Planning robot tasks safely under uncertainty using convex optimization
Belief Space Planning for Risk Signal Temporal Logic via Mixed-Integer Convex Programming
Robotics
Summary
Robots often need to complete tasks that have specific timing and location rules, but these tasks are tricky when the robot isn’t sure about its position because of noisy sensors. The authors show a way to plan robot actions while accounting for this uncertainty, using a kind of logic called Risk Signal Temporal Logic (RiSTL). Their approach transforms the planning problem into a special kind of math problem that can find the best solution reliably. They tested their method with simulations to show it works well.
What this means in practice
- •For robot motion planners: Create robot plans that meet complex timing rules while actively reducing uncertainty from noisy sensors.
- •For autonomous vehicle developers: Generate risk-aware driving strategies that improve safety by optimizing decisions with uncertain vehicle state estimates.
Authors
Shaohang Han, Joris Verhagen, Kaier Liang, Jana Tumova
Abstract
Signal Temporal Logic (STL) specifies robot tasks with spatio-temporal requirements, and its robustness semantics allow planning by trajectory optimization. In practice, robots estimate their state from noisy measurements, and when the information gained from a measurement depends on the state, the robot can actively reduce its uncertainty by planning in the belief space. The resulting problem is, however, generally non-convex, for which gradient-based methods are neither complete nor globally optimal. In this paper, we consider Risk STL (RiSTL) planning in Gaussian belief space and show that an information-form parameterization of the belief, together with a convex relaxation of the belief dynamics, yields a mixed-integer convex program (MICP). We prove that the MICP is sound and complete, and that the relaxation preserves the globally optimal input trajectories. We validate the effectiveness of our method in numerical simulations.