Joint–coordinate adjoint method for optimal control of multibody systems

Abstract This paper presents a joint–coordinate adjoint method for optimal control of multi-rigid-body systems. Initially formulated as set differential-algebraic equations, the system is brought into minimal form by projecting original expressions joint’s motion and constraint force subspaces. Consequently, cumbersome partial derivatives corresponding to joint-space equations are avoided, approach algorithmically more straightforward. The analogies between formulation Hamilton’s in mixed redundant-joint coordinates necessary conditions arising from minimization cost functional demonstrated text. observed parallels directly lead definition joint variables. Through numerical studies, performance proposed investigated double pendulum on cart. results demonstrate successful application joint-coordinate method. outcome can be easily generalized complex