Erratum: Direct Trajectory Optimization of Rigid Body Dynamical Systems through Contact
The Authors, Editors, and Publisher wish to include a reference to a body of work that was announced to us following publication of this article that independently produced similar results, and was in fact published before our manuscript (1-3). This work formulated nonlinear programs (NLP) in the mathematical programming with equilibrium constraints (MPEC) framework, and included formulations for autonomous and non-autonomous discontinuous transitions with or without unilateral constraints, for both elastic and inelastic collisions, and for time-stepping-based shooting methods.
These methods are the first we know of to remove the combinatorial complexity of hybrid mode scheduling and produce a polynomial time NLP. Our manuscript presents a different but similar framework, which differs by emphasizing sparseness in the program and solution techniques used by modern sequential quadratic programming solvers to scale the solution techniques to large systems (up to 22 discrete variables and over 4 million resulting modes).
1) Yunt, Kerim; Glocker, Christoph. Trajectory optimization of mechanical hybrid systems using SUMT. In: Advanced Motion Control, 2006. 9th IEEE International Workshop on. IEEE, 2005. S. 665-671.
2) Yunt, Kerim; Glocker, Christoph. A combined continuation and penalty method for the determination of optimal hybrid mechanical trajectories. In: IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty. Springer Netherlands, 2007. S. 187-196.
3) Yunt, Kerim; An Augmented Lagrangian-based Shooting Method for the Optimal Trajectory Generation of Switching Lagrangian Systems. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications & Algorithms 18 (2011) 615-645, 2011 Watam Press.