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 rough terrain while avoiding entering dangerous regions, which functions are little bit more difficult for other robots such as wheeled robots. However, there are several issues related to these robots.
First, we cannot ignore the effect of nonlinearity. Nonlinearity is not preferred in terms of math, but in terms of physics, nonlinearity realizes the agile dynamics of legged robots. So, how to deal with this nonlinearity is one research problem. One useful approach would be to assume the system as linear systems within a certain region. Another approach may be to use nonlinear programming directly.
Another difficulties such as high-dimensional system, hygrid effect will be discussed in the next blog.