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.

This paper proposes an approach that combines motion planning and hybrid feedback control design in order to find and follow trajectories fulfilling a given complex mission involving time constraints. We use Metric Interval Temporal Logic (MITL) as a rich and rigorous formalism to specify such missions. The solution builds on three main steps: (i) using sampling-based motion planning methods and the untimed version of the mission specification in the form of Zone automaton, we find a sequence of waypoints in the workspace; (ii) based on the clock zones from the satisfying run on the Zone automaton, we compute time-stamps at which these waypoints should be reached; and (iii) to control the system to connect two waypoints in the desired time, we design a low-level feedback controller leveraging Time-varying Control Barrier Functions. Illustrative simulation results are included.

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.

Algorithms for autonomous robotic exploration usually focus on optimizing time and coverage, often in a greedy fashion. However, obstacle inflation is conservative and might limit mapping capabilities and even prevent the robot from moving through narrow, important places. This letter proposes a method to influence the manner the robot moves in the environment by taking into consideration a user-defined spatial preference formulated in a fragment of signal temporal logic (STL). We propose to guide the motion planning toward minimizing the violation of such preference through a cost function that integrates the quantitative semantics, i.e., robustness of STL. To demonstrate the effectiveness of the proposed approach, we integrate it into the autonomous exploration planner (AEP). Results from simulations and real-world experiments are presented, highlighting the benefits of our approach.

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.

Reasoning about probabilistic outcomes on stochastic models is of essence to safety-critical systems. In this paper we focus on risk-aware collision avoidance approaches in workspaces with static and dynamic obstacles. More specifically, for Lagrangian systems operating in workspaces without perfect information about the obstacle-space. In order to avoid collision with static obstacles, we build smooth approximations of the Euclidean distance field, along with its first and second derivatives, using Gaussian Process implicit surfaces. Since the predictive distance returned by such an approximation is a normal distribution, rather than simply using its mean value, we propose a risk-aware Control Barrier function. Risk metrics provide more coherent measures than chance constraint, with the benefit of distinguishing between tail events. We prove that by using the proposed approach, the Lagrangian system is bound to a smaller, but safer (in terms of risk-awareness), subset of the obstacle-free space. Besides that, we also propose a controller for avoiding collisions with ellipsoidal dynamic obstacles. We compose all the controllers together into a nonsmooth barrier function, and design a Quadratic Program-based optimization controller. The proposed approach is a step-forward towards closer integration between mapping algorithms and feedback controllers. Numerical simulations on synthetic environments highlight the capabilities of the approach proposed.