A practical guide to learning and control problems in robotics
solved with secondorder optimization
 1 Introduction
 2 Newton’s method for minimization
 3 Forward kinematics (FK) for a planar robot manipulator
 4 Inverse kinematics (IK) for a planar robot manipulator
 5 Encoding with basis functions
 6 Linear quadratic tracking (LQT)

7
iLQR optimization
 7.1 Batch formulation of iLQR
 7.2 Recursive formulation of iLQR
 7.3 Least squares formulation of recursive iLQR
 7.4 Updates by considering step sizes

7.5
iLQR with quadratic cost on
f(x_{t})
 7.5.1 Robot manipulator
 7.5.2 Bounded joint space
 7.5.3 Bounded task space
 7.5.4 Reaching task with robot manipulator and prismatic object boundaries
 7.5.5 Center of mass
 7.5.6 Bimanual robot
 7.5.7 Obstacle avoidance with ellipsoid shapes
 7.5.8 Maintaining a desired distance to an object
 7.5.9 Manipulability tracking
 7.6 iLQR with control primitives
 7.7 iLQR for spacetime optimization
 7.8 iLQR with offdiagonal elements in the precision matrix
 7.9 Car steering
 7.10 Bicopter
 8 Forward dynamics (FD) for a planar robot manipulator
 References
 A System dynamics at trajectory level
 B Derivation of motion equation for a planar robot
 C Linear systems used in the bimanual tennis serve example
 D Equivalence between LQT and LQR with augmented state space