# Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

## TL;DR

This paper introduces a mixed-integer convex optimization approach for multi-legged robot locomotion that plans contact, gait, and motion simultaneously, enabling robust and efficient traversal of complex terrains without flat terrain or fixed gait assumptions.

## Contribution

It presents a novel convex formulation that couples contact, gait, and motion planning, overcoming limitations of previous methods requiring fixed gaits or flat terrains.

## Key findings

- Successfully validated on HyQ robot across challenging terrains
- Achieves robust locomotion with low computation time
- Increases motion planning flexibility and generality

## Abstract

Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.