Project Proposal

Background & Motivation

As the recent robots become complex and have more joints, it is a major challenge to efficiently compute a collision-free trajectory for the robot that can satisfy stability and other constraints.
Ensuring that the resulting motion is subject to stability constraints is a key issue in motion planning.
Planning of contacts between the robot and obstacles should be integrated with the stability constraints since contacts apply reaction forces to the robot.
Some recent works successfully encode the contacts and stability constraints into their formulation, however these are limited in the single robot planning.

Multi-agent planning algorithms, like RVO, are used to compute collision-free motions of multiple agents.
Most of these algorithms assume the shapes of objects are simple like circle, ellipse (2D), or cylinder (3D).

Optimization-based algorithms define the motion planning problem as an optimization problem which finds a minimum-cost path with some constraint functions. 
If we can encode the contacts and stability constraints with the RVO constraint into the cost function, the algorithm can compute stable motions for multiple robots.

Goal

This project is based on my current optimization-based planner implementation.
There are two goal of the project.
1. Extend the planner, which only can handle single robot, to compute collision-free motions for multiple robots.
2. Extend the planner, which only allows contacts between the feet and the ground, to compute complex motions that can contain contacts of other robot links (e.g. hands) with obstacles.

Relevant Prior Works

Optimization-based Motion Planning in Dynamic Environments (Park et al.)
Discovery of Complex Behaviors through Contact-Invariant Optimization (Mordach et al.)
 A direct method for trajectory optimization of rigid bodies through contact (Posa et al.)
Optimal Reciprocal Collision Avoidance (Van den Berg et al.)

Plan to archive during the course of the project

1. Survey related works.
2. Setup benchmark environments for planning.
3. Integrate RVO cost in the objective function of the trajectory optimization.
4. Add other robot links as potential contact points and update stability constraints.

Tentative Schedule

3 weeks : Survey related works.
6 weeks : Test in simple benchmarks with 2 robots.
9 weeks : Demos on complex benchmarks where satisfying stability is challenging.