Con­sider $k$ ro­bots ini­tially lo­cated at the cen­troid of an equi­lat­eral tri­an­gle $T$ with sides of length 1. The goal of the ro­bots is to evac­u­ate $T$ through an exit at an un­known lo­ca­tion on the bound­ary of $T$. Each robot can move any­where in $T$ in­de­pen­dently of other ro­bots with max­i­mum speed 1. The ob­jec­tive is to min­i­mize the evac­u­a­tion time, which is de­fined as the time re­quired for all $k$ ro­bots to reach the exit. We con­sider this prob­lem in the face-to-face model of com­mu­ni­ca­tion: a robot can com­mu­ni­cate with an­other robot only when they meet in $T$. For $k=2,3,4,5$ ro­bots, we will show an equal-travel al­go­rithm with early meet­ing that gives upper bounds of, re­spec­tively, 2.411, 2.088, 1.981, 1.876 on the evac­u­a­tion time. For $k=2$ ro­bots in par­tic­u­lar, we show how to im­prove the evac­u­a­tion time to 2.383 using a de­tour by the ro­bots.

This is a joint work with Huda Chuang­pishit, Lata Narayanan, and Jaroslav Opa­trny.