November 2, 2007

1. Declarative Programming for Modular RobotsAshley-Rollman, De Rosa, Srinivasa, Pillai, Goldstein, Campbell November 2, 2007

2. Locally Distributed Predicates (LDP) &Meld • Two very different approaches to declarative programming for modular robots • Meld - logic programming • LDP - distributed pattern matching • Both achieve higher goals • Dramatically shorter code • Automatically distributed • Automatic messaging Declarative Programming for Modular Robots

3. LDP Overview • Originated in Distributed Watchpoint system • Needed to describe and detect incorrect distributed state configurations • Locally Distributed Predicates • Locally Distributed: involving a bounded number of connected modules • Predicates: boolean expressions over state, temporal, and topological variables • An LDP program consists of a number of predicates, each with one or more attached actions • Every predicate/action pair is executed in parallel Declarative Programming for Modular Robots

4. Meld Overview • Logic programming language • Inspired by P2 [Loo et. al. 2005] • Consists of facts and rules for deriving new facts • When a fact changes, derived facts are automatically deleted • Programs typically consider local neighborhoods • Additional support for making non-local neighborhoods Declarative Programming for Modular Robots

5. LDP and Meld: A Comparison Declarative Programming for Modular Robots

6. Example: 3D Shape Change Algorithm • <20 lines of Meld or LDP • Connectivity maintenance guaranteed by algorithm Declarative Programming for Modular Robots

7. Example 1: Setting Module State type state(module, min int). state(A, FINAL) :- isSeed(A). state(B, FINAL) :- neighbor(A, B), state(A, FINAL), in(B). forall (a) where (a.isSeed) do a.state = FINAL; forall (a,b) where (a.state = FINAL) & (b.inside) do b.state = FINAL; • If the module is the seed • Set the seed’s state to FINAL • For every module inside the target shape • If it is next to a module in FINAL state • Set the module’s state to FINAL Meld LDP Declarative Programming for Modular Robots

8. LDP and Meld: A Comparison Declarative Programming for Modular Robots

9. Example 2: Evaluation Over all Neighbors forall(a,b) where (b.parent != a.id) do a.$notChild.add(b.id); forall(a) where size(a.$notChild) = size(a.$neighbors) do a.delete(); type deletable(module). type notChild(module, module). notChild(A, B) :- neighbor(A, B), parent(B, C), A != C. deletable(A) :- forall neighbor(A, B) notChild(A, B). • A module can only be deleted if none of its neighbors are children • We first determine which neighbors are not children • If there are no children, the module can be deleted Meld LDP Declarative Programming for Modular Robots

10. LDP and Meld: A Comparison Declarative Programming for Modular Robots

11. Example 3: Self-deleting Gradients Declarative Programming for Modular Robots

12. Example 3: Self-deleting Gradients forall (a,b) where (a.value > b.value) do a.value = b.value + 1; forall (a,b[0,6]) where count(a.value > b[i].value) = 0 & a.value != 0 do a.value = INF; type gradient (module, min int). gradient(A, N) :- neighbor(A, B), gradient(B, M), N = M + 1. • Meld deletes all dependent facts when the root fact is deleted • LDP directly manipulates state variables, so retraction must be manual • LDP must specify the maximum number of neighbors Meld LDP Declarative Programming for Modular Robots

13. LDP and Meld: A Comparison Declarative Programming for Modular Robots

14. Example 4: Spanning Tree Creation Declarative Programming for Modular Robots

15. Example 4: Spanning Tree Creation forall (a) where (a.isRoot = 1) do a.parent = a.id; forall (a,b) where (a.parent != -1) & (b.parent = -1) do b.parent = a.id: type parent(module, first module). parent(A, A) :- root(A). parent(B, A) :- neighbor(B, A), parent(A, _). • Newer versions of Meld use the “first” aggregate to ensure uniqueness • This qualifier is not sufficient for more complex situations Declarative Programming for Modular Robots

16. Example 4b: Spanning Tree Creation forall (a) where (a.isRoot = 1) do a.parent = a.id; forall (a,b) where (a.parent != -1) & (b.parent = -1) do b.parent = a.id: type possibleParent(module, module, int). type bestParent(module, min int). type parent(module, module). parent(A, A) :- root(A). possibleParent(B, A, T) :- neighbor(A, B), parent(A, _) , T = localTimeStamp(). bestParent(B, T) :- possibleParent(B, _, T). parent(B, A) :- possibleParent(B, A, T), bestParent(B, T). • Without “first”, Meld must use timestamps to ensure exactly one unique parent • LDP uses a single state variable, and thus can never have more than one parent Declarative Programming for Modular Robots

17. LDP and Meld: A Comparison Declarative Programming for Modular Robots

18. Future Research • • Performance enhancements/optimizations • Additional language features • Support transactions • Applicability to other application domains • Explore tradeoffs between automated and manual state control • Find a balance that allows programmers to maintain state while gaining some or all of the benefits of automated state Interested in Meld/LDP? Email [mderosa,mpa]@cs.cmu.edu Declarative Programming for Modular Robots