====== Bipedal Robot Locomotion: Kinematics and Plotting  ======
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This week we'll set-up some infrastructure in your Biped Matlab class to visualize arbitrary joint trajectories relative to different (useful) frames of reference.

**1.** Add a new function to your class:

<code>[ frame1, frame2, biped_frames ] = fwd_kinematics( obj, a_ref_frame )</code> 

When ''a_ref_frame'' is set to 'TORSO', the method should compute and return the SE(2) pose of the right and left foot frames (and assign them to method outputs, ''frame1'' and ''frame2'') relative to the torso frame. When ''a_ref_frame'' is set to 'LEFT_FOOT', it should return the SE(2) pose of the torso and right foot frames (again, assigned to method outputs, ''frame1'' and ''frame2'') relative to the left foot frame. And, finally, when ''a_ref_frame'' is set to 'RIGHT_FOOT', it should return the SE(2) pose of the torso and left foot frames relative to the right foot frame.

''biped_frames'' should contain the SE(2) pose of every intermediate frame (or all frames, if you'd like) of the biped; making this output a cell array might be easiest.

This new method will replace last week's ''fwd_kinematics( ... )'' method.

**2.** Add a new property to the Biped class, ''stance'', which will indicate the current reference/stance frame of the biped (eg. it may hold values of 'TORSO', 'LEFT_FOOT' or 'RIGHT_FOOT'). Add a 'setter' method, ''set_stance( obj, a_stance )'' to set this new class property.

**3.** Update ''plotTF( obj )'' to plot your stick figure biped (and any frames) relative to the current ''stance'' frame. The ''stance'' frame's spatial pose (eg. torso, left foot or right foot) should be the identity. This method should make use of your new ''fwd_kinematics( obj, a_ref_frame )'' method.

Pick a joint configuration for the biped. Display a new plot of the biped (in that joint configuration) for each case where ''stance'' is set to 'TORSO', 'LEFT_FOOT' and 'RIGHT_FOOT'.

**4.** Add a new method to your Biped class:

<code>animateTrajectory( obj, a_time, a_joint_traj )</code>

''a_joint_traj'' is a 6 x N matrix specifying the trajectory of all 6 joints over N time instants. ''a_time'' is the corresponding N-length time vector. This new method should, for each time instant of ''a_time'', compute the biped forward kinematics for the joint values at that time instant and update a stick figure plot of the biped (including plotted biped frames). The end result should be a plot/animation that displays the stick figure biped moving through the specified joint trajectory, ''a_joint_traj'', in sync with time vector, ''a_time''.

Construct a 5-10 second long joint trajectory for your biped. Run this method to play an animation of the biped executing that joint trajectory. Do this for each possible value of ''stance'' (ie. 'TORSO', 'LEFT_FOOT', 'RIGHT_FOOT').

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