trajopt documentation

Author: thowell

docs/src/trajectory_optimization.md

@@ -8,26 +8,36 @@ Dojo provides dynamics constraints and Jacobians in order to perform trajectory
 <img src="../../examples/animations/quadruped_min.gif" width="200"/>
 ```
 
+A [Unitree A1](https://www.unitree.com/products/a1/) takes a number of forward steps. There are costs on a kinematic gait and control usage, as well as an augmented Lagrangian (i.e., soft) constraint on the the robot's final pose. The maximal representation is converted to a minimal one for optimization. Additionally, slack controls are utilized early on to aid the optimizer before being driven to zero by a constraint to achieve a dynamically feasible trajectory.
+
 ## [Atlas](../../examples/trajectory_optimization/atlas_min.jl)
 
 ```@raw html
 <img src="../../examples/animations/atlas_ilqr.gif" width="200"/>
 ```
 
+The Atlas v5 humanoid (sans arms) takes a number of forward steps. Similar to the quadruped example, there are costs on control effort and deviations from a kinematic plan, a minimal representation is utilized, and the optimizer is aided by slack controls.
+
 ## [Block](../../examples/trajectory_optimization/box.jl)
 
 ```@raw html
 <img src="../../examples/animations/box_right.gif" width="200"/>
 ```
 
+A block is moved to a goal location by applying forces to its center of mass. The optimizer is initialized with zero control and utilizes smooth gradients from Dojo to find a motion that overcomes friction to slide towards the goal.
+
 ## [Raibert Hopper](../../examples/trajectory_optimization/hopper_max.jl)
 
 ```@raw html
 <img src="../../examples/animations/hopper_max.gif" width="100"/>
 ```
 
+A hopping robot, inspired by the [Raibert Hopper](https://dspace.mit.edu/handle/1721.1/6820), is tasked with moving to a goal location. The optimizer finds a single hop trajectory to reach its goal pose.
+
 ## [Cart-pole](../../examples/trajectory_optimization/cartpole_max.jl)
 
 ```@raw html
 <img src="../../examples/animations/cartpole_max.gif" width="200"/>
 ```
+
+This classic system is tasked with performing a swing-up. Examples are provided performing optimization with both maximal and minimal representations.