PYROBOCOP : Python-based Robotic Control & Optimization Package for Manipulation and Collision Avoidance

Abstract

PYROBOCOP is a lightweight Python-based package for control and optimization of robotic systems described by nonlinear Differential Algebraic Equations (DAEs). In particular, the package can handle systems with contacts that are described by complementarity constraints and provides a general framework for specifying obstacle avoidance constraints. The package performs direct transcription of the DAEs into a set of nonlinear equations by performing orthogonal collocation on finite elements. The resulting optimization problem belongs to the class of Mathematical Programs with Complementarity Constraints (MPCCs). MPCCs fail to satisfy commonly assumed constraint qualifications and require special handling of the complementarity constraints in order for NonLinear Program (NLP) solvers to solve them effectively. PYROBOCOP provides automatic reformulation of the complementarity constraints that enables NLP solvers to perform optimization of robotic systems. The package is interfaced with ADOL-C (Griewank et al. 1996) for obtaining sparse derivatives by automatic differentiation and IPOPT (W ächter and Biegler 2006) for performing optimization. We demonstrate the effectiveness of our approach in terms of speed and flexibility. We provide several numerical examples for several robotic systems with collision avoidance as well as contact constraints represented using complementarity constraints. We provide comparisons with other open source optimization packages like CasADi and Pyomo.

Path Generation Based on Electrostatic Equipotential Curves

“…Potential Field methods are computationally efficient, but struggle with local minimas and therefore cannot be complete. Thanks to non-convexity of collision-free configuration space, most of the optimization-based path planning methods struggle to find feasible solutions in cluttered environments [33], [34].…”