Look-ahead information can be used to automatically steer a bicycle in a closed-loop configuration. A line is drawn in the middle of the lane to be followed, and an arbitrary point is chosen in the vehicle’s longitudinal axis. A look-ahead offset is calculated by measuring the distance between the look-ahead point and the reference line and is used by the system to correct the vehicle’s trajectory. A linearized model of a particular bicycle traveling on a straight-line path at a fixed longitudinal speed is
In this model, V = bicycle’s lateral velocity, r = bicycle’s yaw velocity,
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Control Systems Engineering
- Is there any built in functions in MATLAB that transform a given Direction Cosine Matrix (DCM) to Principal Rotation Paramters (PRP)? For example, If I have a DCM, the function would give the axis, lambda, and the angle, theta. Also, is there any built in functions that would transform a Direction Cosine Matrix to Euler Parameters (EP) and Modified Rodrigiues Parameters and Classical Rodriguess Parameters? If I had the DCM given in the image, what would the code in MATLAB to transform it to PRP, EP, MRP, CRP look like?arrow_forwardSolve the inverse kinematic problem for the following robot of 6 DEGREES OF FREEDOM, using the method ofkinematic decouplingif it is known that its Denavit-Hartenberg parameters are those shown in thetablearrow_forward5.Design a system to measure the bending moment (up and down) and torque in the tail boom of the human-powered aircraft shown below. You will need two Wheatstone bridges. Your system should measure the bending and torque independently, but not be sensitive to any other internal forces, like axial force, transverse shear, or bending moment about the vertical axis (back and forth). (If relevant) A clearly labeled diagram (or diagrams) about your analysis with a coordinate system and relevant labels. Final answer with appropriate units and significant figures. You can use the fprintf() command in MATLAB to format numerical results A 2-3 sentence reflection on your answer. Does it make sense? Why or why not? What are some implications? (a) Make a few clear, labeled sketches showing approximately where you would place the strain gauges. Consider the location (along the length of the boom), positioning (around the circumference of the boom), and orientation of the gauges. Show clearly…arrow_forward
- In 3-D design, the polar coordinates system of the point representation depends on last point origin point O x and y values Olength and anglearrow_forwardHow different the results would be if the linear ram acceleration is 5378 in/s² horizontal direction, sense: to the RIGHT ?arrow_forwardYou walk along the beach towards a dock while your friend rows a boat towards the same dock on a flat lake. Your friend's boat approaches the dock on a straight course, but also rotates about its center-of-mass since your friend is not pulling evenly on the oars. If you knew your own velocity (vwalker), the magnitude of boat's angular velocity (thetaboat), and radius vector from yourself to your friend in the boat (rfriend) at any given time, you could use the following equation to calculate the your friend's velocity: vfriend = vwalker + (thetaboat)k x rfriend where k is a unit vector in the vertical direction. True Falsearrow_forward
- You are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 Use your knowledge of differentiation to sketch the velocity-time graph, clearly marking the critical points. Using the graph sketched in (a) above, estimate the velocity when t = 1.5 s Calculate the velocity of the function when t = 1.5 s by substituting to the velocity function. Compare this value to the value you estimated in b above.arrow_forwardYou are the mechatronics engineer of a manufacturing plant. You decide to perform an analysis on a robot arm of the assembly line with the objective of optimizing its performance. After taking several readings of the speed of the arm’s end effector, you approximate its velocity to the function given below. v(t) = -t4 + 5t3 - 7t2 + 3t + 0.22 0 =< t =< 3 where the velocity is in ms-1 d) Knowing that the distance travelled by an object is the area under its velocity-time graph, determine the distance travelled by the end effector on the interval 0 =< t =< 1 by using the mid-ordinate rule. Simpson’s rule correct to 3 decimal places using four intervals. e) Calculate the same distance as in (d) above by using the appropriate definite integral. f) Compare the distances you calculated in (d) and (e) above and comment on the accuracy of the two methods you used in (d)arrow_forwardHome Exencise= Derive the equations of motion for the following mechani.cal system: Combination of translational and rotational systems)arrow_forward
- As4. This is my third time asking this question. Please DO NOT copy and paste someone else's work or some random notes. I need an answer to this question. There is a mass attached to a spring which is fixed against a wall. The spring is compressed and then released. Friction and is neglected. The velocity and displacement of the mass need to be modeled with an equation or set of equations so that various masses and spring constants can be input into Matlab and their motion can be observed. Motion after being released is only important, the spring being compressed is not important. This could be solved with dynamics, Matlab, there are multiple approaches.arrow_forwardhi ive have nearly completed this model but i am stuck on a couple last parts. Firstly, the holes on the top need to be placed 30 degrees from the y axis as shown in the handout but also the middle part is meant to have triangular "supports" rather than rectangular and im not sure how to cut them down. This is in autodesk inventor but any help here would be appreciated Once again just the top holes being moved 30 degrees and the support being cut down to the triangular shape shown in the handoutarrow_forwardINSTRUCTIONS: Solve the following problem by manually applying the finite element method, following these steps: Pre-processing: Geometry identification. Material properties identification. Load identification. Boundary condition identification. Development of the connectivity matrix for nodes and elements. Processing: Calculation of local stiffness matrices. Assembly of the global stiffness matrix. Assembly of the global force matrix (if required). Application of boundary conditions. Resolution of the system of equations. Derivation of the complete displacement vector (u). Post-processing: Reaction forces calculation. Stress analysis. Problem Statement: the truss nodes and elements (in parentheses) are already numbered. The areas (are in cm^2 ) are underlined. members are made of structural steel, modulus of elasticity is (E) of 20×10^6 N/cm^2 . the lengths are given in cm.arrow_forward
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