Evaluating direct transcription and nonlinear optimization methods for robot motion planning

The video presents hardware experiments on motion planning for the the ballbot Rezero using direct transcription.
Abstract:
This paper studies existing direct transcriptionmethods for trajectory optimization for robot motion planning.These methods have demonstrated to be favorable for planningdynamically feasible motions for high dimensional robots withcomplex dynamics. However, an important disadvantage is theaugmented size and complexity of the associated multivariatenonlinear programming problem (NLP). Due to this complexity,preliminary results suggest that these methods are not suitablefor performing the motion planning for high degree of freedom(DOF) robots online. Furthermore, there is insufficient evidenceabout the successful use of these approaches on real robots. Togain deeper insight into the performance of trajectory optimiza-tion methods, we analyze the influence of the choice of differenttranscription 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 focuson robotics, measuring the performance of the methods interms of computational time, quality of the solution, sensitivityto open parameters (i.e., number of discretization nodes andvariables initialization) and complexity of the problem (e.g.number of constraints, state and action bounds). Additionally,we compare two optimization methodologies, namely SequentialQuadratic Programming (SQP) and Interior Point Methods(IPM), which are used to solve the transcribed problem. Asa performance measure as well as a verification of usingtrajectory optimization on real robots, we are presentinghardware experiments performed on an underactuated, non-minimal-phase, ball-balancing robot with a 10 dimensional statespace and 3 dimensional input space. The benchmark taskssolved with the real robot take into account path constraintsand action bounds. These experiments constitute one of veryfew examples of full-state trajectory optimization applied toreal hardware.

[@Usman-zp6ig]

Hi. I am curious to know which transcription method you used in particular and your experience when solving the NLP by an interior point method. I am currently using the SNOPT implementation of sqp to solve my discretized optimal control problem. Although the solver appears to find a local minimum, I am unable to determine (using the output of SNOPT) whether the local minimum is indeed a stable solution. I would be grateful to know if you've undertaken such analyses. Many thanks. Usman