override
 When performing discrete validation of motions, the length of the longest segment that does not require state validation needs to be specified. This function returns this length, for this state space, as a fraction of the space's maximum extent.
 
void setLongestValidSegmentFraction (double segmentFraction) override
 When performing discrete validation of motions, the length of the longest segment that does not require state validation needs to be specified. This function sets this length as a fraction of the space's maximum extent. More...
 
unsigned int validSegmentCount (const State *state1, const State *state2) const override
 Count how many segments of the "longest valid length" fit on the motion from state1 to state2.
 
void setValidSegmentCountFactor (unsigned int factor) override
 Set factor to be the value to multiply the return value of validSegmentCount(). By default, this value is 1. The higher the value, the smaller the size of the segments considered valid. The effect of this function is immediate (setup() does not need to be called).
 
unsigned int getValidSegmentCountFactor () const override
 Get the value used to multiply the return value of validSegmentCount().
 
double getLongestValidSegmentLength () const override
 Get the longest valid segment at the time setup() was called.
 
void computeSignature (std::vector< int > &signature) const override
 Compute an array of ints that uniquely identifies the structure of the state space. The first element of the signature is the number of integers that follow.
 
unsigned int getDimension () const override
 Get the dimension of the space (not the dimension of the surrounding ambient space)
 
double getMaximumExtent () const override
 Get the maximum value a call to distance() can return (or an upper bound). For unbounded state spaces, this function can return infinity. More...
 
double getMeasure () const override
 Get a measure of the space (this can be thought of as a generalization of volume)
 
void enforceBounds (State *state) const override
 Bring the state within the bounds of the state space. For unbounded spaces this function can be a no-op.
 
bool satisfiesBounds (const State *state) const override
 Check if a state is inside the bounding box. For unbounded spaces this function can always return true.
 
void copyState (State *destination, const State *source) const override
 Copy a state to another. The memory of source and destination should NOT overlap. More...
 
double distance (const State *state1, const State *state2) const override
 Computes distance between two states. This function satisfies the properties of a metric if isMetricSpace() is true, and its return value will always be between 0 and getMaximumExtent()
 
unsigned int getSerializationLength () const override
 Get the number of chars in the serialization of a state in this space.
 
void serialize (void *serialization, const State *state) const override
 Write the binary representation of state to serialization.
 
void deserialize (State *state, const void *serialization) const override
 Read the binary representation of a state from serialization and write it to state.
 
bool equalStates (const State *state1, const State *state2) const override
 Checks whether two states are equal.
 
void interpolate (const State *from, const State *to, double t, State *state) const override
 Computes the state that lies at time t in [0, 1] on the segment that connects from state to to state. The memory location of state is not required to be different from the memory of either from or to.
 
StateSamplerPtr allocDefaultStateSampler () const override
 Allocate an instance of the default uniform state sampler for this space.
 
StateallocState () const override
 Allocate a state that can store a point in the described space.
 
void freeState (State *state) const override
 Free the memory of the allocated state.
 
double * getValueAddressAtIndex (State *state, unsigned int index) const override
 Many states contain a number of double values. This function provides a means to get the memory address of a double value from state state located at position index. The first double value is returned for index = 0. If index is too large (does not point to any double values in the state), the return value is nullptr. More...
 
const double * getValueAddressAtIndex (const State *state, unsigned int index) const
 
const std::vector< ValueLocation > & getValueLocations () const
 
const std::map< std::string, ValueLocation > & getValueLocationsByName () const
 
double * getValueAddressAtLocation (State *state, const ValueLocation &loc) const
 
const double * getValueAddressAtLocation (const State *state, const ValueLocation &loc) const
 
double * getValueAddressAtName (State *state, const std::string &name) const
 
const double * getValueAddressAtName (const State *state, const std::string &name) const
 
void copyToReals (std::vector< double > &reals, const State *source) const override
 Copy all the real values from a state source to the array reals using getValueAddressAtLocation()
 
void copyFromReals (State *destination, const std::vector< double > &reals) const override
 Copy the values from reals to the state destination using getValueAddressAtLocation()
 
void registerProjections () override
 Register the projections for this state space. Usually, this is at least the default projection. These are implicit projections, set by the implementation of the state space. This is called by setup().
 
void printState (const State *state, std::ostream &out=std::cout) const override
 Print a state to a stream.
 
void printSettings (std::ostream &out) const override
 Print the settings for this state space to a stream.
 
void printProjections (std::ostream &out) const override
 Print the list of registered projections. This function is also called by printSettings()
 
void sanityChecks (double zero, double eps, unsigned int flags) const override
 Perform sanity checks for this state space. Throws an exception if failures are found. More...
 
void sanityChecks () const override
 Convenience function that allows derived state spaces to choose which checks should pass (see SanityChecks flags) and how strict the checks are. This just calls sanityChecks() with some default arguments.
 
StateSamplerPtr allocSubspaceStateSampler (const StateSpace *subspace) const override
 Allocate a sampler that actually samples only components that are part of subspace.
 
void computeLocations () override
 Compute the location information for various components of the state space. Either this function or setup() must be called before any calls to getValueAddressAtName(), getValueAddressAtLocation() (and other functions where those are used).
 
void setup () override
 Perform final setup steps. This function is automatically called by the SpaceInformation. If any default projections are to be registered, this call will set them and call their setup() functions. It is safe to call this function multiple times. At a subsequent call, projections that have been previously user configured are not re-instantiated, but their setup() method is still called.
 
const StateSpacePtrgetSpace () const
 
- Public Member Functions inherited from ompl::base::StateSpace
 StateSpace (const StateSpace &)=delete
 
StateSpaceoperator= (const StateSpace &)=delete
 
 StateSpace ()
 Constructor. Assigns a unique name to the space.
 
template<class T >
T * as ()
 Cast this instance to a desired type. More...
 
template<class T >
const T * as () const
 Cast this instance to a desired type. More...
 
const std::string & getName () const
 Get the name of the state space.
 
void setName (const std::string &name)
 Set the name of the state space.
 
int getType () const
 Get the type of the state space. The type can be used to verify whether two space instances are of the same type (e.g., SO2)
 
bool includes (const StateSpacePtr &other) const
 Return true if other is a space included (perhaps equal, perhaps a subspace) in this one.
 
bool includes (const StateSpace *other) const
 Return true if other is a space included (perhaps equal, perhaps a subspace) in this one.
 
bool covers (const StateSpacePtr &other) const
 Return true if other is a space that is either included (perhaps equal, perhaps a subspace) in this one, or all of its subspaces are included in this one.
 
bool covers (const StateSpace *other) const
 Return true if other is a space that is either included (perhaps equal, perhaps a subspace) in this one, or all of its subspaces are included in this one.
 
ParamSetparams ()
 Get the parameters for this space.
 
const ParamSetparams () const
 Get the parameters for this space.
 
StatecloneState (const State *source) const
 Clone a state.
 
void setStateSamplerAllocator (const StateSamplerAllocator &ssa)
 Set the sampler allocator to use.
 
void clearStateSamplerAllocator ()
 Clear the state sampler allocator (reset to default)
 
const double * getValueAddressAtIndex (const State *state, unsigned int index) const
 Const variant of the same function as above;.
 
const std::vector< ValueLocation > & getValueLocations () const
 Get the locations of values of type double contained in a state from this space. The order of the values is consistent with getValueAddressAtIndex(). The setup() function must have been previously called.
 
const std::map< std::string, ValueLocation > & getValueLocationsByName () const
 Get the named locations of values of type double contained in a state from this space. The setup() function must have been previously called.
 
double * getValueAddressAtLocation (State *state, const ValueLocation &loc) const
 Get a pointer to the double value in state that loc points to.
 
const double * getValueAddressAtLocation (const State *state, const ValueLocation &loc) const
 Const variant of the same function as above;.
 
double * getValueAddressAtName (State *state, const std::string &name) const
 Get a pointer to the double value in state that name points to.
 
const double * getValueAddressAtName (const State *state, const std::string &name) const
 Const variant of the same function as above;.
 
void registerProjection (const std::string &name, const ProjectionEvaluatorPtr &projection)
 Register a projection for this state space under a specified name.
 
void registerDefaultProjection (const ProjectionEvaluatorPtr &projection)
 Register the default projection for this state space.
 
ProjectionEvaluatorPtr getProjection (const std::string &name) const
 Get the projection registered under a specific name.
 
ProjectionEvaluatorPtr getDefaultProjection () const
 Get the default projection.
 
bool hasProjection (const std::string &name) const
 Check if a projection with a specified name is available.
 
bool hasDefaultProjection () const
 Check if a default projection is available.
 
const std::map< std::string, ProjectionEvaluatorPtr > & getRegisteredProjections () const
 Get all the registered projections.
 
StateSamplerPtr allocSubspaceStateSampler (const StateSpacePtr &subspace) const
 Allocate a sampler that actually samples only components that are part of subspace.
 
StategetSubstateAtLocation (State *state, const SubstateLocation &loc) const
 Get the substate of state that is pointed to by loc.
 
const StategetSubstateAtLocation (const State *state, const SubstateLocation &loc) const
 Get the substate of state that is pointed to by loc.
 
const std::map< std::string, SubstateLocation > & getSubstateLocationsByName () const
 Get the list of known substate locations (keys of the map corrspond to names of subspaces)
 
void getCommonSubspaces (const StateSpacePtr &other, std::vector< std::string > &subspaces) const
 Get the set of subspaces that this space and other have in common. The computed list of subspaces does not contain spaces that cover each other, even though they may be common, as that is redundant information.
 
void getCommonSubspaces (const StateSpace *other, std::vector< std::string > &subspaces) const
 Get the set of subspaces that this space and other have in common. The computed list of subspaces does not contain spaces that cover each other, even though they may be common, as that is redundant information.
 
void diagram (std::ostream &out) const
 Print a Graphviz digraph that represents the containment diagram for the state space.
 
void list (std::ostream &out) const
 Print the list of all contained state space instances.
 

Additional Inherited Members

- Public Types inherited from ompl::base::AtlasStateSpace
typedef std::function< double(AtlasChart *)> AtlasChartBiasFunction
 
using NNElement = std::pair< const StateType *, std::size_t >
 
- Public Types inherited from ompl::base::ConstrainedStateSpace
enum  SanityChecks {
  CONSTRAINED_STATESPACE_SAMPLERS = (1 << 1), CONSTRAINED_STATESPACE_GEODESIC_SATISFY = (1 << 2), CONSTRAINED_STATESPACE_GEODESIC_CONTINUITY = (1 << 3), CONSTRAINED_STATESPACE_GEODESIC_INTERPOLATE = (1 << 4),
  CONSTRAINED_STATESPACE_JACOBIAN = (1 << 5)
}
 Flags used in a bit mask for constrained state space sanity checks, constraintSanityChecks(). More...
 
- Public Types inherited from ompl::base::StateSpace
enum  SanityChecks {
  STATESPACE_DISTANCE_DIFFERENT_STATES = (1 << 1), STATESPACE_DISTANCE_SYMMETRIC = (1 << 2), STATESPACE_INTERPOLATION = (1 << 3), STATESPACE_TRIANGLE_INEQUALITY = (1 << 4),
  STATESPACE_DISTANCE_BOUND = (1 << 5), STATESPACE_RESPECT_BOUNDS = (1 << 6), STATESPACE_ENFORCE_BOUNDS_NO_OP = (1 << 7), STATESPACE_SERIALIZATION = (1 << 8)
}
 Flags to use in a bit mask for state space sanity checks. Some basic checks do not have flags associated (they are always executed; for example, whether copyState() works as expected) More...
 
typedef ompl::base::State StateType
 Define the type of state allocated by this space.
 
- Static Public Member Functions inherited from ompl::base::StateSpace
static void Diagram (std::ostream &out)
 Print a Graphviz digraph that represents the containment diagram for all the instantiated state spaces.
 
static void List (std::ostream &out)
 Print the list of available state space instances.
 
- Protected Attributes inherited from ompl::base::AtlasStateSpace
std::vector< StateType * > anchors_
 Set of states on which there are anchored charts.
 
std::vector< AtlasChart * > charts_
 Set of charts.
 
PDF< AtlasChart * > chartPDF_
 PDF of charts according to a bias function.
 
NearestNeighborsGNAT< NNElement > chartNN_
 Set of chart centers and indices, accessible by nearest-neighbor queries to the chart centers.
 
AtlasChartBiasFunction biasFunction_
 Function to bias chart sampling.
 
bool separate_
 Enable or disable halfspace separation of the charts.
 
RNG rng_
 Random number generator.
 
double epsilon_ {ompl::magic::ATLAS_STATE_SPACE_EPSILON}
 Maximum distance between a chart and the manifold inside its validity region.
 
double rho_
 Maximum radius of chart validity region.
 
double cos_alpha_
 Cosine of the maximum angle between a chart and the manifold inside its validity region.
 
double exploration_
 Balance between explorationa and refinement.
 
double rho_s_
 Sampling radius within a chart. Inferred from rho and exploration parameters.
 
double backoff_ {ompl::magic::ATLAS_STATE_SPACE_BACKOFF}
 Step size reduction factor during manifold traversal.
 
unsigned int maxChartsPerExtension_ {ompl::magic::ATLAS_STATE_SPACE_MAX_CHARTS_PER_EXTENSION}
 Maximum number of charts that can be created in one manifold traversal.
 
- Protected Attributes inherited from ompl::base::ConstrainedStateSpace
SpaceInformationsi_ {nullptr}
 SpaceInformation associated with this space. Required for early collision checking in manifold traversal.
 
const ConstraintPtr constraint_
 Constraint function that defines the manifold.
 
const unsigned int n_
 Ambient space dimension.
 
const unsigned int k_
 Manifold dimension.
 
double delta_
 Step size when traversing the manifold and collision checking.
 
double lambda_ {ompl::magic::CONSTRAINED_STATE_SPACE_LAMBDA}
 Manifold traversal from x to y is stopped if accumulated distance is greater than d(x,y) times this. Additionally, if d(x, y) is greater than lambda * delta between two points, search is discontinued.
 
bool setup_ {false}
 Whether setup() has been called.
 
- Protected Attributes inherited from ompl::base::WrapperStateSpace
const StateSpacePtr space_
 
- Protected Attributes inherited from ompl::base::StateSpace
int type_
 A type assigned for this state space.
 
StateSamplerAllocator ssa_
 An optional state sampler allocator.
 
double maxExtent_
 The extent of this space at the time setup() was called.
 
double longestValidSegmentFraction_
 The fraction of the longest valid segment.
 
double longestValidSegment_
 The longest valid segment at the time setup() was called.
 
unsigned int longestValidSegmentCountFactor_
 The factor to multiply the value returned by validSegmentCount(). Rarely used but useful for things like doubling the resolution.
 
std::map< std::string, ProjectionEvaluatorPtrprojections_
 List of available projections.
 
ParamSet params_
 The set of parameters for this space.
 
std::vector< ValueLocationvalueLocationsInOrder_
 The value locations for all varliables of type double contained in a state; The locations point to values in the same order as that returned by getValueAddressAtIndex()
 
std::map< std::string, ValueLocationvalueLocationsByName_
 All the known value locations, by name. The names of state spaces access the first element of a state. RealVectorStateSpace dimensions are used to access individual dimensions.
 
std::map< std::string, SubstateLocationsubstateLocationsByName_
 All the known substat locations, by name.
 
- Static Protected Attributes inherited from ompl::base::StateSpace
static const std::string DEFAULT_PROJECTION_NAME = ""
 The name used for the default projection.
 

Detailed Description

ConstrainedStateSpace encapsulating a planner-agnostic lazy atlas algorithm for planning on a constraint manifold.

Short Description
TangentBundleStateSpace implements a lazy atlas-based methodology for constrained sampling-based planning, where the underlying constraint manifold is locally parameterized by charts (AtlasChart). The underlying constraint manifold can then be sampled and explored using the collection of these charts (an atlas). The difference between TangentBundleStateSpace and AtlasStateSpace is three-fold: TangentBundleStateSpace takes a lazy approach to evaluating the constraint function when traversing the manifold, TangentBundleStateSpace uses biased sampling for selected charts by default, and TangentBundleStateSpace does not use halfspace separation of charts.
External Documentation
This state space is inspired by the work on Tangent Bundle RRT.

B. Kim, T. T. Um, C. Suh, and F. C. Park, "Tangent bundle RRT: A randomized algorithm for constrained motion planning," Robotica 34.1 (2016): 202-225. DOI: 10.1017/S0263574714001234.

For more information on constrained sampling-based planning using atlas-based methods, see the following review paper. The section on atlas-based methods cites most of the relevant literature.

Z. Kingston, M. Moll, and L. E. Kavraki, “Sampling-Based Methods for Motion Planning with Constraints,” Annual Review of Control, Robotics, and Autonomous Systems, 2018. DOI: 10.1146/annurev-control-060117-105226 [PDF].

Definition at line 80 of file TangentBundleStateSpace.h.


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