07 Jan

#### Research Plan

Title: Safe Trajectory Optimization of Legged Robots with End-to-End Chance-Constraints with Auto Risk-Tuning Summary: Risk-Aware TO is able to generate various trajectories based on user-defined spacification. However, the commanded violation probability Risk-Aware TO uses does not match to...

31 Dec

#### Difficulty of safe motion planning for nonlinear hybrid robots

In this blog, I try to motivate the research focusing on motion planning for nonlinear hybrid robots such as legged robots, manipulators. As you know, these robotic systems have very good capabilities for conducting their tasks. For example, legged robot can basically traverse any direction under ro...

16 Nov

#### How to deal with obstacles in Trajectory Optimization?

In this tutorial, I show how to deal with obstacles in TO. Let's consider a robot moving in a 2D space. The robot needs to avoid rectangle obstacles. Here, I assume that the shape of the obstacles is represented by its lower left and upper right points, $$\left(x_{\min }, y_{\min }\right)$$ and \...

26 Oct

#### Lazy Weighted A*

There are several works that somehow deal with the expensive computation time for edge evaluations in graph-search planning algorithms. Here I explain one of the state-of-art algorithms to deal with this problem, which is lazy weighted A* (LWA). LWA works as follows. First, LWA assumes that the tr...

03 Oct

#### Motion Planning 3: Trajectory Optimization

Optimization-based motion planning approaches, such asNonlinear Programming (NLP) and Mixed-Integer Programming (MIP), solve optimization problems, and find solutions using gradient descent while satisfying constraints. For instance, CHOMP optimizes a cost functional using covariant gradient descent...

01 Sep

#### Presentation video @ IROS 2020

Presentation video of our latest work, "Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming", accepted for RA-L and IROS 2020, is now on YouTube! Our new motion planner is able to generate various trajectories for multi-limbed robots under sto...

05 Aug

#### Motion Planning 2: Sampling-Based Methods

Sampling-based motion planning approaches, such as Probabilistic RoadMap Method (PRM) and Rapidly-exploring Random Trees (RRT) , avoid the discretization problems of graph-based algorithms by randomly sampling the continuous domain. This scales more effectively to high-dimensional problems, but make...

04 Aug

#### CasADi: an open-source tool for nonlinear optimization and algorithmic differentiation

For my latest work, I heavily used CasADi to formulate the stochastic nonlinear optimization problem. Here, I'd like to illustrate several preliminaries and tips that hopefully may be useful for others. CasADi is an open-source wrapper mainly for nonlinear programmings (NLPs), although you can...

30 Jul

#### Motion Planning 1: Graph-Search-Based Methods

In this blog post, I explain graph-search based motion planning algorithms, which overlay a grid on configuration space and assume that each configuration is corresponding to a grid node. Then, the robot is allowed to traverse to adjacent grid points as long as the edge between the nodes is collisio...

02 Jul

#### Motion Planning 0

Motion planning is a key component for robots to realize navigation. A number of great works have been conducted in the world. They are grid-based approaches, sampling-based approaches, and trajectory optimization. I'll summarize the pros and cons of each motion planning algorithms in the future. ...