A practical guide to learning and control problems in robotics
solved with second-order 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