# Finding a Feasible Initial Solution for Flatness-Based Multi-Link Manipulator Motion Planning under State and Control Constraints

## TL;DR

This paper introduces a method to generate feasible initial solutions for flatness-based multi-link manipulator motion planning problems with constraints, improving the reliability of solving non-convex optimization tasks.

## Contribution

The paper proposes a novel approach to initialize feasible solutions by analyzing final time effects and scaling trajectories, enhancing motion planning under constraints.

## Key findings

- Successfully generated feasible initial solutions for constrained manipulators
- Integrated the method with inverse dynamics algorithms for practical testing
- Demonstrated effectiveness through numerical experiments

## Abstract

In this paper, we present a method to initialize at a feasible point and unfailingly solve a non-convex optimization problem in which a set-point motion is planned for a multi-link manipulator under state and control constraints. We construct an initial feasible solution by analyzing the final time effect for feasibility problems of flatness based motion planning problems. More specifically, we first find a feasible time-optimal trajectory under state constraints without a control constraint by solving a linear programming problem. Then, we find a feasible trajectory under control constraints by scaling the trajectory. To evaluate the practical applicability of the proposed method, we did numerical experiments to solve a multi-link manipulator motion planning problem by combining the method with recursive inverse dynamics algorithms.