Convergence Analysis of Hybrid Control Systems in the Form of Backward Chained Behavior Trees

Abstract

A robot control system is often composed of a set of low level continuous controllers and a switching policy that decides which of those continuous controllers to apply at each time instant. The switching policy can be either a Finite State Machine (FSM), a Behavior Tree (BT) or some other structure. In previous work we have shown how to create BTs using a backward chained approach that results in a reactive goal directed policy. This policy can be thought of as providing disturbance rejection at the task level in the sense that if a disturbance changes the state in such a way that the currently running continuous controller cannot handle it, the policy will switch to the appropriate continuous controller. In this letter we show how to provide convergence guarantees for such policies.

Continuous-Time Behavior Trees as Discontinuous Dynamical Systems

“…Let 0, 1, 2 ∈ V such that 1 < S 2 and p(1) = p(2) = 0. We now apply each case of (12) to Ω 1 , assuming 2 ∈ S ∩ F, which implies 0 ∈ S ∩ F according to (10) and (11).…”

“…For a BT, this translates to reaching the so-called success region, a state where the BT returns success. Important results on sufficient conditions for convergence to the success region have been presented in [9], [10], but in both cases the analysis was limited to a particular subclass of BTs. In this letter we propose sufficient conditions that can be use to analyze any BT design.…”

Handling Concurrency in Behavior Trees

“…Robotics applications of BTs span from manipulation [2]- [4] to non-expert programming [5]- [7]. Other works include task planning [8], human-robot interaction [9]- [11], learning [12]- [15], UAV [16]- [21], multi-robot systems [22]- [25], and system analysis [26]- [28]. The Boston Dynamics's Spot uses BTs to model the robot's mission [29], the Navigation Stack and the task planner of ROS2 uses BTs to encode the high level robot's behavior [30], [31].…”

Formalizing the Execution Context of Behavior Trees for Runtime Verification of Deliberative Policies

“…They are gaining popularity in robotics because they are highly flexible, reusable, and well suited to define deliberative elements in the model-based design of control architectures. The use of BTs in robotics [1] spans from manipulation [2]- [4] to task planning [5], [6], human-robot interaction [7]- [9] to learning [10], [11], UAVs [12], [13], and system analysis [14]- [16]. Moreover, BTs are used in the Boston Dynamics's Spot SDKs to model the robot's mission [17] and in the Navigation Stack of ROS2 [18].…”