MTSOS: calling MTSOS

MTSOS can either be called from within MATLAB or as a standard C function.

MATLAB

[b u v fx iterate timed] = MTSOS(S,flags,parameters)

Inputs

S	a matrix, representing , the path the vehicle must traverse, evaluated at the discretization points
flags	modifies behavior; does not need to be set
flags.display	0: default, no information printed 1: very limited information reported (iteration number, current residual, decrement); most useful for tracking progress of a large problem
flags..kappa	1: default, used for a barrier method 0: use a fixed value of defined in parameter.kappa
flags.timer	0: default, reports no timing 1: reports timing values for development purposes, not useful for the general user
parameters	problem and algorithm specific information, consisting of several required and many optional parameters
parameters.initial_velocity	REQUIRED: initial generalized speed of the vehicle, as defined in Minimum-Time Speed Optimization Along a Fixed Path
parameters.U_size	REQUIRED: , the number of control inputs to the vehicle
parameters.alpha	default, 0.01: back tracking line search parameter as defined in Convex Optimization ;
parameters.beta	default, 0.75: back tracking line search parameter as defined in Convex Optimization ;
parameters.epsilon	default, 0.1: the accuracy desired from the algorithm;
parameters.initial_b	a length vector of initial values for the algorithm to use (instead of its heuristic — make b small)
parameters.intial_u	an matrix of initial values for the algorithm to use (instead of setting all controls to zero)
parameters.kappa	default, 0.1: initial value of ;
parameters.MAX_ITERATIONS	default, 100: the maximum iterations the interior point method performs before the algorithm exits
parameters.variables	a vector of data available in the dynamics and barrier functions (in the test file: mass of the vehicle and maximum force that can be applied)

Outputs

b	a length vector of the optimal values as defined in Minimum-Time Speed Optimization Along a Fixed Path
u	an matrix of the control inputs required for optimal traversal of the trajectory
v	a length vector of the dual variables associated with the equality constraints; entries correspond to the matrix of Minimum-Time Speed Optimization Along a Fixed Path
fx	the optimal traverse time of the path
timed	a field for the returning of internal timing for development, not useful to the general user

C

int so_MTSOS(problem_params* p_params, algorithm_flags* flags,

algorithm_params* a_params, optional_params* o_params,
double** p_b, double** p_u, double** p_v, double* pfx,
double** p_timers, int* piterations)

Inputs

problem_params	a structure of REQUIRED problem data with attributes given below
double initial_velocity	initial generalized speed of the vehicle, as defined in Minimum-Time Speed Optimization Along a Fixed Path
double* S	a length array, representing , the path the vehicle must traverse, evaulated at discretization points , concatenated
int S_length	, the number of points in S
int State_size	, the number of states of the vehicle
int U_size	, the number of control inputs to the vehicle
algorithm_flags	a structure containing several flags to modify algorithm behavior
int display	0 : default, no information is reported 1: very limited information is reported (iteration number, current residual, decrement); most useful for tracking progress of a large problem
int kappa	1 : default, used for a barrier method 0 : use a fixed value of defined in algorithm_params.kappa
int timer	0 : default, reports no timing 1 : reports timing values for development purposes, not useful for the general user
algorithm_params	a structure of parameters to change the algorithm from its default values; pass in NULL to use the default values
double alpha	default, 0.01: back tracking line search parameter as defined in Convex Optimization ;
double beta	default, 0.75: back tracking line search parameter as defined in Convex Optimization ;
double epsilon	default, 0.1: the accuracy desired from the algorithm;
double kappa	default, 0.1: initial value of ;
int MAX_ITERATIONS	default, 100: the maximum iterations the interior point method performs before the algorithm exits
optional_params	a structure of optional information for the algorithm
double* initial_b	a length array of initial values for the algorithm to use (instead of its heuristic — make b small)
double* intial_u	a length array of initial values for the algorithm to use (instead of setting all controls to zero), concatenated
double* variables	an array of data available in the dynamics and barrier functions (in the test file: mass of the vehicle and the maximum force that can be applied)
int variables_length	the length of the array in variables

Outputs

Pass in the necessary pointers and references and MTSOS will allocate the pointers and populate them. The user is responsible for freeing these arrays.

RETURN int	1 : everything ran smoothly 0 : an error occurred
double** p_b	a length array of the optimal values as defined in Minimum-Time Speed Optimization Along a Fixed Path
double** p_u	a length array of the optimal controls , representing an matrix in column first order
double** p_v	a length array of the dual variables corresponding to the equality constraints represented by the matrix as defined in Minimum-Time Speed Optimization Along a Fixed Path
double* pfx	optimal time to traverse the path (a reference to a double)
double** p_timers	timing data useful for development, but not of interest to most users
int* piterations	the number of iterations of the interior point method required to reach the solution (a reference to an int)