Update spatial_bicycle_models.py
Add comments. SimpleBicycleModel checked. New Convention: each function call with control signals (D, delta) according to order in control signal returned by MPCmaster
matssteinweg
parent
eabf75c9ad
commit
53d30d46b4
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@ -1,7 +1,4 @@
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import numpy as np
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import math
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import time
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import cvxpy as cp
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from abc import ABC, abstractmethod
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@ -10,9 +7,9 @@ from abc import ABC, abstractmethod
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#########################
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class TemporalState:
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def __init__(self, x, y, psi, v_x=0, v_y=0):
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def __init__(self, x, y, psi, v_x, v_y):
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"""
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Temporal State Vector containing x, y coordinates and heading psi
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Temporal State Vector containing car pose (x, y, psi) and velocity
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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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@ -31,6 +28,10 @@ class TemporalState:
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########################
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class SpatialState(ABC):
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"""
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Spatial State Vector - Abstract Base Class.
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"""
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@abstractmethod
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def __init__(self):
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pass
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@ -41,19 +42,28 @@ class SpatialState(ABC):
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def __len__(self):
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return len(vars(self))
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def list_states(self):
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return list(vars(self).keys())
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def __iadd__(self, other):
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"""
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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, state in enumerate(vars(self).values()):
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vars(self)[list(vars(self).keys())[state_id]] += other[state_id]
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return self
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def list_states(self):
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"""
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Return list of names of all states.
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"""
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return list(vars(self).keys())
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class SimpleSpatialState(SpatialState):
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def __init__(self, e_y, e_psi, v):
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"""
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Temporal State Vector containing x, y coordinates and heading psi
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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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:param e_y: orthogonal deviation from center-line | [m]
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:param e_psi: yaw angle relative to path | [rad]
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:param v: absolute velocity | [m/s]
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@ -68,10 +78,14 @@ class SimpleSpatialState(SpatialState):
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class ExtendedSpatialState(SpatialState):
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def __init__(self, e_y, e_psi, v_x, v_y, omega, t):
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"""
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Temporal State Vector containing x, y coordinates and heading psi
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Extended Spatial State Vector containing separate velocities in x and
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y direction, angular velocity and time
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:param e_y: orthogonal deviation from center-line | [m]
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:param e_psi: yaw angle relative to path | [rad]
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:param v: absolute velocity | [m/s]
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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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:param omega: anglular velocity of the car | [rad/s]
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:param t: simulation time| [s]
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"""
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super(ExtendedSpatialState, self).__init__()
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@ -90,8 +104,8 @@ class ExtendedSpatialState(SpatialState):
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class SpatialBicycleModel(ABC):
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def __init__(self, reference_path):
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"""
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Construct spatial bicycle model.
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:param reference_path: reference path model is supposed to follow
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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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"""
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# Precision
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@ -100,28 +114,34 @@ class SpatialBicycleModel(ABC):
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# Reference Path
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self.reference_path = reference_path
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# set initial distance traveled
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# Set initial distance traveled
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self.s = 0.0
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# set initial waypoint ID
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# Set initial waypoint ID
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self.wp_id = 0
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# set initial waypoint
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# Set initial waypoint
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self.current_waypoint = self.reference_path.waypoints[self.wp_id]
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# initialize spatial state
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# Declare spatial state variable | Initialization in sub-class
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self.spatial_state = None
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def s2t(self, reference_waypoint=None, predicted_state=None):
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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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"""
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Convert spatial state to temporal state. Either convert self.spatial
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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 (e_y, e_psi).
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and reference_state.
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:return x, y, psi
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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 predicted_state is None:
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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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@ -133,52 +153,53 @@ class SpatialBicycleModel(ABC):
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else:
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# compute temporal state variables
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x = reference_waypoint.x - predicted_state[0] * np.sin(
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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 + predicted_state[0] * np.cos(
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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 + predicted_state[1]
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psi = reference_waypoint.psi + reference_state[1]
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return x, y, psi
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def drive(self, delta, D):
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def drive(self, D, delta):
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"""
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Update states of spatial bicycle model.
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:param delta: angular velocity | [rad]
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Update states of spatial bicycle model. Model drive to the next
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waypoint on the reference path.
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:param D: acceleration command | [-1, 1]
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:param delta: angular velocity | [rad]
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"""
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# get spatial derivatives
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spatial_derivatives = self.get_spatial_derivatives(delta, D)
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# Get spatial derivatives
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spatial_derivatives = self.get_spatial_derivatives(D, delta)
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# get delta_s
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# Get delta_s | distance to next waypoint
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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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# update spatial state (euler method)
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# Update spatial state (Forward Euler Approximation)
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self.spatial_state += spatial_derivatives * delta_s
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# assert that unique projections exists
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# Assert that unique projections of car pose onto path exists
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assert self.spatial_state.e_y < (1 / (self.current_waypoint.kappa +
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self.eps))
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# increase waypoint ID
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# Increase waypoint ID
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self.wp_id += 1
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# update current waypoint
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# Update current waypoint
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self.current_waypoint = self.reference_path.waypoints[self.wp_id]
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# update temporal_state to match spatial state
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# Update temporal_state to match spatial state
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self.temporal_state = self.s2t()
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# update s
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# Update s | total driven distance along path
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self.s += delta_s
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# linearize model around new operating point
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# Linearize model around new operating point
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self.A, self.B = self.linearize()
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@abstractmethod
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def get_spatial_derivatives(self, delta, D):
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def get_spatial_derivatives(self, D, delta):
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pass
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@abstractmethod
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@ -193,12 +214,15 @@ class SpatialBicycleModel(ABC):
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class SimpleBicycleModel(SpatialBicycleModel):
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def __init__(self, reference_path, e_y, e_psi, v):
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"""
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Construct spatial bicycle model.
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:param e_y: initial deviation from reference path | [m]
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:param e_psi: initial heading offset from reference path | [rad]
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:param v: initial velocity | [m/s]
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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 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 v: initial velocity | [m/s]
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"""
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# Initialize base class
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super(SimpleBicycleModel, self).__init__(reference_path)
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# Constants
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@ -209,69 +233,62 @@ class SimpleBicycleModel(SpatialBicycleModel):
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self.Cr2 = 0.1
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self.Cr0 = 0.6
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# Spatial state
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# Initialize spatial state
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self.spatial_state = SimpleSpatialState(e_y, e_psi, v)
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# Temporal state
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# Initialize temporal state
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self.temporal_state = self.s2t()
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# Linear System Matrices
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# Compute linear system matrices | Used for MPC
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self.A, self.B = self.linearize()
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def s2t(self, reference_waypoint=None, predicted_state=None):
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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
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:return temporal state equivalent to self.spatial_state
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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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# compute velocity information
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if predicted_state is None and reference_waypoint is None:
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# get information from base class
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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(SimpleBicycleModel, self).s2t()
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# Compute simplified velocities
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v_x = self.spatial_state.v
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v_y = 0
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else:
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# get information from base class
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# Get pose information from base class implementation
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x, y, psi = super(SimpleBicycleModel, self).s2t(reference_waypoint,
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predicted_state)
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v_x = predicted_state[2]
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reference_state)
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v_x = reference_state[2]
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v_y = 0
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return TemporalState(x, y, psi, v_x, v_y)
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def get_velocities(self, delta):
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def get_temporal_derivatives(self, D, delta):
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"""
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Compute relevant velocity components for current update.
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:param delta: steering command
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:return: velocities in x, y and waypoint direction
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"""
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# approximation for small delta
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v_x = self.spatial_state.v
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v_y = self.spatial_state.v * delta * self.C1
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# velocity along waypoint direction
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v_sigma = v_x * np.cos(self.spatial_state.e_psi) - v_y * np.sin(
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self.spatial_state.e_psi)
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return v_x, v_y, v_sigma
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def get_temporal_derivatives(self, v_sigma, delta, D):
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"""
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Compute temporal derivatives needed for state update.
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:param v_sigma: velocity along the path
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:param delta: steering command
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:param D: dutycycle of DC motor
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Compute relevant temporal derivatives needed for state update.
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:param D: duty-cycle of DC motor | [-1, 1]
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:param delta: steering command | [rad]
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:return: temporal derivatives of distance, angle and velocity
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"""
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# velocity along path
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# Compute velocity components | Approximation for small delta
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v_x = self.spatial_state.v
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v_y = self.spatial_state.v * delta * self.C1
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# Compute velocity along waypoint direction
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v_sigma = v_x * np.cos(self.spatial_state.e_psi) - v_y * np.sin(
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self.spatial_state.e_psi)
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# Compute velocity along path
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s_dot = 1 / (1 - (self.spatial_state.e_y * self.current_waypoint.kappa)) * v_sigma
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# angle rate of change
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# Compute yaw angle rate of change
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psi_dot = self.spatial_state.v * delta * self.C2
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# acceleration
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# Compute acceleration
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v_dot = (self.Cm1 - self.Cm2 * self.spatial_state.v) * D - self.Cr2 * (
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self.spatial_state.v ** 2) - self.Cr0 - (
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self.spatial_state.v * delta) ** 2 * self.C2 * self.C1 ** 2
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@ -281,149 +298,159 @@ class SimpleBicycleModel(SpatialBicycleModel):
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def get_spatial_derivatives(self, delta, D):
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"""
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Compute spatial derivatives of all state variables for update.
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:param delta: steering angle
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:param D: duty-cycle
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:return: spatial derivatives for all state variables
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:param delta: steering angle | [rad]
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:param D: duty-cycle of DC motor | [-1, 1]
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:return: numpy array with spatial derivatives for all state variables
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"""
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# Compute velocities
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v_x, v_y, v_sigma = self.get_velocities(delta)
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# Compute temporal derivatives
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s_dot, psi_dot, v_dot = self.get_temporal_derivatives(D, delta)
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# Compute state derivatives
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s_dot, psi_dot, v_dot = self.get_temporal_derivatives(v_sigma, delta,
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D)
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d_e_y = (self.spatial_state.v * np.sin(self.spatial_state.e_psi)
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# Compute spatial derivatives
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d_e_y_d_s = (self.spatial_state.v * np.sin(self.spatial_state.e_psi)
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+ self.spatial_state.v * delta * self.C1 * np.cos(
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self.spatial_state.e_psi)) \
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/ (s_dot + self.eps)
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d_e_psi = (psi_dot / (s_dot + self.eps) - self.current_waypoint.kappa)
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d_v = v_dot / (s_dot + self.eps)
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d_t = 1 / (s_dot + self.eps)
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self.spatial_state.e_psi)) / s_dot
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d_e_psi_d_s = psi_dot / s_dot - self.current_waypoint.kappa
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d_v_d_s = v_dot / s_dot
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return np.array([d_e_y, d_e_psi, d_v])
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return np.array([d_e_y_d_s, d_e_psi_d_s, d_v_d_s])
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def linearize(self, delta=0, D=0):
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def linearize(self, D=0, delta=0):
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"""
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Linearize the system equations around the current state and waypoint.
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:param delta: reference steering angle
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:param D: reference duty-cycle
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:param delta: reference steering angle | [rad]
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:param D: reference duty-cycle of DC-motor | [-1, 1]
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"""
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# get current state
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# Get current state | operating point to linearize around
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e_y = self.spatial_state.e_y
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e_psi = self.spatial_state.e_psi
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v = self.spatial_state.v
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# get information about current waypoint
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# Get curvature of current waypoint
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kappa = self.reference_path.waypoints[self.wp_id].kappa
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# get delta_s
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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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# set helper variables
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v_x = v
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v_y = v * delta * self.C1
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##############################
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# Helper Partial Derivatives #
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##############################
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# Compute velocity components
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v_x = v
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v_y = v * delta * self.C1
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# Compute partial derivatives of s_dot w.r.t. each state variable,
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# input variable and kappa
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s_dot = 1 / (1 - e_y*kappa) * (v_x * np.cos(e_psi) - v_y * np.sin(e_psi))
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d_s_dot_d_e_y = kappa / (1-e_y*kappa)**2 * (v_x * np.cos(e_psi) - v_y * np.sin(e_psi))
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d_s_dot_d_e_psi = 1 / (1 - e_y*kappa) * (-v_x * np.sin(e_psi) - v_y * np.cos(e_psi))
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d_s_dot_d_v = 1 / (1 - e_y*kappa) * (np.cos(e_psi) - delta * self.C1 * np.sin(e_psi))
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d_s_dot_d_t = 0
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# d_s_dot_d_D = 0
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d_s_dot_d_delta = 1 / (1 - e_y*kappa) * (- v * self.C1 * np.sin(e_psi))
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d_s_dot_d_D = 0
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d_s_dot_d_kappa = e_y / (1-e_y*kappa)**2 * (v_x * np.cos(e_psi) - v_y * np.sin(e_psi))
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# Check
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c_1 = (v_x * np.sin(e_psi) + v_y * np.cos(e_psi))
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d_c_1_d_e_y = 0
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d_c_1_d_e_psi = v_x * np.cos(e_psi) - v_y * np.sin(e_psi)
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d_c_1_d_v = np.sin(e_psi) + self.C1 * delta * np.cos(e_psi)
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d_c_1_d_t = 0
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d_c_1_d_delta = self.C1 * v * np.cos(e_psi)
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d_c_1_d_D = 0
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# Check
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# Compute partial derivatives of v_psi w.r.t. each state variable,
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# input variable and kappa
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v_psi = (v_x * np.sin(e_psi) + v_y * np.cos(e_psi))
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# d_v_psi_d_e_y = 0
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d_v_psi_d_e_psi = v_x * np.cos(e_psi) - v_y * np.sin(e_psi)
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d_v_psi_d_v = np.sin(e_psi) + self.C1 * delta * np.cos(e_psi)
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# d_v_psi_d_D = 0
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d_v_psi_d_delta = self.C1 * v * np.cos(e_psi)
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# d_v_psi_d_kappa = 0
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# Compute partial derivatives of psi_dot w.r.t. each state variable,
|
||||
# input variable and kappa
|
||||
psi_dot = v * delta * self.C2
|
||||
d_psi_dot_d_e_y = 0
|
||||
d_psi_dot_d_e_psi = 0
|
||||
# d_psi_dot_d_e_y = 0
|
||||
# d_psi_dot_d_e_psi = 0
|
||||
d_psi_dot_d_v = delta * self.C2
|
||||
d_psi_dot_d_t = 0
|
||||
# d_psi_dot_d_D = 0
|
||||
d_psi_dot_d_delta = v * self.C2
|
||||
d_psi_dot_d_D = 0
|
||||
# Check
|
||||
# d_psi_dot_d_kappa = 0
|
||||
|
||||
v_dot = (self.Cm1 - self.Cm2 * v) * D - self.Cr2 * (v ** 2) - self.Cr0 - (
|
||||
v * delta) ** 2 * self.C2 * (self.C1 ** 2)
|
||||
d_v_dot_d_e_y = 0
|
||||
d_v_dot_d_e_psi = 0
|
||||
d_v_dot_d_v = -self.Cm2 * D - 2 * self.Cr2 * v - 2 * v * (delta ** 2) * self.C2 * (self.C1 ** 2)
|
||||
d_v_dot_d_t = 0
|
||||
d_v_dot_d_delta = -2 * (v ** 2) * delta * self.C2 * self.C1 ** 2
|
||||
# Compute partial derivatives of v_dot w.r.t. each state variable,
|
||||
# input variable and kappa
|
||||
v_dot = (self.Cm1 - self.Cm2 * v) * D - self.Cr2 * (v ** 2) - self.Cr0 \
|
||||
- (v * delta) ** 2 * self.C2 * (self.C1 ** 2)
|
||||
# d_v_dot_d_e_y = 0
|
||||
# d_v_dot_d_e_psi = 0
|
||||
d_v_dot_d_v = -self.Cm2 * D - 2 * self.Cr2 * v - 2 * v * (delta ** 2) \
|
||||
* self.C2 * (self.C1 ** 2)
|
||||
d_v_dot_d_D = self.Cm1 - self.Cm2 * v
|
||||
# Check
|
||||
d_v_dot_d_delta = -2 * (v ** 2) * delta * self.C2 * self.C1 ** 2
|
||||
# d_v_dot_d_kappa = 0
|
||||
|
||||
#######################
|
||||
# Partial Derivatives #
|
||||
#######################
|
||||
#############################
|
||||
# State Partial Derivatives #
|
||||
#############################
|
||||
|
||||
# derivatives for E_Y
|
||||
d_e_y_d_e_y = -c_1 * d_s_dot_d_e_y / (s_dot**2)
|
||||
d_e_y_d_e_psi = (d_c_1_d_e_psi * s_dot - d_s_dot_d_e_psi * c_1) / (s_dot**2)
|
||||
d_e_y_d_v = (d_c_1_d_v * s_dot - d_s_dot_d_v * c_1) / (s_dot**2)
|
||||
d_e_y_d_t = 0
|
||||
# Use pre-computed helper derivatives to compute spatial derivatives of
|
||||
# all state variables using Quotient Rule
|
||||
|
||||
# Compute partial derivatives of e_y w.r.t. each state variable,
|
||||
# input variable and kappa
|
||||
# e_y = v_psi / s_dot
|
||||
d_e_y_d_e_y = - d_s_dot_d_e_y * v_psi / (s_dot**2)
|
||||
d_e_y_d_e_psi = (d_v_psi_d_e_psi * s_dot - d_s_dot_d_e_psi * v_psi) / (s_dot**2)
|
||||
d_e_y_d_v = (d_v_psi_d_v * s_dot - d_s_dot_d_v * v_psi) / (s_dot**2)
|
||||
d_e_y_d_D = 0
|
||||
d_e_y_d_delta = (d_c_1_d_delta * s_dot - d_s_dot_d_delta * c_1) / (s_dot**2)
|
||||
d_e_y_d_kappa = -d_s_dot_d_kappa * c_1 / (s_dot**2)
|
||||
d_e_y_d_delta = (d_v_psi_d_delta * s_dot - d_s_dot_d_delta * v_psi) / (s_dot**2)
|
||||
d_e_y_d_kappa = - d_s_dot_d_kappa * v_psi / (s_dot**2)
|
||||
|
||||
# derivatives for E_PSI
|
||||
d_e_psi_d_e_y = - psi_dot * d_s_dot_d_e_y / (s_dot**2)
|
||||
d_e_psi_d_e_psi = - psi_dot * d_s_dot_d_e_psi / (s_dot**2)
|
||||
d_e_psi_d_v = (d_psi_dot_d_v * s_dot - psi_dot * d_s_dot_d_v) / (s_dot**2)
|
||||
d_e_psi_d_t = 0
|
||||
d_e_psi_d_delta = (d_psi_dot_d_delta * s_dot - psi_dot * d_s_dot_d_delta) / (s_dot**2)
|
||||
# Compute partial derivatives of e_psi w.r.t. each state variable,
|
||||
# input variable and kappa
|
||||
# e_psi = psi_dot / s_dot - kappa
|
||||
d_e_psi_d_e_y = - d_s_dot_d_e_y * psi_dot / (s_dot**2)
|
||||
d_e_psi_d_e_psi = - d_s_dot_d_e_psi * psi_dot / (s_dot**2)
|
||||
d_e_psi_d_v = (d_psi_dot_d_v * s_dot - d_s_dot_d_v * psi_dot) / (s_dot**2)
|
||||
d_e_psi_d_D = 0
|
||||
d_e_psi_d_kappa = -d_s_dot_d_kappa * psi_dot / (s_dot**2) - 1
|
||||
d_e_psi_d_delta = (d_psi_dot_d_delta * s_dot - d_s_dot_d_delta * psi_dot) / (s_dot**2)
|
||||
d_e_psi_d_kappa = - d_s_dot_d_kappa * psi_dot / (s_dot**2) - 1
|
||||
|
||||
# derivatives for V
|
||||
# Compute partial derivatives of v w.r.t. each state variable,
|
||||
# input variable and kappa
|
||||
# v = v_dot / s_dot
|
||||
d_v_d_e_y = - d_s_dot_d_e_y * v_dot / (s_dot**2)
|
||||
d_v_d_e_psi = - d_s_dot_d_e_psi * v_dot / (s_dot**2)
|
||||
d_v_d_v = (d_v_dot_d_v * s_dot - d_s_dot_d_v * v_dot) / (s_dot**2)
|
||||
d_v_d_t = 0
|
||||
d_v_d_delta = (d_v_dot_d_delta * s_dot - d_s_dot_d_delta * v_dot) / (s_dot**2)
|
||||
d_v_d_D = d_v_dot_d_D * s_dot / (s_dot**2)
|
||||
d_v_d_kappa = -d_s_dot_d_kappa * v_dot / (s_dot**2)
|
||||
d_v_d_delta = (d_v_dot_d_delta * s_dot - d_s_dot_d_delta * v_dot) / (s_dot**2)
|
||||
d_v_d_kappa = - d_s_dot_d_kappa * v_dot / (s_dot**2)
|
||||
|
||||
# derivatives for T
|
||||
d_t_d_e_y = - d_s_dot_d_e_y / (s_dot**2)
|
||||
d_t_d_e_psi = - d_s_dot_d_e_psi / (s_dot ** 2)
|
||||
d_t_d_v = - d_s_dot_d_v / (s_dot ** 2)
|
||||
d_t_d_t = 0
|
||||
d_t_d_delta = - d_s_dot_d_delta / (s_dot ** 2)
|
||||
d_t_d_D = 0
|
||||
d_t_d_kappa = - d_s_dot_d_kappa / (s_dot ** 2)
|
||||
#############
|
||||
# Jacobians #
|
||||
#############
|
||||
|
||||
a_1 = np.array([d_e_y_d_e_y, d_e_y_d_e_psi, d_e_y_d_v, d_e_y_d_kappa]) * delta_s
|
||||
a_2 = np.array([d_e_psi_d_e_y, d_e_psi_d_e_psi, d_e_psi_d_v, d_e_psi_d_kappa]) * delta_s
|
||||
a_3 = np.array([d_v_d_e_y, d_v_d_e_psi, d_v_d_v, d_v_d_kappa]) * delta_s
|
||||
a_4 = np.array([0, 0, 0, 1])
|
||||
A = np.stack((a_1, a_2, a_3, a_4), axis=0)
|
||||
A[0, 0] += 1
|
||||
A[1, 1] += 1
|
||||
A[2, 2] += 1
|
||||
# Construct Jacobian Matrix
|
||||
a_1 = np.array([d_e_y_d_e_y, d_e_y_d_e_psi, d_e_y_d_v, d_e_y_d_kappa])
|
||||
a_2 = np.array([d_e_psi_d_e_y, d_e_psi_d_e_psi, d_e_psi_d_v, d_e_psi_d_kappa])
|
||||
a_3 = np.array([d_v_d_e_y, d_v_d_e_psi, d_v_d_v, d_v_d_kappa])
|
||||
|
||||
b_1 = np.array([d_e_y_d_D, d_e_y_d_delta]) * delta_s
|
||||
b_2 = np.array([d_e_psi_d_D, d_e_psi_d_delta]) * delta_s
|
||||
b_3 = np.array([d_v_d_D, d_v_d_delta]) * delta_s
|
||||
b_1 = np.array([d_e_y_d_D, d_e_y_d_delta])
|
||||
b_2 = np.array([d_e_psi_d_D, d_e_psi_d_delta])
|
||||
b_3 = np.array([d_v_d_D, d_v_d_delta])
|
||||
|
||||
# Add extra row for kappa | Allows for updating kappa during MPC
|
||||
# optimization
|
||||
a_4 = np.array([0, 0, 0, 0])
|
||||
b_4 = np.array([0, 0])
|
||||
B = np.stack((b_1, b_2, b_3, b_4), axis=0)
|
||||
|
||||
# set system matrices
|
||||
Ja = np.stack((a_1, a_2, a_3, a_4), axis=0)
|
||||
Jb = np.stack((b_1, b_2, b_3, b_4), axis=0)
|
||||
|
||||
###################
|
||||
# System Matrices #
|
||||
###################
|
||||
|
||||
# Construct system matrices from Jacobians. Multiply by sampling
|
||||
# distance delta_s + add identity matrix (Forward Euler Approximation)
|
||||
A = Ja * delta_s + np.identity(Ja.shape[1])
|
||||
B = Jb * delta_s
|
||||
|
||||
return A, B
|
||||
|
||||
|
||||
|
|
@ -770,13 +797,3 @@ class ExtendedBicycleModel(SpatialBicycleModel):
|
|||
|
||||
# set system matrices
|
||||
return A, B
|
||||
|
||||
|
||||
if __name__ == '__main__':
|
||||
|
||||
state = ExtendedSpatialState(0, 1, 2, 3, 4, 5)
|
||||
print(state[0:2])
|
||||
print(len(state))
|
||||
print(state.list_states())
|
||||
state += np.array([1, 1, 1, 2, 1, 1])
|
||||
print(vars(state))
|
||||
Loading…
Reference in New Issue