Safe Control Synthesis for Multicopter via Control Barrier Function Backstepping

A safe controller for multicopter is proposed using control barrier function. Multicopter dynamics are reformulated to deal with mixed-relative-degree and non-strict-feedback-form dynamics, and a time-varying safe backstepping controller is designed. Despite the time-varying variation, it is proven that the control input can be obtained by solving quadratic programming with affine inequality constraints. The proposed controller does not utilize a cascade control system design, unlike existing studies on the safe control of multicopter. Various safety constraints on angular velocity, total thrust direction, velocity, and position can be considered. Numerical simulation results support that the proposed safe controller does not violate all safety constraints including low- and high-level dynamics.Comment: 6 pages, 2 figures, accepted for IEEE Conference on Decision and Control (CDC) 202

Parameterized Convex Minorant for Objective Function Approximation in Amortized Optimization

Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for parameterized non-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find a global minimizer reliably and quickly by using convex optimization algorithms.Comment: 12 pages, 4 figure

Collision avoidance strategies for unmanned aerial vehicles in formation flight

Collision avoidance strategies for multiple UAVs (Unmanned Aerial Vehicles) based on geometry are investigated in this study. The proposed strategies allow a group of UAVs to avoid obstacles and separate if necessary through a simple algorithm with low computation by expanding the collision-cone approach to formation of UAVs. The geometric approach uses line-of-sight vectors and relative velocity vectors where dynamic constraints are included in the formation. Each UAV can determine which plane and direction are available for collision avoidance. An analysis is performed to define an envelope for collision avoidance, where angular rate limits and obstacle detection range limits are considered. Based on the collision avoidance envelope, each UAV in a formation determines whether the formation can be maintained or not while avoiding obstacles. Numerical simulations are performed to demonstrate the performance of the proposed strategies

Generalized formulation of linear nonquadratic weighted optimal error shaping guidance laws

This study presents a novel extension to the theory of optimal guidance laws represented by the nontraditional class of performance indices: nonquadratic-type signal Lp" role="presentation">Lp norm for the input weighted by an arbitrary positive function. Various missile guidance problems are generally formulated into a scalar terminal control problem based on the understanding of the predictor–corrector nature. Then, a new approach to derive the optimal feedback law, minimizing the nonquadratic performance index, is proposed by using the Hölderian inequality. The proposed extension allows a more general family of formulations for the design of closed-form feedback solutions to various guidance problems to be treated in a unified framework. The equivalence between the proposed approach and other design methodologies is investigated. In general, the type of input norm mainly determines the variability of input during the engagement while trading off against the rate of error convergence. The analytic solution derived in this study is verified by comparison with the solution from numerical optimization, and the effect of the exponent p" role="presentation">p in the performance index on the trajectory and command is demonstrated by numerical simulations

Integrated Design of Rotary UAV Guidance and Control Systems Utiliz- ing Sliding Mode Control Technique

Abstract In this paper, the Integrated Guidance and Control (IGC) law is proposed for the Rotary Unmanned Aerial Vehicle (RUAV). The objective of the IGC law is to consider the nonlinear dynamic characteristics of the RUAV and to design a guidance law which takes into consideration the nonlinear relationship between kinematics and dynamics. In order to control the RUAV system, sliding mode control scheme is adopted. As the RUAV is an under-actuated system, a slack variable approach is used to generate the available control inputs. Through the Lyapunov stability theorem, the stability of the proposed IGC law is proved. In order to verify the performance of the IGC law, numerical simulations are performed for waypoint tracking missions

Composite model reference adaptive control with parameter convergence under finite excitation

A new parameter estimation method is proposed in the framework of composite model reference adaptive control for improved parameter convergence without persistent excitation. The regressor filtering scheme is adopted to perform the parameter estimation with signals that can be obtained easily. A new framework for residual signal construction is proposed. The incoming data is first accumulated to build the information matrix, and then its quality is evaluated with respect to a chosen measure to select and store the best one. The information matrix is built to have full rank after sufficient but not persistent excitation. In this way, the exponential convergence of both tracking error and parameter estimation error can be guaranteed without persistent oscillation in the external command which drives the system. Numerical simulations are performed to verify the theoretical findings and to demonstrate the advantages of the proposed adaptation law over the standard direct adaptation law

Analytic approach to impact time guidance with look angle constraint using exact time-to-go solution

This paper proposes an analytic approach for impact time control guidance laws against stationary targets using biased proportional navigation. The proposed guidance scheme realizes the impact time control in two different ways: the first approach directly uses the exact time-to-go error to satisfy both the impact time control and the field-of-view constraint, while the second approach adopts a look angle tracking law to indirectly control the impact time, with the reference profile of the look angle generated using the exact time-to-go solution. The stability properties of the proposed guidance laws are discussed, and numerical simulations are carried out to evaluate their performance in terms of accuracy and efficiency

Data-efficient active weighting algorithm for composite adaptive control systems

We propose an active weighting algorithm for composite adaptive control to reduce the state and estimate errors while maintaining the estimation quality. Unlike previous studies that construct the composite term by simply stacking, removing, and pausing observed data, the proposed method efficiently utilizes the data by providing a theoretical set of weights for observations that can actively manipulate the composite term to have desired characteristics. As an example, a convex optimization formulation is provided, which maximizes the minimum eigenvalue while keeping other constraints, and an illustrative numerical simulation is also presented

Online trajectory replan for gliding vehicle considering terminal velocity constraint

Controlling the terminal velocity can improve the effectiveness of guided missiles. In particular, a ballistic missile propelled by solid rocket motors can successfully accomplish its mission when it hits the target at an appropriate speed. In this study, a method for modifying the trajectory of gliding vehicle, i.e., gliding ballistic missiles is proposed to meet the terminal velocity constraint by reflecting the effects of the environment during a flight. The proposed framework consisting of trajectory generation and dynamic propagation compensates for errors due to uncertainties in real time. The trajectory generation step provides various trajectories that satisfy the given constraints based on information about the current state. The dynamic propagation step efficiently predicts the terminal velocity for each of the generated trajectories and finds the trajectory with the lowest terminal speed error. A numerical simulation is performed considering various conditions to demonstrate the performance of the proposed method