Pseudo code with arbitrary values of a Simple Bicycle Model given steering change. The x-axis points to the forward direction or the longitudinal direction The y-axis, which represents the lateral direction is positive when it points to the right of the driver The z-axis points to the ground satisfying theContinue Reading
Hybrid A* is a function that differs from A* by the fact that it is continuous but isn’t complete, that is, it can’t always find an optimal solution or a solution, but every solution that it does find is continuous and constrain-able.Continue Reading
MPC is used to optimize control inputs by approximating a reference trajectory using dt, N and T variables in a finite(2-3 seconds) time-horizon. This reference trajectory should encompass very small values of dt which will be multiplied by N (should be a number that when multiplied by dt is 2-3Continue Reading
Is a force(tension force to be exact) that makes a body follow a curved path with a center. The force’s direction is always to the instantaneous center of the path and orthogonal to the motion of the body. The body’s acceleration can be calculated as: a= v^2/r (where v squaredContinue Reading
Unbalanced forces create acceleration in the direction of the Net force. Fy = my” Which is the translational acceleration in the y direction Unbalanced moments create acceleration in the direction of the Net moment/torque around a given axis, where α is the angular acceleration(rad/sec*sec),I – moment of Inertia(3X3). τ =Continue Reading
When a rotor spins it produces thrust(F) and also induces moment(M)(torque) both are measured by radians/sec with omega(ω). The moment induced is in the counter direction(A.K.A yaw – which is rotation around the Z value) when ω is 2*PI the rotor is doing 1 full rotation per second. The formulasContinue Reading
Potential field (represented by a number or tensor, that has a value for each point in space-time) combines attraction to the goal, and repulsion from obstacles in order to plan a path for an autonomous system. most commonly used attractive potential function is: where, ε is a positive scaling factor, p(q, qgoal)Continue Reading
RRT is a searching algorithm applied by building a space filling tree from samples drawn randomly of high-dimensional search spaces . import networkx as nx import numpy as np from sklearn.neighbors import KDTree class RRT: def __init__(self,x_init): self.tree = nx.DiGraph() self.tree.add_node(x_init) def nearest_neighbour(x_rand,rrr): dist=1000 x_rand = np.array(x_rand) for node inContinue Reading
Start by building a very simple network: import numpy as np class NeuralNetwork: def __init__(self, x,y): self.input = x self.y = y self.Weights1 = np.random.randn(self.input.shape[1],5) self.Weights2 = np.random.randn(5,1) self.output = np.zeros(self.y.shape) def sigmoid_z(self,x): #create a sigmoid function z = 1/(1 + np.exp(-x)) return z def sigmoid_z_derivative(self,x): return self.sigmoid_z(x)*(1-self.sigmoid_z(x)) def forwardpropogation(self):Continue Reading
The following two functions should be launched in two separate python threads. They show how easy ROS enables to create a pub/sub relationship for transferring messages between nodes. sub.py *import rospy* from std_msgs.msg import String def talker(): pub = rospy.Publisher(‘chatter’, String, queue_size=10) rospy.init_node(‘talker’, anonymous=True) rate = rospy.Rate(10) # 10hz whileContinue Reading