I am currently exploring the tractor-trailer reversing control logic used in the Navigation Toolbox example titled "Reverse-Capable Motion Planning for Tractor-Trailer Model Using plannerControlRRT." While analyzing the helper files, I came across the virtualToActualSteering function inside exampleHelperPurePursuitGetSteering.m. The code comments explicitly state that this function was generated by the Symbolic Math Toolbox version 8.6.
Here is the generated code block:
function alphaDes = virtualToActualSteering(beta, L1, L2, M)
%virtualToActualSteering Convert trailer’s virtual steer command to truck steering angle
%
% This function was generated by the Symbolic Math Toolbox version 8.6.
% 13-Aug-2020 15:29:19
t2 = sign(beta);
t3 = L2.^2;
t4 = beta.*t2;
t5 = tan(t4);
t6 = t5.^2;
t7 = t6+1.0;
alphaDes = t2.*atan(-(L1.*M.*t5-sqrt(t7).*abs(t5).*sqrt(L1.^2.*t3))./(t3.*t7-M.^2));
end
I would like to deeply understand how this mathematical relationship is derived. Specifically, I want to know which base kinematic equations, differential constraints, and geometric relationships of the truck-trailer system were fed into the Symbolic Math Toolbox to yield this exact analytical solution. Could anyone share the underlying theoretical background, the differential equations involved, or the symbolic derivation steps used to achieve this exact formulation?
Thank you in advance for your help.I am currently exploring the tractor-trailer reversing control logic used in the Navigation Toolbox example titled "Reverse-Capable Motion Planning for Tractor-Trailer Model Using plannerControlRRT." While analyzing the helper files, I came across the virtualToActualSteering function inside exampleHelperPurePursuitGetSteering.m. The code comments explicitly state that this function was generated by the Symbolic Math Toolbox version 8.6.
Here is the generated code block:
function alphaDes = virtualToActualSteering(beta, L1, L2, M)
%virtualToActualSteering Convert trailer’s virtual steer command to truck steering angle
%
% This function was generated by the Symbolic Math Toolbox version 8.6.
% 13-Aug-2020 15:29:19
t2 = sign(beta);
t3 = L2.^2;
t4 = beta.*t2;
t5 = tan(t4);
t6 = t5.^2;
t7 = t6+1.0;
alphaDes = t2.*atan(-(L1.*M.*t5-sqrt(t7).*abs(t5).*sqrt(L1.^2.*t3))./(t3.*t7-M.^2));
end
I would like to deeply understand how this mathematical relationship is derived. Specifically, I want to know which base kinematic equations, differential constraints, and geometric relationships of the truck-trailer system were fed into the Symbolic Math Toolbox to yield this exact analytical solution. Could anyone share the underlying theoretical background, the differential equations involved, or the symbolic derivation steps used to achieve this exact formulation?
Thank you in advance for your help. I am currently exploring the tractor-trailer reversing control logic used in the Navigation Toolbox example titled "Reverse-Capable Motion Planning for Tractor-Trailer Model Using plannerControlRRT." While analyzing the helper files, I came across the virtualToActualSteering function inside exampleHelperPurePursuitGetSteering.m. The code comments explicitly state that this function was generated by the Symbolic Math Toolbox version 8.6.
Here is the generated code block:
function alphaDes = virtualToActualSteering(beta, L1, L2, M)
%virtualToActualSteering Convert trailer’s virtual steer command to truck steering angle
%
% This function was generated by the Symbolic Math Toolbox version 8.6.
% 13-Aug-2020 15:29:19
t2 = sign(beta);
t3 = L2.^2;
t4 = beta.*t2;
t5 = tan(t4);
t6 = t5.^2;
t7 = t6+1.0;
alphaDes = t2.*atan(-(L1.*M.*t5-sqrt(t7).*abs(t5).*sqrt(L1.^2.*t3))./(t3.*t7-M.^2));
end
I would like to deeply understand how this mathematical relationship is derived. Specifically, I want to know which base kinematic equations, differential constraints, and geometric relationships of the truck-trailer system were fed into the Symbolic Math Toolbox to yield this exact analytical solution. Could anyone share the underlying theoretical background, the differential equations involved, or the symbolic derivation steps used to achieve this exact formulation?
Thank you in advance for your help. truck-trailer MATLAB Answers — New Questions
