# 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 the actual violation probability in hardware experiments.
- This is because in our IROS 2020, we assume that the uncertainty arises from the contact forces. But, in reality, we have many other uncertainties coming from a variety of components in robots (e.g., modeling error, environment estimation error, sensor noise, controller)
- One approach might be risk-aware TO with exploration-exploitation framework that explores environment if the commanded violation probability does not match to the actual violation probability and exploits the risk-aware TO.
- One fundamental problem I need to work on is that TO needs to consider how to map the commanded violation probability to the actual violation probability. One way is that we can use end-to-end learning approach to get this relation. (Note: while working on end-to-end chance-constraints, I am invesigating the end-to-end chance-constraints that consists of controller chance-constraints as well as planning chance-constraints)
- Second contribution would be auto-risk-tuning. In general, the violation probability is fixed during the planning. However, I observed that it is beneficial if we can automatically tune the violation probability online.
- Thirdly, while I start by working on toy problem (e.g., UAV 2D), I formulate this framework for legged robots, which is very beneficial for legged robots community.
- By proposing this framework, the robot is able to generate the robust trajectories in real hardware with guarantees, which is critical for safety-critical applications such as autonomous driving cars. In addition, I think our proposed algorithm can be used for online setting under a priori unknown environment.

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