Hamilton-Jacobi Reachability Analysis for Hybrid Systems with Controlled and Forced Transitions

Hybrid dynamical systems with non-linear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of such hybrid systems can still prove to be a challenging problem because it requires simultaneous reasoning about continuous state evolution and discrete mode switching. In this work, we address this problem by extending classical Hamilton-Jacobi (HJ) reachability analysis, a formal verification method for continuous non-linear dynamics in the presence of bounded inputs and disturbances, to hybrid dynamical systems. Our framework can compute reachable sets for hybrid systems consisting of multiple discrete modes, each with its own set of non-linear continuous dynamics, discrete transitions that can be directly commanded or forced by a discrete control input, while still accounting for control bounds and adversarial disturbances in the state evolution. Along with the reachable set, the proposed framework also provides an optimal continuous and discrete controller to ensure system safety. We demonstrate our framework in simulation on an aircraft collision avoidance problem, as well as on a real-world testbed to solve the optimal mode planning problem for a quadruped with multiple gaits

Distributed Feedback Controllers for Stable Cooperative Locomotion of Quadrupedal Robots: A Virtual Constraint Approach

This paper aims to develop distributed feedback control algorithms that allow cooperative locomotion of quadrupedal robots which are coupled to each other by holonomic constraints. These constraints can arise from collaborative manipulation of objects during locomotion. In addressing this problem, the complex hybrid dynamical models that describe collaborative legged locomotion are studied. The complex periodic orbits (i.e., gaits) of these sophisticated and high-dimensional hybrid systems are investigated. We consider a set of virtual constraints that stabilizes locomotion of a single agent. The paper then generates modified and local virtual constraints for each agent that allow stable collaborative locomotion. Optimal distributed feedback controllers, based on nonlinear control and quadratic programming, are developed to impose the local virtual constraints. To demonstrate the power of the analytical foundation, an extensive numerical simulation for cooperative locomotion of two quadrupedal robots with robotic manipulators is presented. The numerical complex hybrid model has 64 continuous-time domains, 192 discrete-time transitions, 96 state variables, and 36 control inputs

Input to State Stability of Bipedal Walking Robots: Application to DURUS

Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end result being stable bipedal walking. The principal contribution of this paper is to establish sufficiency conditions for yielding input to state stable (ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and phase-based uncertainties. In particular, it will be shown formally that exponential input to state stabilization (e-ISS) of the continuous dynamics, and hybrid invariance conditions are enough to realize stable walking in the 23-DOF bipedal robot DURUS. This main result will be supported through successful and sustained walking of the bipedal robot DURUS in a laboratory environment.Comment: 16 pages, 10 figure

Safety verification of a fault tolerant reconfigurable autonomous goal-based robotic control system

Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is simulated in MDS and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems

Conversion and verification procedure for goal-based control programs

Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is developed and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems

Review of real brain-controlled wheelchairs

This paper presents a review of the state of the art regarding wheelchairs driven by a brain-computer interface (BCI). Using a brain-controlled wheelchair (BCW), disabled users could handle a wheelchair through their brain activity, granting autonomy to move through an experimental environment. A classification is established, based on the characteristics of the BCW, such as the type of electroencephalographic (EEG) signal used, the navigation system employed by the wheelchair, the task for the participants, or the metrics used to evaluate the performance. Furthermore, these factors are compared according to the type of signal used, in order to clarify the differences among them. Finally, the trend of current research in this field is discussed, as well as the challenges that should be solved in the future

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Hybrid automata dicretising agents for formal modelling of robots

Some of the fundamental capabilities required by autonomous vehicles and systems for their intelligent decision making are: modelling of the environment and forming data abstractions for symbolic, logic based reasoning. The paper formulates a discrete agent framework that abstracts and controls a hybrid system that is a composition of hybrid automata modelled continuous individual processes. Theoretical foundations are laid down for a class of general model composition agents (MCAs) with an advanced subclass of rational physical agents (RPAs). We define MCAs as the most basic structures for the description of complex autonomous robotic systems. The RPA’s have logic based decision making that is obtained by an extension of the hybrid systems concepts using a set of abstractions. The theory presented helps the creation of robots with reliable performance and safe operation in their environment. The paper emphasizes the abstraction aspects of the overall hybrid system that emerges from parallel composition of sets of RPAs and MCAs

Safety Verification of Fault Tolerant Goal-based Control Programs with Estimation Uncertainty

Fault tolerance and safety verification of control systems that have state variable estimation uncertainty are essential for the success of autonomous robotic systems. A software control architecture called mission data system, developed at the Jet Propulsion Laboratory, uses goal networks as the control program for autonomous systems. Certain types of goal networks can be converted into linear hybrid systems and verified for safety using existing symbolic model checking software. A process for calculating the probability of failure of certain classes of verifiable goal networks due to state estimation uncertainty is presented. A verifiable example task is presented and the failure probability of the control program based on estimation uncertainty is found