Abstract: Stochastic nonlinear model predictive control (SNMPC) allows to directly take uncertainty of the dynamics and/or of the system's environment into account, e.g., by including probabilistic chance constraints. However, SNMPC requires the approximate computation of the probability distributions for the state variables that are propagated through the nonlinear system dynamics. This invention proposes the use of Gaussian-assumed density filters (ADF) to perform high-accuracy propagation of mean and covariance information of the state variables through the nonlinear system dynamics, resulting in a tractable SNMPC approach with improved control performance. In addition, the use of a matrix factorization for the covariance matrix variables in the constrained optimal control problem (OCP) formulation guarantees positive definiteness of the full trajectory of covariance matrices in each iteration of any optimization algorithm.

Abstract: A control system for controlling movement of a vehicle, is disclosed. The control system is configured to construct a graph having multiple nodes defining states of the vehicle. The multiple nodes comprise an initial node defining initial state and a target node defining target state. Each pair of nodes is connected by an edge defined by collision-free motion primitives where the nodes comprise motion cusps. Multiple nodes connected through edges form a first path. A first number of motion cusps in the first path is determined and the graph is expanded to add new nodes until a termination condition is met on determining that the first number of motion cusps is above a threshold. The expansion of the graph is subjected to a constraint associated with a total number of motion cusps. Further a second path is determined having lesser motion cusps than the first path.

Abstract: A global multi-vehicle decision making system is disclosed for providing real-time motion planning and coordination of one or multiple connected and automated and/or semi-automated vehicles (CAVs) in an interconnected traffic network that includes one or multiple non-controlled vehicles (NCVs), one or multiple conflict zones and one or multiple conflict-free road segments. The system includes a receiver configured to acquire infrastructure sensing signals, at least one memory configured to store map and programs, and at least one processor configured to perform steps of formulating a global mixed-integer programming (MIP) problem using the infrastructure sensing signals, computing a motion plan for each CAV and each NCV in the traffic network by solving the global MIP problem, computing an optimal sequence of entering/exiting times and a sequence of average velocities for each CAV and each NCV, and computing a velocity profile and/or one or multiple planned stops for each CAV.

Abstract: The present disclosure provides a system and a method for controlling a motion of a device from an initial state to a target state in an environment having obstacles that form constraints on the motion of the device. The method includes executing a learned function trained with machine learning to generate a feasible or infeasible trajectory connecting the initial state of the device with the target state of the device while penalizing an extent of violation of at least some of the constraints to produce an initial trajectory. The method further includes solving a convex optimization problem subject to the constraints to produce an optimal trajectory that minimizes deviation from the initial trajectory and controlling the motion of the device according to the optimal trajectory.

Abstract: The present disclosure provides a system and a method for controlling a motion of a robot from a starting point to a target point within a bounded space with a floorplan including one or multiple obstacles. The method includes solving for an electric potential in a bounded virtual space formed by scaling the floorplan of the bounded space with the one or multiple obstacles and applying charge to at least one bound of the bounded virtual space while treating the scaled obstacles as metallic surfaces with a constant potential value, wherein the electric potential provides multiple equipotential curves within the bounded virtual space. The method further includes selecting an equipotential curve with a potential value different from a potential value of an obstacle equipotential curve, determining a motion path based on the selected equipotential curve, and controlling the motion of the robot based on the determined motion path.

Abstract: A controller uses a motion trajectory for controlling a motion of a device to perform a task subject to constraints. The controller evaluates a parametric function to output predicted values for a set of discrete variables in a mixed-integer convex programming (MICP) problem for performing the task defined by the parameters. The controller fixes a first subset of discrete variables in the MICP to the predicted values outputted by the trained parametric function and updates at least some of the predicted values of a remaining subset of discrete variables to values are uniquely defined by the fixed values for the first subset of discrete variables and the constraints. Hence, the controller transforms the MICP into a convex programming (CP) problem, solves the CP problem subject to the constraints to produce a feasible motion trajectory, and controls the device according to the motion trajectory.

Abstract: The present disclosure provides a system and a method for jointly controlling one or multiple connected autonomous vehicles (CAVs) and one or multiple manual connected vehicles (MCVs) moving to form traffic on the same or intersecting roads. The method includes collecting states of each of the CAVs, each of the MCVs, and each of traffic signs regulating the traffic, and solving a multi-variable mixed-integer problem (MIP) optimizing a cost function for values of control commands changing states of each CAV and values of control commands changing states of each of the traffic signs. The cost function is optimized subject to a motion model of each of the CAVs, subject to constraints modeling general traffic rules, subject to timing constraints, and subject to a motion model of each MCV. The method further includes transmitting the optimized values of the control commands to the corresponding CAVs and corresponding traffic signs.

Abstract: A control system controls a vehicle using a probabilistic motion planner and an adaptive predictive controller. The probabilistic motion planner produces a sequence of parametric probability distributions over a sequence of target states for the vehicle with parameters defining a first and higher order moments. The adaptive predictive controller optimizes a cost function over a prediction horizon to produce a sequence of control commands to one or multiple actuators of the vehicle. The cost function balances a cost of tracking of different state variables in the sequence of the target states defined by the first moments. The balancing is performed by weighting different state variables using one or multiple of the higher order moments of the probability distribution.

Abstract: A stochastic model predictive controller (SMPC) estimates a current state of the system and a probability distribution of uncertainty of a parameter of dynamics of the system based on measurements of outputs of the system, and updates a control model of the system including a function of dynamics of the system modeling the uncertainty of the parameter with first and second order moments of the estimated probability distribution of uncertainty of the parameter. The SMPC determines a control input to control the system by optimizing the updated control model of the system at the current state over a prediction horizon and controls the system based on the control input to change the state of the system.

Abstract: To control a hybrid dynamical system, a predictive feedback controller formulates a mixed-integer nonlinear programming (MINLP) problem including nonlinear functions of continuous optimization variables representing the continuous elements of the operation of the hybrid dynamical system and/or one or multiple linear functions of integer optimization variables representing the discrete elements of the operation of the hybrid dynamical system. The MINLP problem is formulated into a separable format ensuring that the discrete elements of the operation are present only in the linear functions of the MINLP problem. The MINLP problem is solved over multiple iterations using a partial convexification of a portion of a space of the solution including a current solution guess. The partial convexification produces a convex approximation of the nonlinear functions of the MINLP without approximating the linear functions of the MINLP to produce a partially convexified MINLP.

Abstract: A control system for controlling a motion of a vehicle to a target driving goal uses a decision-maker configured to determine a sequence of intermediate goals leading to the next target goal by optimizing the motion of the vehicle subject to a first model and tightened driving constraints formed by tightening driving constraints by a safety margin, and uses a motion planner configured to determine a motion trajectory of the vehicle tracking the sequence of intermediate goals by optimizing the motion of the vehicle subject to the second model. The driving constraints include mixed logical inequalities of temporal logic formulae specified by traffic rules to define an area where the temporal logic formulae are satisfied, while the tightened driving constraints shrink the area by the safety margin, which is a function of a difference between the second model and the first model approximating the second model.

Abstract: To control a hybrid dynamical system, a predictive feedback controller formulates a mixed-integer nonlinear programming (MINLP) problem including nonlinear functions of continuous optimization variables representing the continuous elements of the operation of the hybrid dynamical system and/or one or multiple linear functions of integer optimization variables representing the discrete elements of the operation of the hybrid dynamical system. The MINLP problem is formulated into a separable format ensuring that the discrete elements of the operation are present only in the linear functions of the MINLP problem. The MINLP problem is solved over multiple iterations using a partial convexification of a portion of a space of the solution including a current solution guess. The partial convexification produces a convex approximation of the nonlinear functions of the MINLP without approximating the linear functions of the MINLP to produce a partially convexified MINLP.

Abstract: A method for controlling a system by a controller comprises accepting a current state of the system and selecting, using a trained function of the current state, a solver from a set of solvers. The method further comprises solving an optimal control optimization problem using the selected solver to produce a current control input, such that for at least some different control steps, the predictive controller solves a formulation of the optimal control optimization problem with different solvers having different accuracies, requiring different computational resources, or both and submitting the current control input to the system thereby changing the current state of the system.

Abstract: A processor of a computing device comprises: a rearrangement unit to rearrange a plurality of elements included in each of a Hessian matrix of an evaluation function and a coefficient matrix of the linear constraint; a generation unit to generate a simultaneous linear equation for finding the optimal solution, based on the evaluation function including the rearranged Hessian matrix and the linear constraint including the rearranged coefficient matrix; and a search unit to find the optimal solution using the simultaneous linear equation. The rearrangement unit rearranges the plurality of elements so as to gather a sparse element of the plurality of elements included in the Hessian matrix, and rearranges the plurality of elements so as to gather a sparse element of the plurality of elements included in the coefficient matrix.

Abstract: A processor of a computing device comprises: a generation unit to generate an active constraint set based on an inequality constraint set and an initial solution; a search unit to find a solution of a simultaneous linear equation generated based on the active constraint set and an evaluation function; and an updating unit to update the active constraint set based on the solution obtained by the search unit. The generation unit adds, to the active constraint set, the first inequality constraint determined as being not linearly dependent on one or more second inequality constraints included in the active constraint set.

Abstract: A controller for controlling a motion of at least one device subject to constraints on the motion, is disclosed. The controller comprises a processor and a memory, where the controller inputs parameters of the task including the state of the at least one device to a neural network trained to output an estimated motion trajectory for performing the task. Further, the controller extracts at least some of the integer values of a solution to a mixed-integer optimization problem for planning an execution of the task that results in the estimated motion trajectory. Further, the controller solves the mixed-integer optimization problem for the parameters of the task with corresponding integer values fixed to the extracted integer values to produce an optimized motion trajectory subject to the constraint and changes the state of the at least one device to track the optimized motion trajectory.

Abstract: Connected and automated vehicles (CAVs) have shown the potential to improve safety, increase road throughput, and optimize energy efficiency and emissions in several complicated traffic scenarios. This invention describes a mixed-integer programming (MIP) optimization method for global multi-vehicle decision making and motion planning of CAVs in a highly dynamic environment that consists of multiple human-driven, i.e., conventional or manual, vehicles and multiple conflict zones, such as merging points and intersections. The proposed approach ensures safety, high throughput and energy efficiency by solving a global multi-vehicle constrained optimization problem. The solution provides a feasible and optimal time schedule through road segments and conflict zones for the automated vehicles, by using information from the position, velocity, and destination of the manual vehicles, which cannot be directly controlled.

Abstract: Stochastic nonlinear model predictive control (SNMPC) allows to directly take uncertainty of the dynamics and/or of the system's environment into account, e.g., by including probabilistic chance constraints. However, SNMPC requires the approximate computation of the probability distributions for the state variables that are propagated through the nonlinear system dynamics. This invention proposes the use of Gaussian-assumed density filters (ADF) to perform high-accuracy propagation of mean and covariance information of the state variables through the nonlinear system dynamics, resulting in a tractable SNMPC approach with improved control performance. In addition, the use of a matrix factorization for the covariance matrix variables in the constrained optimal control problem (OCP) formulation guarantees positive definiteness of the full trajectory of covariance matrices in each iteration of any optimization algorithm.

Abstract: A stochastic model predictive controller (SMPC) estimates a current state of the system and a probability distribution of uncertainty of a parameter of dynamics of the system based on measurements of outputs of the system, and updates a control model of the system including a function of dynamics of the system modeling the uncertainty of the parameter with first and second order moments of the estimated probability distribution of uncertainty of the parameter. The SMPC determines a control input to control the system by optimizing the updated control model of the system at the current state over a prediction horizon and controls the system based on the control input to change the state of the system.

Abstract: A system is controlled by solving a mixed-integer optimal control optimization problem using branch-and-bound (B&B) optimization that searches for a global optimal solution within a search space. The B&B optimization iteratively partitions the search space into a nested tree of regions, and prunes at least one region from the nested tree of regions before finding a local optimal solution for each region when a dual objective value of a projection of a sub-optimal dual solution estimate for each region into a dual feasible space is greater than an upper bound or lesser than a lower bound of the global optimal solution maintained by the B&B optimization.