Tidy up a bit. Remove inconsistencies.
Modify s2t and t2s to work with both, state objects and np arrays.master
matssteinweg
parent
77d346b82e
commit
281fc19b6d
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@ -1,10 +1,13 @@
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import numpy as np
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from abc import abstractmethod
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try:
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from abc import ABC
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except:
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# for Python 2.7
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from abc import ABCMeta
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class ABC(object):
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__metaclass__ = ABCMeta
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pass
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@ -16,6 +19,7 @@ import math
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CAR = '#F1C40F'
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CAR_OUTLINE = '#B7950B'
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#########################
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# Temporal State Vector #
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#########################
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@ -23,12 +27,10 @@ CAR_OUTLINE = '#B7950B'
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class TemporalState:
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def __init__(self, x, y, psi):
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"""
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Temporal State Vector containing car pose (x, y, psi) and velocity
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Temporal State Vector containing car pose (x, y, psi)
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:param x: x position in global coordinate system | [m]
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:param y: y position in global coordinate system | [m]
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:param psi: yaw angle | [rad]
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:param v_x: velocity in x direction (car frame) | [m/s]
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:param v_y: velocity in y direction (car frame) | [m/s]
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"""
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self.x = x
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self.y = y
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@ -41,7 +43,6 @@ class TemporalState:
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Overload Sum-Add operator.
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:param other: numpy array to be added to state vector
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"""
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for state_id in range(len(self.members)):
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vars(self)[self.members[state_id]] += other[state_id]
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return self
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@ -59,7 +60,8 @@ class SpatialState(ABC):
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@abstractmethod
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def __init__(self):
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self.members = None
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pass
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self.e_y = None
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self.e_psi = None
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def __getitem__(self, item):
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if isinstance(item, int):
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@ -92,7 +94,7 @@ class SpatialState(ABC):
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class SimpleSpatialState(SpatialState):
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def __init__(self, e_y, e_psi, t):
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def __init__(self, e_y=0.0, e_psi=0.0, t=0.0):
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"""
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Simplified Spatial State Vector containing orthogonal deviation from
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reference path (e_y), difference in orientation (e_psi) and velocity
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@ -114,18 +116,21 @@ class SimpleSpatialState(SpatialState):
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####################################
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class SpatialBicycleModel(ABC):
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def __init__(self, reference_path, length, width):
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def __init__(self, reference_path, length, width, Ts):
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"""
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Abstract Base Class for Spatial Reformulation of Bicycle Model.
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:param reference_path: reference path object to follow
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:param length: length of car in m
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:param width: width of car in m
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:param Ts: sampling time of model
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"""
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# Precision
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self.eps = 1e-12
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# Car Parameters
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self.l = length
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self.w = width
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self.length = length
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self.width = width
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self.safety_margin = self._compute_safety_margin()
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# Reference Path
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@ -134,8 +139,8 @@ class SpatialBicycleModel(ABC):
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# Set initial distance traveled
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self.s = 0.0
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# Set sampling time to None (Initialization required)
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self.sampling_time = None
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# Set sampling time
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self.Ts = Ts
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# Set initial waypoint ID
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self.wp_id = 0
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@ -149,69 +154,76 @@ class SpatialBicycleModel(ABC):
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# Declare temporal state variable | Initialization in sub-class
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self.temporal_state = None
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# Declare system matrices of linearized model | Used for MPC
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self.A, self.B = None, None
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def s2t(self, reference_waypoint=None, reference_state=None):
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def s2t(self, reference_waypoint, reference_state):
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"""
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Convert spatial state to temporal state. Either convert self.spatial_
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state with current waypoint as reference or provide reference waypoint
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and reference_state.
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:return x, y, psi
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Convert spatial state to temporal state given a reference waypoint.
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:param reference_waypoint: waypoint object to use as reference
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:param reference_state: state vector as np.array to use as reference
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:return Temporal State equivalent to reference state
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"""
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# Compute spatial state for current waypoint if no waypoint given
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if reference_waypoint is None and reference_state is None:
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# compute temporal state variables
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x = self.current_waypoint.x - self.spatial_state.e_y * np.sin(
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self.current_waypoint.psi)
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y = self.current_waypoint.y + self.spatial_state.e_y * np.cos(
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self.current_waypoint.psi)
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psi = self.current_waypoint.psi + self.spatial_state.e_psi
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else:
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# compute temporal state variables
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# Compute temporal state variables
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if isinstance(reference_state, np.ndarray):
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x = reference_waypoint.x - reference_state[0] * np.sin(
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reference_waypoint.psi)
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y = reference_waypoint.y + reference_state[0] * np.cos(
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reference_waypoint.psi)
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psi = reference_waypoint.psi + reference_state[1]
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elif isinstance(reference_state, SpatialState):
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x = reference_waypoint.x - reference_state.e_y * np.sin(
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reference_waypoint.psi)
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y = reference_waypoint.y + reference_state.e_y * np.cos(
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reference_waypoint.psi)
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psi = reference_waypoint.psi + reference_state.e_psi
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else:
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print('Reference State type not supported!')
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x, y, psi = None, None, None
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exit(1)
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return x, y, psi
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return TemporalState(x, y, psi)
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def t2s(self):
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def t2s(self, reference_waypoint, reference_state):
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"""
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Convert spatial state to temporal state. Either convert self.spatial_
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state with current waypoint as reference or provide reference waypoint
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and reference_state.
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:return x, y, psi
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:return Spatial State equivalent to reference state
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"""
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# compute temporal state variables
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e_y = np.cos(self.current_waypoint.psi) * \
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(self.temporal_state.y - self.current_waypoint.y) - \
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np.sin(self.current_waypoint.psi) * (self.temporal_state.x -
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self.current_waypoint.x)
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e_psi = self.temporal_state.psi - self.current_waypoint.psi
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e_psi = np.mod(e_psi + math.pi, 2*math.pi) - math.pi
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t = 0
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# Compute spatial state variables
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if isinstance(reference_state, np.ndarray):
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e_y = np.cos(reference_waypoint.psi) * \
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(reference_state[1] - reference_waypoint.y) - \
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np.sin(reference_waypoint.psi) * (reference_state[0] -
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reference_waypoint.x)
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e_psi = reference_state[2] - reference_waypoint.psi
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# Ensure e_psi is kept within range (-pi, pi]
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e_psi = np.mod(e_psi + math.pi, 2 * math.pi) - math.pi
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elif isinstance(reference_state, TemporalState):
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e_y = np.cos(reference_waypoint.psi) * \
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(reference_state.y - reference_waypoint.y) - \
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np.sin(reference_waypoint.psi) * (reference_state.x -
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reference_waypoint.x)
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e_psi = reference_state.psi - reference_waypoint.psi
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# Ensure e_psi is kept within range (-pi, pi]
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e_psi = np.mod(e_psi + math.pi, 2 * math.pi) - math.pi
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else:
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print('Reference State type not supported!')
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e_y, e_psi = None, None
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exit(1)
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# time state can be set to zero since it's only relevant for the MPC
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# prediction horizon
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t = 0.0
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return SimpleSpatialState(e_y, e_psi, t)
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def set_sampling_time(self, Ts):
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"""
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Set sampling time of bicycle model.
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:param Ts: sampling time in s
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"""
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self.Ts = Ts
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def drive(self, u):
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"""
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Drive.
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:param u: input vector
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:return: numpy array with spatial derivatives for all state variables
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:param u: input vector containing [v, delta]
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"""
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# Get input signals
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@ -220,7 +232,7 @@ class SpatialBicycleModel(ABC):
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# Compute temporal state derivatives
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x_dot = v * np.cos(self.temporal_state.psi)
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y_dot = v * np.sin(self.temporal_state.psi)
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psi_dot = v / self.l * np.tan(delta)
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psi_dot = v / self.length * np.tan(delta)
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temporal_derivatives = np.array([x_dot, y_dot, psi_dot])
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# Update spatial state (Forward Euler Approximation)
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@ -239,15 +251,13 @@ class SpatialBicycleModel(ABC):
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"""
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# Model ellipsoid around the car
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length = self.l / np.sqrt(2)
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width = self.w / np.sqrt(2)
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widht = 0
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return length, width
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safety_margin = self.width / np.sqrt(2)
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return safety_margin
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def get_current_waypoint(self):
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"""
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Create waypoint on reference path at current location of car by
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interpolation information from given path waypoints.
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Get closest waypoint on reference path based on car's current location.
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"""
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# Compute cumulative path length
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@ -256,7 +266,7 @@ class SpatialBicycleModel(ABC):
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# so far
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greater_than_threshold = length_cum > self.s
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next_wp_id = greater_than_threshold.searchsorted(True)
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# Get previous index for interpolation
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# Get previous index
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prev_wp_id = next_wp_id - 1
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# Get distance traveled for both enclosing waypoints
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@ -269,19 +279,6 @@ class SpatialBicycleModel(ABC):
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else:
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self.wp_id = prev_wp_id
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self.current_waypoint = self.reference_path.waypoints[prev_wp_id]
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#
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# # Weight for next waypoint
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# w = (s_next - self.s) / (s_next - s_prev)
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#
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# # Interpolate between the two waypoints
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# prev_wp = self.reference_path.waypoints[prev_wp_id]
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# next_wp = self.reference_path.waypoints[next_wp_id]
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# x = w * next_wp.x + (1 - w) * prev_wp.x
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# y = w * next_wp.y + (1 - w) * prev_wp.y
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# psi = w * next_wp.psi + (1 - w) * prev_wp.psi
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# kappa = w * next_wp.kappa + (1 - w) * prev_wp.kappa
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def show(self):
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"""
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@ -293,24 +290,22 @@ class SpatialBicycleModel(ABC):
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# Get current angle with respect to x-axis
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yaw = np.rad2deg(self.temporal_state.psi)
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# Draw rectangle
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car = plt_patches.Rectangle(cog, width=self.l, height=self.w,
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angle=yaw, facecolor=CAR, edgecolor=CAR_OUTLINE, zorder=20)
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car = plt_patches.Rectangle(cog, width=self.length, height=self.width,
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angle=yaw, facecolor=CAR,
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edgecolor=CAR_OUTLINE, zorder=20)
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# Shift center rectangle to match center of the car
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car.set_x(car.get_x() - (self.l/2 * np.cos(self.temporal_state.psi) -
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self.w/2 * np.sin(self.temporal_state.psi)))
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car.set_y(car.get_y() - (self.w/2 * np.cos(self.temporal_state.psi) +
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self.l/2 * np.sin(self.temporal_state.psi)))
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# Show safety margin
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safety_margin = plt_patches.Ellipse(cog, width=2*self.safety_margin[0],
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height=2*self.safety_margin[1],
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angle=yaw,
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fill=False, edgecolor=CAR, zorder=20)
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car.set_x(car.get_x() - (self.length / 2 *
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np.cos(self.temporal_state.psi) -
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self.width / 2 *
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np.sin(self.temporal_state.psi)))
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car.set_y(car.get_y() - (self.width / 2 *
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np.cos(self.temporal_state.psi) +
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self.length / 2 *
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np.sin(self.temporal_state.psi)))
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# Add rectangle to current axis
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ax = plt.gca()
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#ax.add_patch(safety_margin)
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ax.add_patch(car)
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@abstractmethod
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@ -318,7 +313,7 @@ class SpatialBicycleModel(ABC):
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pass
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@abstractmethod
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def linearize(self):
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def linearize(self, v_ref, kappa_ref, delta_s):
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pass
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@ -327,49 +322,29 @@ class SpatialBicycleModel(ABC):
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#################
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class BicycleModel(SpatialBicycleModel):
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def __init__(self, length, width, reference_path, e_y, e_psi, t):
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def __init__(self, reference_path, length, width, Ts):
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"""
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Simplified Spatial Bicycle Model. Spatial Reformulation of Kinematic
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Bicycle Model. Uses Simplified Spatial State.
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:param reference_path: reference path model is supposed to follow
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:param length: length of the car in m
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:param width: with of the car in m
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:param reference_path: reference path model is supposed to follow
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:param e_y: deviation from reference path | [m]
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:param e_psi: heading offset from reference path | [rad]
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:param Ts: sampling time of model in s
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"""
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# Initialize base class
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super(BicycleModel, self).__init__(reference_path, length=length,
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width=width)
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width=width, Ts=Ts)
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# Initialize spatial state
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self.spatial_state = SimpleSpatialState(e_y, e_psi, t)
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self.spatial_state = SimpleSpatialState()
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# Number of spatial state variables
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self.n_states = len(self.spatial_state)
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# Initialize temporal state
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self.temporal_state = self.s2t()
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def s2t(self, reference_waypoint=None, reference_state=None):
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"""
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Convert spatial state to temporal state. Either convert self.spatial_
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state with current waypoint as reference or provide reference waypoint
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and reference_state.
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:return temporal state equivalent to self.spatial_state or provided
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reference state
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"""
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if reference_state is None and reference_waypoint is None:
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# Get pose information from base class implementation
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x, y, psi = super(BicycleModel, self).s2t()
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# Compute simplified velocities
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else:
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# Get pose information from base class implementation
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x, y, psi = super(BicycleModel, self).s2t(reference_waypoint,
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reference_state)
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return TemporalState(x, y, psi)
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self.temporal_state = self.s2t(reference_state=self.spatial_state,
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reference_waypoint=self.current_waypoint)
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def get_temporal_derivatives(self, state, input, kappa):
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"""
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@ -380,6 +355,7 @@ class BicycleModel(SpatialBicycleModel):
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:return: temporal derivatives of distance, angle and velocity
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"""
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# Get state and input variables
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e_y, e_psi, t = state
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v, delta = input
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@ -387,7 +363,7 @@ class BicycleModel(SpatialBicycleModel):
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s_dot = 1 / (1 - (e_y * kappa)) * v * np.cos(e_psi)
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# Compute yaw angle rate of change
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psi_dot = v / self.l * np.tan(delta)
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psi_dot = v / self.length * np.tan(delta)
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return s_dot, psi_dot
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@ -400,6 +376,7 @@ class BicycleModel(SpatialBicycleModel):
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:return: numpy array with spatial derivatives for all state variables
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"""
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# Get state and input variables
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e_y, e_psi, t = state
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v, delta = input
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@ -413,36 +390,30 @@ class BicycleModel(SpatialBicycleModel):
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return np.array([d_e_y_d_s, d_e_psi_d_s, d_t_d_s])
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def linearize(self, v=None, kappa_r=None, delta_s=None):
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def linearize(self, v_ref, kappa_ref, delta_s):
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"""
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Linearize the system equations around the current state and waypoint.
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:param kappa_r: kappa of waypoint around which to linearize
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Linearize the system equations around provided reference values.
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:param v_ref: velocity reference around which to linearize
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:param kappa_ref: kappa of waypoint around which to linearize
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:param delta_s: distance between current waypoint and next waypoint
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"""
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# Get linearization state
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if kappa_r is None and delta_s is None:
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# Get curvature of linearization waypoint
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kappa_r = self.reference_path.waypoints[self.wp_id].kappa
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# Get delta_s
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next_waypoint = self.reference_path.waypoints[self.wp_id + 1]
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delta_s = next_waypoint - self.current_waypoint
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###################
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# System Matrices #
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###################
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# Construct Jacobian Matrix
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a_1 = np.array([1, delta_s, 0])
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a_2 = np.array([-kappa_r**2*delta_s, 1, 0])
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a_3 = np.array([-kappa_r/v*delta_s, 0, 1])
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a_1 = np.array([1, delta_s, 0])
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a_2 = np.array([-kappa_ref ** 2 * delta_s, 1, 0])
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a_3 = np.array([-kappa_ref / v_ref * delta_s, 0, 1])
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b_1 = np.array([0, 0])
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b_2 = np.array([0, delta_s])
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b_3 = np.array([-1/(v**2)*delta_s, 0])
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b_1 = np.array([0, 0])
|
||||
b_2 = np.array([0, delta_s])
|
||||
b_3 = np.array([-1 / (v_ref ** 2) * delta_s, 0])
|
||||
|
||||
f = np.array([0.0, 0.0, 1/v*delta_s])
|
||||
f = np.array([0.0, 0.0, 1 / v_ref * delta_s])
|
||||
|
||||
A = np.stack((a_1, a_2, a_3), axis=0)
|
||||
B = np.stack((b_1, b_2, b_3), axis=0)
|
||||
|
||||
return f, A, B
|
||||
return f, A, B
|
||||
|
|
|
|||
Loading…
Reference in New Issue