Added a new demo: minTimeBvp

also cleaned up the demo readme file

demo/minTimeBvp/MAIN.m

@@ -0,0 +1,90 @@
+% MAIN - Minimum Time Boundary Value Problem
+%
+% Solve a minimum-time boundary value problem with simple dynamics (chain
+% integrator) and limits on the state and control. Scalar trajectory.
+%
+% Here we will solve a scalar trajectory, where the position, velocity, 
+% and acceleration are states. The jerk (derivative of acceleration) will
+% be the only control.
+% 
+
+clc; clear;
+addpath ../../
+
+% Kinematic Limits:
+xLim = [0, 4]; % position
+vLim = [-2, 2]; % velocity
+aLim = [-4, 4]; % acceleration
+jLim = 5*[-8, 8]; % jerk 
+
+% Boundary value problem:
+xBegin = xLim(1);  % initial state
+vBegin = 0;
+aBegin = 0;
+xFinal = xLim(2);  % final state
+vFinal = 0;
+aFinal = 0;
+
+% User-defined dynamics and objective functions
+problem.func.dynamics = @(t,x,u)( scalarChainIntegrator(x,u) );
+problem.func.bndObj = @(t0,x0,tF,xF)( tF - t0 ); % minimum time  -- primary objective
+problem.func.pathObj = @(t,x,u)( 0.001*u.^2 ); %minimum jerk  -- regularization
+
+% Problem boundsTime
+problem.bounds.initialTime.low = 0;
+problem.bounds.initialTime.upp = 0;
+problem.bounds.finalTime.low = 0.1;
+problem.bounds.finalTime.upp = 10;
+
+problem.bounds.state.low = [xLim(1); vLim(1); aLim(1)];
+problem.bounds.state.upp = [xLim(2); vLim(2); aLim(2)];
+problem.bounds.initialState.low = [xBegin; vBegin; aBegin];
+problem.bounds.initialState.upp = [xBegin; vBegin; aBegin];
+problem.bounds.finalState.low = [xFinal; vFinal; aFinal];
+problem.bounds.finalState.upp = [xFinal; vFinal; aFinal];
+
+problem.bounds.control.low = jLim(1);
+problem.bounds.control.upp = jLim(2); 
+
+% Guess at the initial trajectory
+problem.guess.time = [0,2];
+problem.guess.state = [[xBegin; vBegin; aBegin], [xFinal; vFinal; aFinal]];
+problem.guess.control = [0, 0];
+
+% Select a solver:
+problem.options(1).method = 'trapezoid';
+problem.options(1).trapezoid.nGrid = 8;
+problem.options(2).method = 'trapezoid';
+problem.options(2).trapezoid.nGrid = 16;
+problem.options(3).method = 'hermiteSimpson';
+problem.options(3).hermiteSimpson.nSegment = 15;
+
+% Solve the problem
+soln = optimTraj(problem);
+t = soln(end).grid.time;
+q = soln(end).grid.state(1,:);
+dq = soln(end).grid.state(2,:);
+ddq = soln(end).grid.state(3,:);
+u = soln(end).grid.control;
+
+% Plot the solution:
+figure(1); clf;
+
+subplot(4,1,1)
+plot(t,q)
+ylabel('q')
+title('Minimum-time boundary value problem');
+
+subplot(4,1,2)
+plot(t,dq)
+ylabel('dq')
+
+subplot(4,1,3)
+plot(t,ddq)
+ylabel('ddq')
+
+subplot(4,1,4)
+plot(t,u)
+ylabel('dddq')
+
+

demo/minTimeBvp/README.md

@@ -0,0 +1,3 @@
+# README  --  Minimum-Time Boundary Value Problem
+
+This example show how to compute the a minimum-time solution for boundary value problem with kinematic limits: position, velocity, acceleration, and jerk.

demo/minTimeBvp/scalarChainIntegrator.m

@@ -0,0 +1,17 @@
+function dx = scalarChainIntegrator(x,u)
+% dx = scalarChainIntegrator(x,u)
+%
+% Computes the dynamics for a scalar chain integrator:
+%     dx(1) = x(2)
+%     dx(2) = x(3)
+%     ...
+%     dx(n) = u
+%
+
+if size(x,1) == 1
+    dx = u;
+else
+    dx = [x(2:end, :); u];
+end
+
+end

demo/readme.md

@@ -1,40 +1,39 @@
-# README.txt -- OptimTraj/demo
+# README.txt  --  `OptimTraj/demo`
 
-This directory contains a collection of example problems for trajectory optimization, all solved using OptimTraj. Each example contains a MAIN.m file, which is the entry-point file for the example. 
+This directory contains a collection of example problems for trajectory optimization, all solved using `OptimTraj`. Each example contains a MAIN.m file, which is the entry-point file for the example.
 
-If the dynamics or constraints are complicated, then a script Derive_*.m is provided to use the symbolic toolbox to derive these equations. Any files with the autoGen_fileName.m are created by the Matlab symbolic toolbox, and should not be edited. In each case, they will be called by a regular function named fileName.m.
+If the dynamics or constraints are complicated, then a script `Derive_*.m` is provided to use the symbolic toolbox to derive these equations. Any files with the `autoGen_fileName.m` are created by the Matlab symbolic toolbox, and should not be edited. In each case, they will be called by a regular function named `fileName.m`.
 
-If you find any errors, have comments, or would like to suggest an example problem, just send me an email. Contact Info can be found at either page:
--->  https://github.com/MatthewPeterKelly
--->  www.matthewpeterkelly.com
+If you find any errors, have comments, or would like to suggest an example problem, just send me an email. Contact info can be found at either page:
+ - [https://github.com/MatthewPeterKelly](https://github.com/MatthewPeterKelly)
+ - [www.matthewpeterkelly.com](www.matthewpeterkelly.com)
 
+## List of Examples:
+The examples are arranged in order from most simple to most complex.
 
-List of Examples:    (Easy --> Hard)
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+- **pendulum:**
+  a simple demo showing basic functionality. Shows how to use analytic gradients.
 
-pendulum:
-  --> a simple demo showing basic functionality. Shows how to use analytic gradients.
+- **minTimeBvp**
+  solves a minimum-time trajectory for a scalar system that has limits on position, velocity, acceleration, and jerk (derivative of acceleration).
 
-cart-pole:
-  --> A standard benchmark for trajectory optimization. Easy to solve for most choices of parameters. 
+- **cart-pole:**
+  A standard benchmark for trajectory optimization. Easy to solve for most choices of parameters.
 
-simpleWalker:
-  --> A double-pendulum model for a walking robot. Pretty easy to set up and solve. 
+- **simpleWalker:**,
+  A double-pendulum model for a walking robot. Pretty easy to set up and solve.
 
-toyCar:
-  --> A fun toy problem finding an optimal trajectory for a car driving over a hilly landscape. Turns out to be a bit tricky due to discontinuity in the solution to the problem. 
+- **toyCar:**
+  A fun toy problem finding an optimal trajectory for a car driving over a hilly landscape. Turns out to be a bit tricky due to discontinuity in the solution to the problem.
 
-acrobot:
-  --> A standard trajectory optimization problem. Somewhat tricky to solve, but easy to set up.
-
-goddard roacket:
-  --> Hard to solve, easy to set up. Optimal rocket thrust trajectory.
-
-five-link biped:
-  --> Easy to solve, very difficult to set up. Requires advanced knowledge of dynamics and hybrid systems.
-
-pointMass:
-  --> A pathological example. Shows various ways to handle discontinuities.
+- **acrobot:**
+  A standard trajectory optimization problem. Somewhat tricky to solve, but easy to set up.
 
+- **goddard rocket:**
+  Hard to solve, easy to set up. Optimal rocket thrust trajectory.
 
+- **five-link biped:**
+  Easy to solve, very difficult to set up. Requires advanced knowledge of dynamics and hybrid systems.
 
+- **pointMass:**
+  A pathological example. Shows various ways to handle discontinuities.