  Integrated Task and Motion Planning (ITMP) for mobile robots in a dynamic
environment with moving obstacles is a challenging research question and
attracts more and more attentions recently. Most existing methods either
restrict to static environments or lack performance guarantees. This motivates
us to investigate the ITMP problem using formal methods and propose a bottom-up
compositional design approach called CoSMoP (Composition of Safe Motion
Primitives). Our basic idea is to synthesize a global motion plan through
composing simple local moves and actions, and to achieve its performance
guarantee through modular and incremental verifications. The design consists of
two steps. First, basic motion primitives are designed and verified locally.
Then, a global motion path is built upon these certified motion primitives by
concatenating them together. In particular, we model the motion primitives as
hybrid automata and verify their safety through formulating as Differential
Dynamic Logic (d$\mathcal{L}$). Furthermore, these proven safe motion
primitives are composed based on an encoding to Satisfiability Modulo Theories
(SMT) that takes into account the geometric constraints. Since d$\mathcal{L}$
allows compositional verification, the sequential composition of the safe
motion primitives also preserves safety properties. Therefore, the CoSMoP
generates correct plans for given task specifications that are formally proven
safe even for moving obstacles. Illustrative examples are presented to show the
effectiveness of the methods.
