Abstract
In this paper, we investigate the LQR-like optimal control problem on the special orthogonal group SO(3). Using the dynamic programming approach, we derive a Hamilton- Jacobi-Bellman equation in the general case where a generic distance on SO(3) is used in the cost functional. We show that the geodesic distance on SO(3) yields results analogous to the well known results for linear systems. Static and dynamic Riccati-like equations for both infinite and finite time-horizon optimal control problems are obtained.
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