OCS2 Toolbox
Summary
OCS2 is a C++ toolbox tailored for Optimal Control for Switched Systems (OCS2). The toolbox provides an efficient implementation of the following algorith
- SLQ: Continuous-time domin DDP
- iLQR: Discrete-time domain DDP
- SQP: Multiple-shooting algorithm based on HPIPM
- PISOC: Path integral stochatic optimal control
OCS2 handles general path constraints through Augmented Lagrangian or relaxed barrier methods. To facilitate the application of OCS2 in robotic tasks, it provides the user with additional tools to set up the system dynamics (such as kinematic or dynamic models) and cost/constraints (such as self-collision avoidance and end-effector tracking) from a URDF model. The library also provides an automatic differentiation tool to calculate derivatives of the system dynamics, constraints, and cost. To facilitate its deployment on robotic platforms, the OCS2 provides tools for ROS interfaces. The toolbox’s efficient and numerically stable implementations in conjunction with its user-friendly interface have paved the way for employing it on numerous robotic applications with limited onboard computation power.
For more information refer to the project's Documentation Page
It works fine if I define the inputTrajectory value as a vector of input size full of zeros but the results are not satisfying as it always stops at each point. As I have a redundant system, I have no idea what the desired input trajectories should be as they should be the result of the mpc optimization.
How should I define my input to ensure that the MPC runs successfully?
The differential is then:
To goal is to find the following jacobians:
similarly,
It is not clear what the analytical expression for $\frac{\partial {\dot{q}}_j}{\partial {\bar{h}}_G}$ is from the above equation. However, it's clear that $\frac{\partial {\dot{q}}_j}{\partial {\bar{h}}_G} \neq {0}$. Similarly, the entire bottom row block of $\frac{\partial {v}}{\partial {x}}$ shouldn't be ${0}$, but left as ${0}$ 
Again, similar to $\frac{\partial {\dot{q}}_j}{\partial {\bar{h}}_G}$, it's not clear what the analytical expression should be for $\frac{\partial {q}_j}{\partial {q}_b}$ given the relation derived in above equation.
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