Sampling-based synthesis of maximally-satisfying controllers for temporal logic specifications

In control theory, models of physical processes, such as systems of differential equations, are usually checked against specifications, such as stability and set invariance. In formal methods, rich specifications, such as languages and formulae of temporal logics, are checked against models of software programs and digital circuits, such as finite transition graphs. With the development and integration of cyber physical and safety critical systems, there is an increasing need for computational tools for verification and control of complex systems from rich, temporal logic specifications. The formal verification and synthesis problems have been shown to be undecidable even for very simple classes of infinitespace continuous and hybrid systems. However, provably correct but conservative approaches, in which the satisfaction of a property by a dynamical system is implied by the satisfaction of the property by a finite over-approximation (abstraction) of the system, have received a lot of attention in recent years. Some classes of systems allowing for computationally efficient verification and control from temporal logic specifications are reviewed. For continuous and discrete-time linear systems and continuous-time multi-linear systems, it is shown that finite abstractions can be constructed through polyhedral operations only. By using techniques from model checking and automata games, this allows for verification and control from specifications given as Linear Temporal Logic (LTL) formulae over linear predicates in the state variables. A connection between the existence of Lyapunov functions and finite bisimulations is established for discrete-time linear and switched linear systems. Finally, optimality and correctness requirements are combined in a model predictive approach to generate control strategies for discrete-time linear systems. The usefulness of these computational tools is illustrated with various examples such as verification and synthesis of biological circuits in synthetic biology and motion planning and control in robotics.

Motion planning of robots based on the Markov decision process (MDP) is now one of the most important topics of robotics research. In motion planning of robots by the MDP, an efficient way to divide robot motion is essential because discrete expressions of states and transitions are used in the calculation. In preparing the discrete expressions of robot motion, it is important that the motion follows the MDP, second, that the time and the amount of memory for the planning calculation are reduced, and that the maneuverability and smoothness of the robot motion are not lost. This paper proposes a new discrete expression of robot motion that can meet these requirements considering the effect of robot dynamics to robot kinematics. The method uses a continuous-time continuous-variable neuron model, which has the stimulation and adaptation properties. The performance of the proposed method was examined by simulation of the motion planning of an under actuated underwater robot and under actuated manipulator with a free joint. The results show the high reliability and flexibility of the method.

In this paper, the problem of motion planning for a mobile robot is addressed in which motion planning scenarios such as reachability, invariance, surveillance and sequencing missions are formulated with Linear Temporal Logic (LTL). First, by using the idea of invariant set theory, a novel algorithm is proposed for checking the satisfaction of temporal logic planning specification in the offline phase. Then, an optimal control strategy is designed in the presence of bounded additive disturbances to meet the given temporal logic specification and system constraints. Illustrative case studies for a robot with a double integrator model are presented to demonstrate the applicability of the proposed approach in motion planning tasks.

This paper deals with motion planning and control for mobile robots. The various components of an integrated architecture for the mobile robot Hilare pulling a trailer are presented. The nonholonomic path planner is based on an original steering method accounting for the small-time controllability of the system. Then the path is transformed into a trajectory by including the dynamical constraints of the system (bounded velocity and bounded acceleration). Finally, the motion control is addressed. Due to the geometric transformation for a virtual robot, we show how to reduce the problem to a classical approach of trajectory tracking for a mobile robot moving forward only. The experimental results presented include two types of robot-trailer connection systems.

The generation of motion for robots obeys classically to a two-step paradigm. The first step is the planning, where the typical problem is to find a geometric path that allows the robot to reach the desired configuration starting from the current position while ensuring obstacle avoidance and enforcing the satisfaction of kinematic constraints. Motion planning lays its grounding on the decidability properties of this classic geometrical problem. Moreover, the traditional approaches that are used to find solutions rely on the global probabilistic certainty of the convergence of path construction stochastically sampled in the configuration-space. The second step of motion generation is the control, where the robot has to perform the planned motion while ensuring the respect of dynamical constraints. Motion control seeks primarily for local controllability or at least the stability of the motion. The basic instances of this problems have long been tackled using local state-space control. However, the typical nonlinearity of the dynamics, together with the non controllability of its linearization, lead more and more solutions to resort to model predictive control. These methods make it possible to predict the outcome of a control strategy in a future horizon and to improve it accordingly, commonly by using numerical optimizations which take into account the safety constraints and efficiency intents. However, since few years, the improvement of computational capabilities and numerical algorithms allows more and more to deal with complex dynamical systems and for longer horizons. This allows then these approaches to untighten the local nature of their applications and progressively start wider explorations of their reachable space. This evolution brings us to the question of the rising overlap between planning and control. Today, most planning problems would take too much time to be solved online with numerical approaches. Does that imply that the generation of motion will theoretically never be free of the necessity of a prior planning? Or on the contrary, is planning only a numerical issue?

Automatic synthesis from linear temporal logic (LTL) specifications is widely used in robotic motion planning and control of autonomous systems. A common specification pattern in such applications consists of an LTL formula describing the requirements on the behaviour of the system, together with a set of additional desirable properties. We study the synthesis problem in settings where the overall specification is unrealizable, more precisely, when some of the desirable properties have to be (temporarily) violated in order to satisfy the system’s objective. We provide a quantitative semantics of sets of safety specifications, and use it to formalize the “best-effort” satisfaction of such soft specifications while satisfying the hard LTL specification. We propose an algorithm for synthesizing implementations that are optimal with respect to this quantitative semantics. Our method builds upon the idea of bounded synthesis, and we develop a MaxSAT encoding which allows for maximizing the quantitative satisfaction of the soft specifications. We evaluate our algorithm on scenarios from robotics and power distribution networks.

Sampling-based Motion Planning with Temporal Logic Missions and Spatial Preferences

Motion planning and control issue of quadruped robots is a challenging topic because it requires a lot of professional knowledge and tedious manual design based on traditional control methods. This paper proposes a novel method of training quadruped robots to generate locomotion gaits by combining the deep reinforcement learning. The control problem of quadruped robots is modeled as a Markov Decision Process, and a universal quadruped robot motion control reward mechanism is developed. A variety of gaits for the quadruped robot is generated by adding a gait reference frame. Two deep reinforcement learning algorithms are used for training and comparison. The desired gait locomotion control strategy is generated through training so that the robot can realize stable walking with the desired gait. Finally, the proposed method is tested and evaluated in a simulation environment using the A1 quadruped robot model.

In this paper, different research trends that use symbolic techniques for robot motion planning and control are illustrated. As it often happens in new research areas, contributions to this topic started at about the same time by different groups with different emphasis, approaches, and notation. This article tries to describe a framework in which many of the current methods and ideas can be placed and to provide a coherent picture of what the authors want to do, what have they got so far, and what the main missing pieces are. Generally speaking, the aim of symbolic control as is envisioned in this article is to enable the usage of methods of formal logic, languages, and automata theory for solving effectively complex planning problems for robots and teams of robots. The results presented in this article can be divided in two groups: top-down approaches, whereby formal logic tools are employed on rather abstract models of robots; and bottom up approaches, whose aim is to provide means by which such abstractions are possible and effective. The two ends do not quite tie as yet, and much work remains to be done in both directions to obtain generally applicable methods. However, the prospects of symbolic control of robots are definitely promising, and the challenging nature of problems to be solved warrants for the interest of a wide community of researchers

The experience of the design of the nonlinear position control confirmed the remarkable potential of backstepping and fuzzy logic in the development of effective decision laws capable of overcoming the inherent limitations of model-based control strategies. This paper focuses on design of hybrid backstepping and fuzzy position logic controls of mobile robot that satisfied a good position tracking performance with simultaneously satisfactory control of velocities, which has an impact on wheel torques. In our previously designed backstepping controller a good tracking performance was obtained. However, its main shortcoming is unsatisfactory control velocities values, particularly at the beginning of tracking. Control parameters of backstepping controller and membership functions of fuzzy controller are adjusted by genetic algorithms. Advantage of the proposed fuzzy controller, and also hybrid backstepping controller, lies in the fact that control velocities (and consequently, the control torques) cannot exceed certain limits. Consequently, these controllers radically decreased the control velocities without major impact on tracking performance. Finally, from the simulation results obtained, it can be concluded that the proposed hybrid backstepping and fuzzy design achieve the desired results. Future work will include the investigation of a fuzzy stability of the proposed fuzzy logic position system.

The need for combined task and motion planning (CTAMP) in robotics is well known as robotic technologies become more mature. The goal of CTAMP is to determine a proper sequence of a robot’s actions based on symbolic and geometric reasoning. Because of the fundamental difference in symbolic and geometric reasoning, a CTAMP system often requires an interface module between the two reasoning modules. We propose a CTAMP system in which a symbolic action sequence is generated in task planning, and each action is verified geometrically in motion planning using the off-the-shelf planners and reasoners. The approach is that a set of action models is defined with PDDL in the interface module (action library) and the required information to each planner is automatically provided by the interface module. The proposed method was successfully implemented in three simulated experiments that involve manipulation tasks. According to our findings, the proposed method is effective in responding to changes in the environment and uncertainty with errors in recognition of the environment and the robot motion control.

Robot motion planning is a core technology for complex manipulation tasks, widely applied in industrial automation, human-robot collaboration, and service robotics. Traditional planning methods face a dilemma between efficiency and solution quality under complex constraints: sampling-based methods can be inefficient, optimization-based methods may get trapped in local optima, and learning-based methods often generalize poorly. Recently, diffusion-model-based planners have achieved high-quality trajectory generation and can incorporate constraints via gradient guidance. However, most existing approaches apply step-wise guidance at every reverse step, causing excessive inference time; moreover, guidance in early high-noise stages is often low-fidelity and yields limited benefit, wasting computation. We propose AMPD (Adaptive Motion Planning Diffusion), which leverages diffusion noise dynamics to improve real-time efficiency while preserving feasibility. AMPD introduces two complementary designs: (1) a smoothness-aware training objective (SmoothLoss) that shapes the learned prior toward physically plausible trajectories, reducing the need for corrective guidance; and (2) a time-adaptive guidance schedule that allocates guidance computation to denoising stages where gradients are more informative. Experiments on the densely constrained EnvNarrowPassageDense2D benchmark demonstrate that AMPD improves both efficiency and safety over the diffusion baseline MPD, reducing inference time from 1.184s to 0.812s (~1.46× speedup) while increasing the feasible-sample fraction from 73.10% to 91.40%, and decreasing collision intensity from 0.74% to 0.08%. Furthermore, extended evaluations on an extreme maze environment validate the planner’s scalability. AMPD maintains robust performance (89.2% success rate, sub-second inference) where baselines fail due to local optima or timeouts.

The robotic servicing of satellites on-orbit will play an important role in extending their lifespan and mitigating space debris expansion. However, most maneuvers related to these goals present a set of unique challenges which are hard to assess in reality. On the other hand, a reliable prediction of the feasibility of servicing maneuvers is increasingly required. This paper presents a simulation-driven framework in which satellites approaching for servicing purposes is first decomposed in heterogeneous system components fulfilling specific mission critical objectives. These include vision-based tracking and estimation of the state of target satellites as well as robotic motion planning and control to reach a desired point on the satellite. A subsequent integration of these components allows to systematically capture key processes behind satellites approaching on-orbit in a holistic fashion. The high modularization and systematical interplays between the constituting system components enable a flexible and gradual enhancement of simulation fidelity. The significance of simulation results has been evaluated with respect to real setups. These results substantiate the effectiveness of the approach to facilitate complex and hazardous space activities while cutting down costs.

This paper presents a fuzzy-flatness technique for the efficient manipulation of mobile robots with nonholonomic constraints. A decoupled “path trajectory” planning approach is firstly defined to ensure the generation of reference trajectories that respect the nonholonomic constraints. An auto-tuned endogenous feedback control law is then designed to ensure good tracking of the desired tasks despite uncertainties. The controller gains are adjusted online by using a suitable fuzzy controller. Based on the developed algorithm and the laboratory test prototype Pioneer-3dx, numerical tests were carried out to evaluate the performances of the proposed approach.

The analytical sensitivity analysis, i.e., the analytical first-order partial derivatives of dynamical equations, is one key to improving descent-based optimization methods for motion planning and control of robots. This paper proposes an efficient algorithm that recursively evaluates the analytic gradient of the dynamical equations of a multibody system. The theory of projective geometric algebra (PGA) is used to generate the algorithm. It provides a systemic and geometrically intuitive interpretation for the multibody system dynamics, and the resulting algorithm is highly efficient, with concise formula. The algorithm is first applied to the open-chain system and extended for the cases when kinematic loops are contained. The runtime varying with respect to the degree-of-freedom (DOF) of the system is analyzed. The results are compared with that obtained from the algorithm based on spatial vector algebra (SVA) using open-source matlab codes. A 2DOF serial robot, a 3DOF robot with a kinematic loop and the PUMA560 robot are used for the validation of the minimum-effort motion planning, and it is verified that the proposed algorithm improves the efficiency.