-- Mobile robot navigation systems are increasingly relied upon in dynamic and complex environments, yet they often struggle with map inaccuracies and the resulting inefficient path planning. This paper presents MRHaD, a Mixed Reality-based Hand-drawn Map Editing Interface that enables intuitive, real-time map modifications through natural hand gestures. By integrating the MR head-mounted display with the robotic navigation system, operators can directly create hand-drawn restricted zones (HRZ), thereby bridging the gap between 2D map representations and the real-world environment. Comparative experiments against conventional 2D editing methods demonstrate that MRHaD significantly improves editing efficiency, map accuracy, and overall usability, contributing to safer and more efficient mobile robot operations. The proposed approach provides a robust technical foundation for advancing human-robot collaboration and establishing innovative interaction models that enhance the hybrid future of robotics and human society. I. INTRODUCTION Recent advances in autonomous mobile robots have opened up new opportunities for human-robot collaboration in various application domains, including logistics, healthcare, and public spaces [1], [2], [3]. Typically, these robots use pre-constructed environmental maps and dynamically adjust their paths based on real-time environmental sensing with various onboard sensors. Path planning methods are generally divided into two categories: global planning and local planning [4].

Deep reinforcement learning (DRL) has attracted much attention as an approach to solve sequential decision making problems without mathematical models of systems or environments. In general, a constraint may be imposed on the decision making. In this study, we consider the optimal decision making problems with constraints to complete temporal high-level tasks in the continuous state-action domain. We describe the constraints using signal temporal logic (STL), which is useful for time sensitive control tasks since it can specify continuous signals within a bounded time interval. To deal with the STL constraints, we introduce an extended constrained Markov decision process (CMDP), which is called a $\tau$-CMDP. We formulate the STL constrained optimal decision making problem as the $\tau$-CMDP and propose a two-phase constrained DRL algorithm using the Lagrangian relaxation method. Through simulations, we also demonstrate the learning performance of the proposed algorithm.

We present a model-free reinforcement learning algorithm to find an optimal policy for a finite-horizon Markov decision process while guaranteeing a desired lower bound on the probability of satisfying a signal temporal logic (STL) specification. We propose a method to effectively augment the MDP state space to capture the required state history and express the STL objective as a reachability objective. The planning problem can then be formulated as a finite-horizon constrained Markov decision process (CMDP). For a general finite horizon CMDP problem with unknown transition probability, we develop a reinforcement learning scheme that can leverage any model-free RL algorithm to provide an approximately optimal policy out of the general space of non-stationary randomized policies. We illustrate the effectiveness of our approach in the context of robotic motion planning for complex missions under uncertainty and performance objectives.

Signal temporal logic (STL) is an expressive language to specify time-bound real-world robotic tasks and safety specifications. Recently, there has been an interest in learning optimal policies to satisfy STL specifications via reinforcement learning (RL). Learning to satisfy STL specifications often needs a sufficient length of state history to compute reward and the next action. The need for history results in exponential state-space growth for the learning problem. Thus the learning problem becomes computationally intractable for most real-world applications. In this paper, we propose a compact means to capture state history in a new augmented state-space representation. An approximation to the objective (maximizing probability of satisfaction) is proposed and solved for in the new augmented state-space. We show the performance bound of the approximate solution and compare it with the solution of an existing technique via simulations.

We present a framework that enables online planning for robotic systems in dynamic environments. The PLANrm framework presented in this work utilizes the theory of robustness and monitoring of Metric Temporal Logic (MTL) specifications to inspect and modify available plans to both avoid obstacles and satisfy specifications in a dynamic environment. The use of MTL allows the practitioner to set complex event and timing based specifications that need to be satisfied in the execution of the plan. The monitoring algorithm inspects the possible paths in a bounded window and selects and adjusts a path to satisfy the specifications. In this paper, we present initial results on the framework and an extended summary of the algorithmic results. The approach is illustrated using a running example of a car-like model with a number of MTL specifications.