This paper describes a concept for a collision avoidance system for ships, which is based on model predictive control. A finite set of alternative control behaviors are generated by varying two parameters: offsets to the guidance course angle commanded to the autopilot and changes to the propulsion command ranging from nominal speed to full reverse. Using simulated predictions of the trajectories of the obstacles and ship, compliance with the Convention on the International Regulations for Preventing Collisions at Sea and collision hazards associated with each of the alternative control behaviors are evaluated on a finite prediction horizon, and the optimal control behavior is selected. Robustness to sensing error, predicted obstacle behavior, and environmental conditions can be ensured by evaluating multiple scenarios for each control behavior. The method is conceptually and computationally simple and yet quite versatile as it can account for the dynamics of the ship, the dynamics of the steering and propulsion system, forces due to wind and ocean current, and any number of obstacles. Simulations show that the method is effective and can manage complex scenarios with multiple dynamic obstacles and uncertainty associated with sensors and predictions.

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Ship Collision Avoidance and COLREGS Compliance Using Simulation-Based Control Behavior Selection With Predictive Hazard Assessment

This paper attempts to develop a unified receding horizon optimization (RHO) scheme for the integrated path planning and tracking control of an autonomous underwater vehicle (AUV). Considering that the effective sensing range of onboard sensors is practically short, we formulate the path planning into RHO problems with the spline path template. The planned path is subsequently viewed as the state trajectory of a virtual reference system having the same kinematic and dynamic properties as the AUV's. Appropriately constructed error dynamics makes the AUV tracking control equivalent to the regulation problem of the error dynamic system, which facilitates the derivation of theoretical results via nonlinear MPC techniques. The model predictive control (MPC) tracking controller is designed so that closed-loop stability can be ensured. Due to the inherent RHO nature, both the path planning and tracking control are incorporated into an unified scheme. Simulation studies are conducted using a realistic dynamic model of the Falcon AUV, which was created in our previous experimental work. The simulation results demonstrate the effectiveness of the proposed control algorithm.

Integrated Path Planning and Tracking Control of an AUV: A Unified Receding Horizon Optimization Approach

Skid-steered vehicles are often used as outdoor mobile robots due to their robust mechanical structure and high maneuverability. Sliding, along with rolling, is inherent to general curvilinear motion, which makes both kinematic and dynamic modeling difficult. For the purpose of motion planning, this paper develops and experimentally verifies dynamic models of a skid-steered wheeled vehicle for general planar (2-D) motion and for linear 3-D motion. These models are characterized by the coefficient of rolling resistance, the coefficient of friction, and the shear deformation modulus, which have terrain-dependent values. The dynamic models also include motor saturation and motor power limitations, which enable correct prediction of vehicle velocities when traversing on hills. It is shown that the closed-loop system that results from inclusion of the dynamics of the [proportional--integral--derivative (PID)] speed controllers for each set of wheels does a much better job than the open-loop model of predicting the vehicle linear and angular velocities. For a vehicle turning with small linear and angular accelerations, the model provides accurate predictions of velocities and reasonable predictions of torques. Hence, the closed-loop model is recommended for motion planning.

Analysis and Experimental Verification for Dynamic Modeling of A Skid-Steered Wheeled Vehicle

This paper presents a viable approach for incorporating collision avoidance strategies into existing guidance and control systems on marine vessels. We propose a method that facilitates the use of simulation-based Model Predictive Control (MPC) for collision avoidance (COLAV) on marine vessels. Any COLAV strategy to be applied in real traffic must adhere to the international regulations for preventing collisions at sea (COLREGS). The proposed MPC COLAV method does not rely on an accurate model of the guidance system to achieve vessel behaviors that are compliant with the COLREGS. Rather, it depends on transitional costs in the MPC objective for collision avoidance maneuvers that are being executed by the marine vessel. Hence, it is straightforward to implement the MPC COLAV on different vessels without specific knowledge of the vessel's guidance strategy. Moreover, it offers the possibility to switch between different (possibly application specific) guidance strategies on the same vessel while running the same MPC COLAV algorithm. We present results from full scale experiments that show the viability of our method in different collision avoidance scenarios.

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MPC-based Collision Avoidance Strategy for Existing Marine Vessel Guidance Systems

In this paper, a distributed linear MPC approach to solve the trajectory planning problem for rotary-wing UAVs is proposed, where the objective of the UAV system is to form a communication network to multiple targets with given radio communication capacities. The approach explicitly incorporates constraints on radio communication path losses, computed by using SPLAT! that is able to take into account terrain models and antenna locations. In order to enhance the online optimization, at each time sample the terrain below each UAV and the communication path losses are approximated with linear functions of the spatial coordinates. This leads to linear MPC sub-problems, which are solved by using convex quadratic programming. An algorithm for automatic initialization and optimal reconfiguration of the communication topology in case of failures or severe radio path loss due to e.g. channel fading, is proposed. The communication network that is provided by the UAVs is considered to be a payload communication capacity that is normally independent of the command and control datalink used to control the UAVs. The performance of the distributed linear MPC trajectory planning and the reconfiguration algorithm is studied on two simulation cases with four UAVs and two targets.

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UAVs Trajectory Planning by Distributed MPC under Radio Communication Path Loss Constraints

Unmanned Underwater Vehicles (UUVs) can be utilized to perform difficult tasks in cluttered environments such as harbor and port protection. However, since UUVs have nonlinear and highly coupled dynamics, motion planning and control can be difficult when completing complex tasks. Introducing models into the motion planning process can produce paths the vehicle can feasibly traverse. As a result, Sampling-Based Model Predictive Control (SBMPC) is proposed to simultaneously generate control inputs and system trajectories for an autonomous underwater vehicle (AUV). The algorithm combines the benefits of sampling-based motion planning with model predictive control (MPC) while avoiding some of the major pitfalls facing both traditional sampling-based planning algorithms and traditional MPC. The method is based on sampling (i.e., discretizing) the input space at each sample period and implementing a goal-directed optimization (e.g., A★) in place of standard numerical optimization. This formulation of MPC readily applies to nonlinear systems and avoids the local minima which can cause a vehicle to become immobilized behind obstacles. The SBMPC algorithm is applied to an AUV in a cluttered environment and an AUV in a common local minima problem.

Motion planning for an autonomous Underwater Vehicle via Sampling Based Model Predictive Control

Path planning is a method that determines a path, consecutive states, between a start state and goal state, LaValle (2006). However, in motion planning that path must be parameterized by time to create a trajectory. Consequently, not only is the path determined, but the time the vehicle moves along the path. To be successful at motion planning, a vehicle model must be incorporated into the trajectory computation. The motivation in utilizing a vehicle model is to provide the opportunity to predict the vehicle’s motion resulting from a variety of system inputs. The kinematic model enforces the vehicle kinematic constraints (i.e. turn radius, etc.), on the vehicle that limit the output space (state space). However, the kinematic model is limited because it does not take into account the forces acting on the vehicle. The dynamic model incorporates more useful information about the vehicle’s motion than the kinematic model. It describes the feasible control inputs, velocities, acceleration and vehicle/terrain interaction phenomena. Motion planning that will require the vehicle to perform close to its limits (i.e. extreme terrains, frequent acceleration, etc.) will need the dynamic model. Examples of missions that would benefit from using a dynamic model in the planning are time optimal motion planning, energy efficient motion planning and planning in the presence of faults, Yu et al. (2010). Sampling-based methods represent a type of model based motion planning algorithm. These methods incorporate the system model. There are current sampling-based planners that should be discussed: The Rapidly-Exploring Random Tree (RRT) Planner, Randomized A (RA) algorithm, and the Synergistic Combination of Layers of Planning (SyCLoP) multi-layered planning framework. The Rapidly-Exploring Random Tree Planner was one of the first single-query sampling based planners and serves as a foundation upon which many current algorithms are developed. The RRT Planner is very efficient and has been used in many applications including manipulator path planning, Kuffner & LaValle. (2000), and robot trajectory planning, LaValle & Kuffner (2001). However, the RRT Planner has the major drawback of lacking any sort of optimization other than a bias towards exploring the search space. The RA algorithm, which was designed based on the RRT Planner, addresses this drawback by combining the RRT Planner with an A algorithm. The SyCLoP framework is 11

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Motion Planning for Mobile Robots Via Sampling-Based Model Predictive Optimization

In this paper a novel method called Sampling-Based Model Predictive Control (SBMPC) is proposed as an efficient MPC algorithm to generate control inputs and system trajectories. The algorithm combines the benefits of sampling-based motion planning with MPC while avoiding some of the major pitfalls facing both traditional sampling-based planning algorithms and traditional MPC. The method is based on sampling (i.e., discretizing) the input space at each sample period and implementing a goal-directed optimization method (e.g., A*) in place of standard numerical optimization. This formulation of MPC readily applies to systems with nonlinear dynamics and avoids the local minima which can limit the performance of MPC algorithms implemented using traditional, derivative-based, nonlinear programming. The SBMPC algorithm is compared with a more standard online MPC algorithm using cluttered environment navigation for an Ackerman steered vehicle and a set point problem for a nonlinear, continuous stirred-tank reactor (CSTR).

Nonlinear Model Predictive Control using sampling and goal-directed optimization

Model Predictive Control (MPC) was originally developed for relatively slow processes in the petroleum and chemical industries and is well known to have diculties in computing control inputs in real time for processes with fast dynamics. In this paper a novel method called Sampling Based Model Predictive Control (SBMPC) is proposed as a resolution complete MPC algorithm to generate control inputs and system trajectories. The algorithm combines the benets of sampling based motion planning with MPC while avoiding some of the major pitfalls facing traditional sampling based planning algorithms. The method is based on sampling (i.e., discretizing) the control space at each sample period and using a goal oriented optimization method such as A in place of standard linear or nonlinear programming or evolutionary algorithms. This formulation of MPC applies easily to systems with nonlinear dynamics and avoids the local minima which can limit the performance of MPC algorithms implemented using nonlinear programming algorithms. Simulation results demonstrate the ecacy of SBMPC in guiding an autonomous ground vehicle from a start posture to a goal posture in regions populated with obstacles.

Sampling Based Model Predictive Control with Application to Autonomous Vehicle Guidance

The motors or engines of an autonomous ground vehicles (AGV) have torque and power limitations, which limit their abilities to climb steep hills, which are defined to be hills that have high grade sections in which the vehicle is forced to decelerate. Traversal of a steep hill requires the vehicle to have sufficient momentum before entering the hill. This problem is part of a larger class of momentum-based motion planning problems such as the problem of lifting heavy objects with manipulators. Hence, solutions to the steep hill climbing problem have much wider applicability. The motion planning here is accomplished using a dynamic model of the skid-steered AGV used in the experiments along with Sampling Based Model Predictive Control (SBMPC), a recently developed input sampling planning algorithm that may be viewed as a generalization of LPA* to the direct use of kinodynamic models. The motion planning is demonstrated experimentally using two scenarios, one in which the robot starts at rest at the bottom of a hill and one in which the robot starts at rest a distance from the hill. The first scenario requires the AGV to first reverse direction so that the vehicle can gather enough momentum before reaching the hill. This corresponds to having the vehicle begin at a local minimum, which results in a problem that many traditional model predictive control methods cannot solve. It is seen that, whereas open loop trajectories can lead to vehicle immobilization, SBMPC successfully uses the information provided by the dynamic model to ensure that the AGV has the requisite momentum.

Charmane V. Caldwell

Papers

Motion planning for an autonomous Underwater Vehicle via Sampling Based Model Predictive Control

Motion Planning for Mobile Robots Via Sampling-Based Model Predictive Optimization

Nonlinear Model Predictive Control using sampling and goal-directed optimization

Sampling Based Model Predictive Control with Application to Autonomous Vehicle Guidance

Motion planning for steep hill climbing