Can't Touch This: Real-Time, Safe Motion Planning and Control for Manipulators Under Uncertainty

Ensuring safe, real-time motion planning in arbitrary environments requires a robotic manipulator to avoid collisions, obey joint limits, and account for uncertainties in the mass and inertia of objects and the robot itself. This paper proposes Autonomous Robust Manipulation via Optimization with Uncertainty-aware Reachability (ARMOUR), a provably-safe, receding-horizon trajectory planner and tracking controller framework for robotic manipulators to address these challenges. ARMOUR first constructs a robust controller that tracks desired trajectories with bounded error despite uncertain dynamics. ARMOUR then uses a novel recursive Newton-Euler method to compute all inputs required to track any trajectory within a continuum of desired trajectories. Finally, ARMOUR over-approximates the swept volume of the manipulator; this enables one to formulate an optimization problem that can be solved in real-time to synthesize provably-safe motions. This paper compares ARMOUR to state of the art methods on a set of challenging manipulation examples in simulation and demonstrates its ability to ensure safety on real hardware in the presence of model uncertainty without sacrificing performance. Project page: https://roahmlab.github.io/armour/.Comment: 20 pages, 6 figure

Reachability-based Identification, Analysis, and Control Synthesis of Robot Systems

We introduce reachability analysis for the formal examination of robots. We propose a novel identification method, which preserves reachset conformance of linear systems. We additionally propose a simultaneous identification and control synthesis scheme to obtain optimal controllers with formal guarantees. In a case study, we examine the effectiveness of using reachability analysis to synthesize a state-feedback controller, a velocity observer, and an output feedback controller.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Autonomous Vehicle Coordination with Wireless Sensor and Actuator Networks

A coordinated team of mobile wireless sensor and actuator nodes can bring numerous benefits for various applications in the field of cooperative surveillance, mapping unknown areas, disaster management, automated highway and space exploration. This article explores the idea of mobile nodes using vehicles on wheels, augmented with wireless, sensing, and control capabilities. One of the vehicles acts as a leader, being remotely driven by the user, the others represent the followers. Each vehicle has a low-power wireless sensor node attached, featuring a 3D accelerometer and a magnetic compass. Speed and orientation are computed in real time using inertial navigation techniques. The leader periodically transmits these measures to the followers, which implement a lightweight fuzzy logic controller for imitating the leader's movement pattern. We report in detail on all development phases, covering design, simulation, controller tuning, inertial sensor evaluation, calibration, scheduling, fixed-point computation, debugging, benchmarking, field experiments, and lessons learned

Finding consensus without computation

A canonical problem for swarms of agents is to collectively choose one of multiple options in their environment. We present a novel control strategy for solving this problem-the first to be free of arithmetic computation. The agents do not communicate with each other nor do they store run-time information. They have a line-of-sight sensor that extracts one ternary digit of information from the environment. At every time step, they directly map this information onto constant-value motor commands. We evaluate the control strategy with both simulated and physical e-puck robots. By default, the robots are expected to choose, and move to, one of two options of equal value. The simulation studies show that the strategy is robust against sensory noise, scalable to large swarm sizes, and generalizes to the problems of choosing between more than two options or between unequal options. The experiments-50 trials conducted with a group of 20 e-puck robots-show that the group achieves consensus in 96% of the trials. Given the extremely low hardware requirements of the strategy, it opens up new possibilities for the design of swarms of robots that are small in size (≪10 -3 m) and large in numbers (≫10 3 )

Applied Safety Critical Control

There is currently a clear gap between control-theoretical results and the reality of robotic implementation, in the sense that it is very difficult to transfer analytical guarantees to practical ones. This is especially problematic when trying to design safety-critical systems where failure is not an option. While there is a vast body of work on safety and reliability in control theory, very little of it is actually used in practice where safety margins are typically empiric and/or heuristic. Nevertheless, it is still widely accepted that a solution to these problems can only emerge from rigorous analysis, mathematics, and methods. In this work, we therefore seek to help bridge this gap by revisiting and expanding existing theoretical results in light of the complexity of hardware implementation. To that end, we begin by making a clear theoretical distinction between systems and models, and outline how the two need to be related for guarantees to transfer from the latter to the former. We then formalize various imperfections of reality that need to be accounted for at a model level to provide theoretical results with better applicability. We then discuss the reality of digital controller implementation and present the mathematical constraints that theoretical control laws must satisfy for them to be implementable on real hardware. In light of these discussions, we derive new realizable set-invariance conditions that, if properly enforced, can guarantee safety with an arbitrary high levels of confidence. We then discuss how these conditions can be rigorously enforced in a systematic and minimally invasive way through convex optimization-based Safety Filters. Multiple safety filter formulations are proposed with varying levels of complexity and applicability. To enable the use of these safety filters, a new algorithm is presented to compute appropriate control invariant sets and guarantee feasibility of the optimization problem defining these filters. The effectiveness of this approach is demonstrated in simulation on a nonlinear inverted pendulum and experimentally on a simple vehicle. The aptitude of the framework to handle a system's dynamics uncertainty is illustrated by varying the mass of the vehicle and showcasing when safety is conserved. Then, the aptitude of this approach to provide guarantees that account for controller implementation's constraints is illustrated by varying the frequency of the control loop and again showcasing when safety is conserved. In the second part of this work, we revisit the safety filtering approach in a way that addresses the scalability issues of the first part of this work. There are two main approaches to safety-critical control. The first one relies on computation of control invariant sets and was presented in the first part of this work. The second approach draws from the topic of optimal control and relies on the ability to realize Model-Predictive-Controllers online to guarantee the safety of a system. In that online approach, safety is ensured at a planning stage by solving the control problem subject for some explicitly defined constraints on the state and control input. Both approaches have distinct advantages but also major drawbacks that hinder their practical effectiveness, namely scalability for the first one and computational complexity for the second one. We therefore present an approach that draws from the advantages of both approaches to deliver efficient and scalable methods of ensuring safety for nonlinear dynamical systems. In particular, we show that identifying a backup control law that stabilizes the system is in fact sufficient to exploit some of the set-invariance conditions presented in the first part of this work. Indeed, one only needs to be able to numerically integrate the closed-loop dynamics of the system over a finite horizon under this backup law to compute all the information necessary for evaluating the regulation map and enforcing safety. The effect of relaxing the stabilization requirements of the backup law is also studied, and weaker but more practical safety guarantees are brought forward. We then explore the relationship between the optimality of the backup law and how conservative the resulting safety filter is. Finally, methods of selecting a safe input with varying levels of trade-off between conservativeness and computational complexity are proposed and illustrated on multiple robotic systems, namely: a two-wheeled inverted pendulum (Segway), an industrial manipulator, a quadrotor, and a lower body exoskeleton.</p

Provable Run Time Safety Assurance for a Non-Linear System

Systems that are modeled by non-linear continuous-time differential equations with uncertain parameters have proven to be exceptionally difficult to formally verify. The past few decades have produced a number of useful verification tools which can be applied to such systems but each is applicable to only a subset of possible verification scenarios. The Level Sets Toolbox (LST) is one such tool which is directly applicable to non-linear systems, however, it is limited to systems of relatively small continuous state space dimension. Other tools such as PHAVer and the SpaceEx invariant of the Le Guernic-Girard (LGG) support function algorithm are specifically designed for hybrid systems with linear dynamics and linear constraints but can accommodate hundreds of continuous states. The application of these linear reachability tools to non-linear models has been achieved by approximating non-linear systems as linear hybrid automata (LHA). Unfortunately, the practical applicability and limitations of this approach are not yet well documented. The purpose of this thesis is to evaluate the performance and dimensionality limitations of PHAVer and the LGG support function algorithm when applied to a LHA approximation of a particular non-linear system. A collision avoidance scenario with autonomous differential drive robots is used as a case study to demonstrate that an over-approximated reachable set boundary can be generated and implemented as a run time safety assurance mechanism