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a#V~g*cvA`_TK&YEKbqkjN&yJ+)&B$ZV^^a9 literal 0 HcmV?d00001 diff --git a/mpc_demo/mpc_demo_pybullet.py b/mpc_demo/mpc_demo_pybullet.py index 123b895..7ae683f 100644 --- a/mpc_demo/mpc_demo_pybullet.py +++ b/mpc_demo/mpc_demo_pybullet.py @@ -56,6 +56,7 @@ def run_sim(): """ """ p.connect(p.GUI) + p.resetDebugVisualizerCamera(cameraDistance=1.0, cameraYaw=-90, cameraPitch=-45, cameraTargetPosition=[-0.1,-0.0,0.65]) p.resetSimulation() @@ -113,12 +114,19 @@ def run_sim(): y_history=[] time.sleep(0.5) + input("Press Enter to continue...") while (1): state = get_state(car) x_history.append(state[0]) y_history.append(state[1]) + #add 1 timestep delay to input + state[0]=state[0]+state[2]*np.cos(state[3])*P.dt + state[1]=state[1]+state[2]*np.sin(state[3])*P.dt + state[2]=state[2]+opt_u[0,0]*P.dt + state[3]=state[3]+opt_u[0,0]*np.tan(opt_u[1,0])/0.3*P.dt + #track path in bullet p.addUserDebugLine([state[0],state[1],0],[state[0],state[1],0.5],[1,0,0]) diff --git a/notebooks/MPC_racecar.ipynb b/notebooks/MPC_racecar.ipynb index 8097591..85b9446 100644 --- a/notebooks/MPC_racecar.ipynb +++ b/notebooks/MPC_racecar.ipynb @@ -32,7 +32,7 @@ "\n", "The inputs of the model are:\n", "\n", - "* $v$ linear velocity of the robot\n", + "* $a$ acceleration of the robot\n", "* $\\delta$ angular velocity of the robot\n", "\n", "These are the differential equations f(x,u) of the model:\n", @@ -715,7 +715,6 @@ "u_bar[0,:]=0.5\n", "u_bar[1,:]=0.1\n", "\n", - " \n", "K=road_curve(x0,track)\n", "\n", "# dynamics starting state w.r.t vehicle frame\n", @@ -728,7 +727,6 @@ " A,B,C=get_linear_model(xt,ut)\n", " xt_plus_one = np.squeeze(np.dot(A,xt)+np.dot(B,ut)+C)\n", " x_bar[:,t]= xt_plus_one\n", - " \n", "\n", "x = cp.Variable((N, T+1))\n", "u = cp.Variable((M, T))\n", diff --git a/notebooks/equations.ipynb b/notebooks/equations.ipynb index dec62be..1f27b9b 100644 --- a/notebooks/equations.ipynb +++ b/notebooks/equations.ipynb @@ -350,7 +350,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 11, "metadata": {}, "outputs": [ { @@ -409,7 +409,7 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 12, "metadata": {}, "outputs": [ { @@ -419,7 +419,7 @@ " -0.58083993])" ] }, - "execution_count": 44, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -430,7 +430,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 13, "metadata": {}, "outputs": [ { @@ -475,12 +475,12 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## With BSLINES" + "## With SPLINES" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -523,10 +523,9 @@ "\n", "#fit poly\n", "import scipy\n", - "from scipy.interpolate import BSpline\n", + "from scipy.interpolate import CubicSpline\n", "from scipy.interpolate import PPoly,splrep\n", "spl=splrep(wp_vehicle_frame[0,:], wp_vehicle_frame[1,:])\n", - "coeff\n", "print( spl)\n", "print(PPoly.from_spline(spl).c)\n", "#coeff=np.polyfit(wp_vehicle_frame[0,:], wp_vehicle_frame[1,:], 5, rcond=None, full=False, w=None, cov=False)\n", @@ -536,6 +535,30 @@ "\n" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def spline_planning(qs, qf, ts, tf, dqs=0.0, dqf=0.0, ddqs=0.0, ddqf=0.0):\n", + " \n", + " bc = np.array([ys, dys, ddys, yf, dyf, ddyf]).T \n", + " \n", + " C = np.array([[1, xs, xs**2, xs**3, xs**4, xs**5], #f(xs)=ys\n", + " [0, 1, 2*xs**1, 3*xs**2, 4*xs**3, 5**xs^4], #df(xs)=dys\n", + " [0, 0, 1, 6*xs**1, 12*xs**2, 20**xs^3], #ddf(xs)=ddys\n", + " [1, xf, xf**2, xf**3, xf**4, xf**5], #f(xf)=yf\n", + " [0, 1, 2*xf**1, 3*xf**2, 4*xf**3, 5**xf^4], #df(xf)=dyf\n", + " [0, 0, 1, 6*xf**1, 12*xf**2, 20**xf^3]]) #ddf(xf)=ddyf\n", + " \n", + " #To compute the polynomial coefficients we solve:\n", + " #Ax = B. \n", + " #Matrices A and B must have the same number of rows\n", + " a = np.linalg.lstsq(C,bc)[0]\n", + " return a" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -577,7 +600,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 15, "metadata": {}, "outputs": [ {