Robust AI Planning for Hybrid Systems



Researcher Tromeur

This project aims to extend planning to hybrid discrete/continuous systems under exogenous uncertainty, and using this technology for proactive, and therefore more effective, management of cyber-physical systems.

Hybrid system models feature discrete and numeric state variables whose values can be changed by discrete instantaneous actions and continuous durative actions and processes. Hybrid planning shares similarities with the control of switched dynamical systems, where the system can be in different modes, each given by set of differential equations. In planning, the set of possible modes is not fixed a priori and depends on which actions are performed and when.

We have pursued a number of approaches to hybrid planning so far including:

  • Discretizing the problem to obtain a numeric sequential planning problem solvable by simpler techniques, such as heuristic search guided by novel heuristics for numeric sequential planning.
  • Translating the discretized problem into Satisfiability Modulo Theory, and exploiting its numeric structure to more efficiently reason about the number of times a numeric action needs to be executed in the plan using SMT.
  • Employing numerical integration methods within the search to solve differential equations and adaptively discretising the search.

Our planners solve problems compactly described in variants of the PDDL+ language, which feature global constraints rather than events.

We have also investigated applications of hybrid planning, scheduling and control to energy-aware meeting scheduling and HVAC control.


This project is funded by Australian Research Council Discovery Project Grant DP140104219, 2014-2016,  AUD 480,000.


Currently, the project has the following partner universities:


The following planning systems, developed under the project are publicly available. There should be more to come!
  • ENHSP (, is a hybrid (classical/numeric) planning systems based on heuristic search that deals with sequential numeric planning and planning with discretised autonomous processes. It also supports numeric/propositional global constraints. This planner (besides other things) employs the techniques presented in "Interval-Based Relaxation for General Numeric Planning - ECAI 2016" and "Heuristics for Numeric Planning - IJCAI 2016"
  • Springroll (, is a SMT based planner for sequential numeric planning with global constraints. This is the system developed for the paper "Numeric Planning with Disjunctive Global Constraints via SMT - ICAPS 2016"


Publications by the ANU members of the project include:

  • E. Scala, P. Haslum and S. Thiébaux. Interval-Based Relaxation for General Numeric Planning. 22nd European Conference on Artificial Intelligence (ECAI-16), IOS Press, The Hague (The Netherlands), September 2016. [pdf] © IOS Press.
  • E. Scala, P. Haslum and S. Thiébaux. Heuristics for Numeric Planning via Subgoaling. International Joint Conference on Artificial Intelligence (IJCAI-16), AAAI Press, New York, NY (USA), July 2016. [pdf] © AAAI Press.
  • M. Ramirez, E. Scala, P. Haslum and S. Thiébaux. Numeric Planning with Disjunctive Global Constraints via SMT. 26th International Conference on Automated Planning and Scheduling (ICAPS-16), AAAI Press, London (UK), June 2016. [pdf] © AAAI Press.
  • B.P. Lim, M. van den Briel, S. Thiébaux, S. Backhaus and R. Bent. HVAC-Aware Occupancy Scheduling. 29th AAAI Conference on Artificial Intelligence, (AAAI-15), AAAI Press, Austin, TX (USA), January 2015. [pdf] © AAAI Press.
  • F. Ivankovic, P. Haslum, S. Thiébaux, V. Shivashankar, and D.S. Nau. Optimal Planning with Global Numerical State Constraints. 24th International Conference on Automated Planning and Scheduling (ICAPS-14), AAAI Press, Portsmouth, NH (USA), June 2014. [pdf] © AAAI Press. Outstanding Student Paper Award.

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