Safety and risk-awareness are important properties for robotic systems, be it for protecting them from potentially dangerous internal states, or for avoiding collisions with obstacles and environmental hazards in disaster scenarios. Ensuring safety may be the role of more than one algorithmic layer in a system, each with varying assumptions and guarantees. This thesis investigates how to provide safety and risk-awareness in a robotic system by leveraging temporal logics, motion planning algorithms, and control theory.

Traditional control theory approaches interpret the collision avoidance safety task as a `stay-away' task; obstacles are abstracted as collections of geometric shapes, and controllers are designed to avoid each shape individually. We propose interpreting the collision avoidance problem as a `stay-within' task: the obstacle-free space is abstracted into safe regions. We propose control laws based on Control Barrier functions that guarantee that the system remains within such safe regions throughout its mission. Our results demonstrate that our controller indirectly avoids obstacles while providing the system the freedom to move within the safe regions, without the necessity to plan and track a safe trajectory. Furthermore, by extending our idea with Metric Interval Temporal Logic, we are able to consider missions with explicit time bounds. 

Temporal logics are often used to define hard constraints on motion plans for robotic systems. However, some missions may require the system to violate constraints to make progress. Therefore, we propose to soften the hard constraints when necessary. Such soft constraints, here coined as spatial preferences, are used to account for relations between the system and the environment, such as distance from obstacles. The proposed minimally-violating motion planning algorithm attempts to find trajectories that satisfy the spatial preferences as much as possible, but violate them when needed. We demonstrate the use of spatial preferences on 3D exploration scenarios with Unmanned Aerial Vehicles, where we provide safer trajectories to the system while improving exploration efficiency. 

In the last part of the thesis, we address safety in scenarios where a precise model of the environment is not available. In such scenarios, the system is required to fulfil the mission while minimizing risk, considering the imprecise model. We leverage Gaussian Processes to build approximate models of the environment, and use their posterior distributions in a risk metric. This risk metric allows us to consider less likely but possible events along the missions. To this end, we propose an online risk-aware motion planning approach, and validate it on disaster scenarios, where exposure to the unmodeled hazards might damage the system. Moreover, we explore risk-awareness between the control and mapping layers, by considering smooth approximations of Euclidean Distance Fields.

Our results indicate that our algorithms provide robotic systems with i) provably-safe controllers, ii) soft safety constraints, and iii) risk-awareness in unmodeled environments. These three properties contribute to safer and risk-aware robotic systems in the real world.

Säkerhet och riskmedvetenhet är viktiga egenskaper för robotsystem, oavsett om det är för att skydda dem från potentiellt farliga interna tillstånd eller för att undvika kollisioner med hinder och miljöfaror i katastrofscenarier. Att garantera säkerhete kan vara rollen för mer än ett lager av algoritmer i ett system, var och en med olika antaganden och garantier. Denna avhandling undersöker hur man skapar säkerhet och riskmedvetenhet i ett robotsystem genom att utnyttja tidslogik, algoritmer för rörelseplanering och reglerteori.

Traditionella metoder inom reglerteori tolkar säkerhetsuppgiften för att undvika kollisioner som en `hålla-sig-utom-uppgift'; hinder abstraheras som samlingar av geometriska former, och regulatorer utformas för att undvika varje form individuellt. Vi föreslår att problemet med kollisionsundvikande tolkas som en `hålla-sig-inom-uppgift': utrymmet fritt från hinder abstraheras till säkra regioner. Vi föreslår regulatorer baserade på kontrollbarriärfunktioner som garanterar att systemet förblir inom sådana säkra regioner under hela sitt uppdrag. Våra resultat visar att vår regulator indirekt undviker hinder samtidigt som den ger systemet frihet att röra sig inom de säkra regionerna, utan att det är nödvändigt att planera och följa en viss säker bana. Genom att utöka vår idé med tidslogik med metriska intervall kan vi dessutom hantera uppdrag med explicita tidsgränser.

Tidslogik används ofta för att definiera strikta begränsningar för rörelseplaner för robotsystem. Vissa uppdrag kan dock kräva att systemet bryter mot begränsningar för att göra framsteg. Därför föreslår vi att mjuka upp de strikta begränsningarna vid behov. Sådana följsamma begränsningar, här kallade för rumsliga preferenser, används för att redogöra för relationer mellan systemet och miljön, såsom avstånd från hinder. Den föreslagna minimalt regelbrytande algoritmen för rörelseplanering försöker hitta banor som uppfyller de rumsliga preferenserna så mycket som möjligt, men kränker dem vid behov. Vi demonstrerar användningen av rumsliga preferenser i tredimensionella utforskningsscenarier med obemannade flygfordon, där vi tillhandahåller säkrare banor till systemet samtidigt som vi förbättrar utforskningseffektiviteten.

I den sista delen av avhandlingen tar vi upp säkerheten i scenarier där en exakt modell av miljön inte är tillgänglig. I sådana scenarier krävs att systemet genomför uppdraget samtidigt som risken minimeras, med hänsyn till den oprecisa modellen. Vi utnyttjar Gaussiska processer för att bygga approximativa modeller av miljön och använder deras a posteriori-fördelningar i ett riskmått. Detta riskmått gör att vi kan överväga mindre sannolika men möjliga händelser längs uppdragen. För detta ändamål föreslår vi ett direkt riskmedvetet tillvägagångssätt för planering av rörelser och validerar det i katastrofscenarier där exponering för omodellerade faror kan skada systemet. Dessutom utforskar vi riskmedvetenhet mellan reglering- och kartläggningsskikten genom att använda släta approximationer av euklidiska avståndsfält.

Våra resultat indikerar att våra algoritmer förser robotiksystem med i) bevisligen säkra regulatorer, ii) följsamma säkerhetsbegränsningar och iii) riskmedvetenhet i omodellerade miljöer. Dessa tre egenskaper bidrar till säkrare och mer riskmedvetna robotsystem i den verkliga världen.

Motion planning is one of the core problems in a wide range of robotic applications. We discuss the use of temporal logics to include complex objectives, constraints, and preferences in motion planning algorithms and focus on three topics: the first one addresses computational tractability of Linear Temporal Logic (LTL) motion planning in systems with uncertain non-holonomic dynamics, i.e. systems whose ability to move in space is constrained. We introduce feedback motion primitives and heuristics to guide motion planning and demonstrate its use on a rover in 2D and a fixed-wing drone in 3D. Second, we introduce combined motion planning and hybrid feedback control design in order to find and follow trajectories under Metric Interval Temporal Logic (MITL) specifications. Our solution creates a path to be tracked, a sequence of obstacle-free polytopes and time stamps, and a controller that tracks the path while staying in the polytopes. Third, we focus on motion planning with spatio-temporal preferences expressed in a fragment of Signal Temporal Logic (STL). We introduce a cost function for a of a path reflecting the satisfaction/violation of the preferences based on the notion of STL spatial and temporal robustness. We integrate the cost into anytime asymptotically optimal motion planning algorithm RRT ⋆ and we show the use of the algorithm in integration with an autonomous exploration planner on a UAV.

Recent trends envisage robots being deployed inareas deemed dangerous to humans, such  as buildings with gasand radiation leaks. In such situations, the model of the underlying  hazardous process might be unknown to the agent a priori, giving rise to the problem of planning for safe behaviour inpartially known environments. We employ Gaussian Process regression to create a probabilistic model of the hazardous process from local noisy samples. The result of this regression is then used by a risk metric, such as the Conditional Value-at-Risk, to reason about the safety at a certain state. The outcome is a risk function that can  be employed in optimal motion planning problems. We demonstrate the use of the proposed function in two approaches. First is a sampling-based motion planning algorithm with an  event-based trigger for online replanning. Second is an adaptation to the  incremental Gaussian Process motion planner (iGPMP2), allowing it to quickly react and adapt to the environment. Both algorithms are evaluated in representative simulation scenarios, where they demonstrate the ability of avoiding high-risk areas.

Recent trends envisage robots being deployed in areas deemed dangerous to humans, such as buildings with gas and radiation leaks. In such situations, the model of the underlying hazardous process might be unknown to the agent a priori, giving rise to the problem of planning for safe behaviour in partially known environments. We employ Gaussian process regression to create a probabilistic model of the hazardous process from local noisy samples. The result of this regression is then used by a risk metric, such as the Conditional Value-at-Risk, to reason about the safety at a certain state. The outcome is a risk function that can be employed in optimal motion planning problems. We demonstrate the use of the proposed function in two approaches. First is a sampling-based motion planning algorithm with an event-based trigger for online replanning. Second is an adaptation to the incremental Gaussian Process motion planner (iGPMP2), allowing it to quickly react and adapt to the environment. Both algorithms are evaluated in representative simulation scenarios, where they demonstrate the ability of avoiding high-risk areas.

Complex mission specifications can be often specified through temporal logics, such as Linear Temporal Logic and its syntactically co-safe fragment, scLTL. Finding trajectories that satisfy such specifications becomes hard if the robot is to fulfil the mission in an initially unknown environment, where neither locations of regions or objects of interest in the environment nor the obstacle space are known a priori. We propose an algorithm that, while exploring the environment, learns important semantic dependencies in the form of a semantic abstraction, and uses it to bias the growth of an Rapidly-exploring random graph towards faster mission completion. Our approach leads to finding trajectories that are much shorter than those found by the sequential approach, which first explores and then plans. Simulations comparing our solution to the sequential approach, carried out in 100 randomized office-like environments, show more than 50% reduction in the trajectory length.

Complex mission specifications can be often specifiedthrough temporal logics, such as Linear Temporal Logic and itssyntactically co-safe fragment, scLTL. Finding trajectories thatsatisfy such specifications becomes hard if the robot is to fulfilthe mission in an initially unknown environment, where neitherlocations of regions or objects of interest in the environmentnor the obstacle space are known a priori. We propose an algorithmthat, while exploring the environment, learns importantsemantic dependencies in the form of a semantic abstraction,and uses it to bias the growth of an Rapidly-exploring randomgraph towards faster mission completion. Our approach leadsto finding trajectories that are much shorter than those foundby the sequential approach, which first explores and then plans.Simulations comparing our solution to the sequential approach,carried out in 100 randomized office-like environments, showmore than 50% reduction in the trajectory length.

We propose a hybrid feedback control law that guarantees both safety and asymptotic stability for a class of Lagrangian systems in environments with obstacles. Rather than performing trajectory planning and implementing a trajectory-tracking feedback control law, our approach requires a sequence of locations in the environment (a path plan) and an abstraction of the obstacle-free space. The problem of following a path plan is then interpreted as a sequence of reach-avoid problems: the system is required to consecutively reach each location of the path plan while staying within safe regions. Obstacle-free ellipsoids are used as a way of defining such safe regions, each of which encloses two consecutive locations. Feasible Control Barrier Functions (CBFs) are created directly from geometric constraints, the ellipsoids, ensuring forward-invariance, and therefore safety. Reachability to each location is guaranteed by asymptotically stabilizing Control Lyapunov Functions (CLFs). Both CBFs and CLFs are then encoded into quadratic programs (QPs) without the need of relaxation variables. Furthermore, we also propose a switching mechanism that guarantees the control law is correct and well-defined even when transitioning between QPs. Simulations show the effectiveness of the proposed approach in two complex scenarios.

We propose a sampling-based motion planning algorithm for systems with complex dynamics and temporal logic specifications allowing to tackle sophisticated missions. By complex dynamics we refer to non-holonomy and  disturbance that prevent  implementation  of  an  exact steer function. We instead construct a set of feedback motion primitives guaranteeing bounded state uncertainty (and thus safety) allowing the system to follow an arbitrarily long trajectory without replanning. The motion primitives allow to use A*-based algorithm to provably accomplish the temporal logic mission. We propose a heuristics for the A*-based algorithm via construction of backward trees. We illustrate the approach on several case studies, including simulations of a rover and fixed wing drone. We further show that construction of backward trees allows for faster re-planning compared to the state-of-the-art. 

While motion planning under temporal logic specifications has been addressed in several state-of-the-art works, spatial aspects have been so far largely neglected. In this work, we enrich the semantics of robot motion specifications by including preferences on spatial relations between its trajectory and various elements in its environment. The spatial preferences are given in a fragment of Signal Temporal Logic (STL) on top of complex missions in syntactically co-safe Linear Temporal Logic (scLTL). We propose a cost function with user-specified parameters, which determines the compromise between efficiency and spatial robustness of a trajectory.  The proposed modification of the incremental sampling-based RRT$^\star$ driven by this cost function guarantees that the motion plan (if found) simultaneously satisfies the mission and asymptotically minimize the cost. The paper includes several case studies showcasing the effects of the user-adjustable parameters on the resulting trajectories.