{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Optimal control problem 1\n", "\n", "Matthew Kelly: An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* import the packages\n", "* serial multiple shooting (loop)\n", "* parallel multiple shooting (map)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "import simulatetraj as a\n", "import casadi as cs\n", "import matplotlib.pyplot as plt\n", "loop=True\n", "map=True" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* refer 2.1 in paper for the optimal control problem.\n", "* Integration object for each shooting interval created. m denotes number of inverals in a shooting interval." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "m=1\n", "sym_dict=a.get_symbols(n_x=2,n_u=1,n_p=0,N=m)\n", "f=cs.vertcat(sym_dict['x'][1],sym_dict['u'])\n", "_=a.scale_ode(sym_dict=sym_dict,f=f)\n", "_=a.integrator(sym_dict=sym_dict,options=None)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* transcribe and solve using Opti()\n", "* traditional for loop" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is Ipopt version 3.14.11, running with linear solver MUMPS 5.4.1.\n", "\n", "Number of nonzeros in equality constraint Jacobian...: 1404\n", "Number of nonzeros in inequality constraint Jacobian.: 0\n", "Number of nonzeros in Lagrangian Hessian.............: 200\n", "\n", "Total number of variables............................: 602\n", " variables with only lower bounds: 0\n", " variables with lower and upper bounds: 0\n", " variables with only upper bounds: 0\n", "Total number of equality constraints.................: 404\n", "Total number of inequality constraints...............: 0\n", " inequality constraints with only lower bounds: 0\n", " inequality constraints with lower and upper bounds: 0\n", " inequality constraints with only upper bounds: 0\n", "\n", "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", " 0 3.3417085e-01 1.00e+00 2.97e-10 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0\n", " 1 1.2000205e+01 3.96e-08 8.08e-08 -1.7 6.97e+00 - 1.00e+00 1.00e+00h 1\n", " 2 1.2000301e+01 1.23e-13 2.19e-13 -8.6 2.62e-05 - 1.00e+00 1.00e+00h 1\n", "\n", "Number of Iterations....: 2\n", "\n", " (scaled) (unscaled)\n", "Objective...............: 1.2000300799006434e+01 1.2000300799006434e+01\n", "Dual infeasibility......: 2.1883536649447421e-13 2.1883536649447421e-13\n", "Constraint violation....: 1.2290168882600483e-13 1.2290168882600483e-13\n", "Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00\n", "Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00\n", "Overall NLP error.......: 2.1883536649447421e-13 2.1883536649447421e-13\n", "\n", "\n", "Number of objective function evaluations = 3\n", "Number of objective gradient evaluations = 3\n", "Number of equality constraint evaluations = 3\n", "Number of inequality constraint evaluations = 0\n", "Number of equality constraint Jacobian evaluations = 3\n", "Number of inequality constraint Jacobian evaluations = 0\n", "Number of Lagrangian Hessian evaluations = 2\n", "Total seconds in IPOPT = 0.139\n", "\n", "EXIT: Optimal Solution Found.\n", " solver : t_proc (avg) t_wall (avg) n_eval\n", " nlp_f | 0 ( 0) 6.00us ( 2.00us) 3\n", " nlp_g | 26.00ms ( 8.67ms) 12.47ms ( 4.16ms) 3\n", " nlp_grad_f | 0 ( 0) 28.00us ( 7.00us) 4\n", " nlp_hess_l | 42.00ms ( 21.00ms) 43.92ms ( 21.96ms) 2\n", " nlp_jac_g | 72.00ms ( 18.00ms) 73.38ms ( 18.34ms) 4\n", " total | 140.00ms (140.00ms) 139.35ms (139.35ms) 1\n", "Objective value: Paper - 12 | code - 12.000300799006434\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if loop:\n", " nlp=cs.Opti()\n", " N=200\n", " grid=cs.linspace(0,1,N+1)\n", " X=nlp.variable(sym_dict['n_x'],N+1)\n", " U=nlp.variable(sym_dict['n_u'],N)\n", " obj=cs.sumsqr(U)*(grid[1]-grid[0])\n", " nlp.minimize(obj)\n", " x0=cs.DM([0,0])\n", " xf=cs.DM([1,0])\n", " nlp.subject_to(X[:,0]-x0==0)\n", " for i in range(N):\n", " a.simulate(sym_dict=sym_dict,t0=grid[i],tf=grid[i+1],x0=X[:,i],u=cs.repmat(U[:,i],1,m))\n", " nlp.subject_to(sym_dict['x_res'][:,-1]-X[:,i+1]==0)\n", " nlp.subject_to(X[:,-1]-xf==0)\n", " nlp.solver('ipopt')\n", " nlp.set_initial(X[0,:],cs.np.linspace(0,1,N+1))\n", " nlp.set_initial(X[1,:],cs.np.linspace(0,1,N+1))\n", " nlp.set_initial(U,cs.np.linspace(0,1,N))\n", " sol=nlp.solve()\n", " obj_val=sol.value(nlp.f)\n", " print(f'Objective value: Paper - 12 | code - {obj_val}')\n", " plt.figure()\n", " plt.plot(grid.full(),sol.value(X[0,:]),label='x_1')\n", " plt.plot(grid.full(),sol.value(X[1,:]),label='x_2')\n", " plt.legend()\n", " plt.grid(True)\n", " plt.show()\n", " plt.figure()\n", " plt.step(grid.full(),cs.np.hstack((cs.np.nan,sol.value(U))),label='u')\n", " plt.legend()\n", " plt.grid(True)\n", " plt.show()\n", "else:\n", " pass " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* same NLP but uses vectorization/maps\n", "* little faster" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "This is Ipopt version 3.14.11, running with linear solver MUMPS 5.4.1.\n", "\n", "Number of nonzeros in equality constraint Jacobian...: 1404\n", "Number of nonzeros in inequality constraint Jacobian.: 0\n", "Number of nonzeros in Lagrangian Hessian.............: 200\n", "\n", "Total number of variables............................: 602\n", " variables with only lower bounds: 0\n", " variables with lower and upper bounds: 0\n", " variables with only upper bounds: 0\n", "Total number of equality constraints.................: 404\n", "Total number of inequality constraints...............: 0\n", " inequality constraints with only lower bounds: 0\n", " inequality constraints with lower and upper bounds: 0\n", " inequality constraints with only upper bounds: 0\n", "\n", "iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls\n", " 0 3.3417085e-01 1.00e+00 3.20e-10 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0\n", " 1 1.2000205e+01 3.93e-08 8.93e-08 -1.7 6.97e+00 - 1.00e+00 1.00e+00h 1\n", " 2 1.2000301e+01 1.34e-13 2.65e-13 -8.6 2.64e-05 - 1.00e+00 1.00e+00h 1\n", "\n", "Number of Iterations....: 2\n", "\n", " (scaled) (unscaled)\n", "Objective...............: 1.2000300799005419e+01 1.2000300799005419e+01\n", "Dual infeasibility......: 2.6486018239735287e-13 2.6486018239735287e-13\n", "Constraint violation....: 1.3411494137471891e-13 1.3411494137471891e-13\n", "Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00\n", "Complementarity.........: 0.0000000000000000e+00 0.0000000000000000e+00\n", "Overall NLP error.......: 2.6486018239735287e-13 2.6486018239735287e-13\n", "\n", "\n", "Number of objective function evaluations = 3\n", "Number of objective gradient evaluations = 3\n", "Number of equality constraint evaluations = 3\n", "Number of inequality constraint evaluations = 0\n", "Number of equality constraint Jacobian evaluations = 3\n", "Number of inequality constraint Jacobian evaluations = 0\n", "Number of Lagrangian Hessian evaluations = 2\n", "Total seconds in IPOPT = 0.099\n", "\n", "EXIT: Optimal Solution Found.\n", " solver : t_proc (avg) t_wall (avg) n_eval\n", " nlp_f | 0 ( 0) 13.00us ( 4.33us) 3\n", " nlp_g | 20.00ms ( 6.67ms) 9.71ms ( 3.24ms) 3\n", " nlp_grad_f | 0 ( 0) 32.00us ( 8.00us) 4\n", " nlp_hess_l | 15.00ms ( 7.50ms) 25.76ms ( 12.88ms) 2\n", " nlp_jac_g | 46.00ms ( 11.50ms) 51.46ms ( 12.87ms) 4\n", " total | 100.00ms (100.00ms) 99.65ms ( 99.65ms) 1\n", "Objective value: Paper - 12 | code - 12.00030079900542\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "if map:\n", " nlp=cs.Opti()\n", " N=200\n", " grid=cs.linspace(0,1,N+1).T\n", " X=nlp.variable(sym_dict['n_x'],N+1)\n", " U=nlp.variable(sym_dict['n_u'],N)\n", " obj=cs.sumsqr(U)*(grid[1]-grid[0])\n", " int_map=sym_dict['x_n'].map(N,'thread',2)\n", " defect=X[:,1:]-int_map(x0=X[:,0:-1],u=U,p=cs.vertcat(grid[:,0:-1],grid[:,1:]))['xf']\n", " x0=cs.DM([0,0])\n", " xf=cs.DM([1,0])\n", " nlp.minimize(obj)\n", " nlp.subject_to(X[:,0]-x0==0)\n", " nlp.subject_to(defect==0)\n", " nlp.subject_to(X[:,-1]-xf==0)\n", " nlp.solver('ipopt')\n", " nlp.set_initial(X[0,:],cs.np.linspace(0,1,N+1))\n", " nlp.set_initial(X[1,:],cs.np.linspace(0,1,N+1))\n", " nlp.set_initial(U,cs.np.linspace(0,1,N))\n", " sol=nlp.solve()\n", " obj_val=sol.value(nlp.f)\n", " print(f'Objective value: Paper - 12 | code - {obj_val}') \n", " plt.figure()\n", " plt.plot(grid.full().flatten(),sol.value(X[0,:]).flatten(),label='x_1')\n", " plt.plot(grid.full().flatten(),sol.value(X[1,:]).flatten(),label='x_2')\n", " plt.legend()\n", " plt.grid(True)\n", " plt.show()\n", " plt.figure()\n", " plt.step(grid.full().flatten(),cs.np.hstack((cs.np.nan,sol.value(U))).flatten(),label='u')\n", " plt.legend()\n", " plt.grid(True)\n", " plt.show()\n", "else:\n", " pass " ] } ], "metadata": { "kernelspec": { "display_name": ".venv", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.4" } }, "nbformat": 4, "nbformat_minor": 2 }