Introducing Multi-Convexity in Path Constrained Trajectory Optimization for Mobile Manipulators
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review
Details
| Original language | English |
|---|---|
| Title of host publication | European Control Conference 2020, ECC 2020 |
| Publisher | IEEE |
| Pages | 1178-1185 |
| Number of pages | 8 |
| ISBN (Electronic) | 9783907144015, 978-3-90714-402-2 |
| ISBN (Print) | 978-1-7281-8813-3 |
| Publication status | Published - 2020 |
| Publication type | A4 Article in a conference publication |
| Event | European Control Conference - Saint Petersburg, Russian Federation Duration: 12 May 2020 → 15 May 2020 |
Conference
| Conference | European Control Conference |
|---|---|
| Country | Russian Federation |
| City | Saint Petersburg |
| Period | 12/05/20 → 15/05/20 |
Abstract
Mobile manipulators have a highly non-linear and non-convex mapping between the end-effector path and the manipulator's joints and position and orientation of the mobile base. As a result, trajectory optimization with end-effector path constraints takes the form of a difficult non-linear optimization problem. In this paper, we present the first multi-convex approximation to this difficult optimization problem that eventually reduces to solving a sequence of globally valid convex quadratic programs (QPs). The proposed optimizer rests on two novel building blocks. First, we introduce a set of auxiliary variables in which the non-linear constraints that arise out of manipulator kinematics and its coupling with the mobile base have a multi-affine form. Projecting the auxiliary variables to the space of actual configuration variables of the mobile manipulator involves a non-convex optimization. Thus, the second building block involves computing a convex surrogate for this non-convex projection. We show how large parts of the proposed optimizer can be solved in parallel providing the possibility of exploiting multi-core CPUs. We validate our trajectory optimization on different benchmark examples. Specifically, we highlight how it solves the cyclicity problem and provides a holistic approach where a diverse set of trajectories can be obtained by trading-off different aspects of manipulator and mobile base motion.