This paper studies existing direct transcription methods for trajectory optimization for robot motion planning. These methods have demonstrated to be favorable for planning dynamically feasible motions for high dimensional robots with complex dynamics. However, an important disadvantage is the augmented size and complexity of the associated multivariate nonlinear programming problem (NLP). Due to this complexity, preliminary results suggest that these methods are not suitable for performing the motion planning for high degree of freedom (DOF) robots online. Furthermore, there is insufficient evidence about the successful use of these approaches on real robots. To gain deeper insight into the performance of trajectory optimization methods, we analyze the influence of the choice of different transcription techniques as well as NLP solvers on the run time. There are different alternatives for the problem transcription, mainly determined by the selection of the integration rule. In this study these alternatives are evaluated with a focus on robotics, measuring the performance of the methods in terms of computational time, quality of the solution, sensitivity to open parameters and complexity of the problem. Additionally, we compare two optimization methodologies, namely Sequential Quadratic Programming (SQP) and Interior Point Methods (IPM), which are used to solve the transcribed problem. As a performance measure as well as a verification of using trajectory optimization on real robots, we are presenting hardware experiments performed on an underactuated, nonminimal-phase, ball-balancing robot with a 10 dimensional state space and 3 dimensional input space. The benchmark tasks solved with the real robot take into account path constraints and actuation limits. These experiments constitute one of very few examples of full-state trajectory optimization applied to real hardware.
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