Planning and control

1.In motion planning, what does the configuration space of a robot represent?

2.A round hospital delivery robot with a 0.3 m radius drives on flat floors. Its planner searches only over x and y, not heading. Why is that acceptable for collision checking?

3.An orchard drone is modeled as a free-flying rigid body. How many degrees of freedom does its pose have?

4.A lab pipetting arm has seven revolute joints and must reach tool poses that need six numbers to describe. What does the extra joint give the planner?

5.Your planner treats a round robot of radius r as a point moving among obstacles on a 2D map. How should you build the obstacles it plans against?

6.A bakery packing arm has three revolute joints whose axes are all vertical and parallel, so it moves only in a horizontal plane. How many task-space quantities can it set independently?

7.A parcel hub sorting arm has six revolute joints plus a gripper that only opens and closes. How many dimensions does the configuration space need when planning the arm's motion to a bin?

8.Why do planners for a seven-joint arm rarely use a uniform grid over joint space?

9.What happens to A* search if the heuristic returns zero for every node?

10.What does it mean for an A* heuristic to be admissible?

11.A heuristic satisfies h(n) <= c(n, m) + h(m) for every edge from n to m, and h(goal) = 0. What extra benefit does this give A* over admissibility alone?

12.A warehouse grid planner allows diagonal moves costing 1.414 and straight moves costing 1. It uses Manhattan distance as the A* heuristic, and some paths come out slightly longer than they should. Why?

13.On an empty 8-connected grid where straight moves cost 1 and diagonal moves cost sqrt(2), what is the shortest path cost from cell (0, 0) to cell (5, 3)?

14.A lawn mower robot plans on a 4-connected grid. An engineer switches the A* heuristic from Manhattan distance to Euclidean distance. What changes?

15.A planner uses weighted A*, ordering nodes by g + 1.5h with an admissible h. What guarantee does it still give?

16.A fleet of airport baggage robots all drive to the same unloading belt from many different starting spots on a fixed map. What is an efficient way to plan for all of them?

17.A library shelving robot plans on a 0.5 m occupancy grid, marking any cell that touches a shelf as occupied. It reports no path through a 0.8 m aisle it physically fits through. What is the most likely cause?

18.Grid-based A* is described as resolution complete. What does that mean?

19.On a large open grid, A* expands huge numbers of nodes that all share the same f value. What tie-breaking rule usually cuts the expansions without losing optimality?

20.A parking garage valet robot is car-like. Its grid A* planner returns paths with sharp 90-degree corners that the robot cannot drive. What is the best fix?

21.A rapidly exploring random tree (RRT) planner is called probabilistically complete. What does that guarantee?

22.A greenhouse picking arm uses plain RRT (rapidly exploring random tree). Paths are jagged and stay jagged even when the planner is given ten times more time. Why?

23.A pharmacy dispensing arm works in a fixed, unchanging cell and gets thousands of motion requests per day between different shelf slots. Which planner family fits best?

24.A sampling planner for a mine inspection crawler almost never finds a path through a narrow gap between two rock walls. What is the usual fix?

25.In RRT, goal biasing means sampling the goal itself some fraction of the time. What happens if that fraction is set very high, such as 80 percent?

26.A welding arm's sampling planner returns a path where every node is collision-free, yet the torch clips a thin fixture bar during execution. What is the most likely cause?

27.A film camera dolly robot gets a raw RRT path that wanders. You need a smooth, timed move. What do you do first?

28.What is the main idea behind RRT-Connect?

29.A PRM (probabilistic roadmap) for a data center tape library robot fails to answer a query, though a path clearly exists. The roadmap turns out to have two separate components on either side of a doorway. What should you do?

30.A rectangular sidewalk delivery robot is 0.6 m long and 0.4 m wide, centered on its rotation point. What is its circumscribed radius?

31.The same planner treats a rectangular robot as a point and inflates obstacles only by the robot's inscribed radius. What risk does this leave?

32.An office mail robot hugs walls closely and staff find it unnerving. The costmap marks lethal cells near walls and adds a cost that decays with distance. What tuning change helps most?

33.A museum guide robot refuses to drive through a spot where a visitor stood several minutes ago. The visitor is long gone. What is the most likely cause?

34.A costmap covers 100 m by 100 m at a resolution of 5 cm per cell. How many cells does it have?

35.A shelf-picking arm uses large bounding spheres around each link for collision checking. The planner fails to find any path into a tight shelf the arm physically fits. What is the most likely cause?

36.A warehouse robot has a 0.25 m radius and its localization error can reach 5 cm. What is the smallest sensible inflation distance for hard obstacles?

37.What does a rolling-window local costmap do?

38.Why do many trajectory optimizers use a signed distance field of the environment?

39.A solar panel cleaning robot moves 5 m along a rail with a trapezoidal velocity profile. Its top speed is 1.0 m/s and acceleration and deceleration are both 0.5 m/s^2. How long does the move take?

40.The same rail robot, with top speed 1.0 m/s and acceleration 0.5 m/s^2, makes a 1 m move. What peak speed does it reach?

41.A pipetting arm in a clinical lab splashes liquid at the start and end of each move. It uses a trapezoidal velocity profile. What change helps most?

42.Why are polynomial trajectories for quadrotors often chosen to minimize snap, the fourth derivative of position?

43.A hotel room-service robot carries open drinks. Lateral acceleration must stay under 0.5 m/s^2. What is its top speed through a turn of radius 2 m?

44.A truck plant handling arm moves joint 1 by 90 degrees and joint 2 by 30 degrees in one synchronized move. Joint 1's speed limit is 45 deg/s and joint 2's is 60 deg/s. Ignoring acceleration, how long must the move take, and how fast does joint 2 go?

45.What does time-optimal path parameterization compute?

46.A gradient-based trajectory optimizer for a dairy milking arm sometimes returns a path that passes through an obstacle and cannot get out. What is the most common remedy?

47.An optimized path for a construction layout robot cuts corners very close to columns. The cost is a weighted sum of smoothness and obstacle terms. What change helps?

48.What position continuity does a trajectory need for its acceleration to be continuous?

49.A differential drive robot has wheels 0.5 m apart. The right wheel moves at 0.6 m/s and the left at 0.4 m/s. What is its turning radius?

50.Which statement about a differential drive robot's motion is correct?

51.A vineyard tractor robot uses a bicycle model with a 2.5 m wheelbase and a maximum steering angle of 30 degrees. What is its minimum turning radius?

52.A loading dock forklift robot must back into tight bays. Its planner connects poses with Dubins curves and often reports no solution. Why?

53.A robot with a 2.5 m minimum turning radius must turn around in a corridor 3 m wide. Treating it as a point at its rear axle, what does it need to do?

54.A differential drive robot has wheels 0.5 m apart and a top wheel speed of 1.0 m/s. The local planner commands v = 0.9 m/s and omega = 1.0 rad/s. What should the base controller do?

55.A trade show booth robot must slide sideways along a display counter without changing its heading. Which base can follow that path directly?

56.Why is a car-like robot called nonholonomic even though it can eventually reach any position and heading in an open lot?

57.A snowplow robot on a large campus map keeps finding newly blocked paths. A full A* replan from scratch each time is too slow. What approach fits?

58.A sidewalk courier robot treats pedestrians as static obstacles at their latest observed position. It often cuts in front of people and has close calls. What is the main fix?

59.In velocity obstacle methods, what is a velocity obstacle?

60.A university campus courier robot replans every 200 ms. Two routes around a pillar cost almost the same, and the robot jerks left and right as the chosen route flips. What is the best fix?

61.A greenhouse transport robot drives at 1.2 m/s toward a cart that is rolling toward it at 0.8 m/s. The gap is 6 m. Assuming both keep their speeds, how long until they meet?

62.Why do many mobile robots split navigation into a global planner and a local planner?

63.A tugger robot drives at 1.5 m/s, brakes at 1.0 m/s^2, and has 0.2 s between detecting an obstacle and starting to brake. About how far does it travel before stopping?

64.A conveyor motor is driven by a fixed voltage that was set to give the right speed with no load. When heavy boxes arrive, the belt slows down. What explains this?

65.The tilt joint on an inspection camera is driven by a P-only controller and sags a little under the camera's off-center weight. What causes the steady offset?

66.What is the main job of the integral term in a PID controller?

67.What does the derivative term in a PID controller mainly add?

68.A quadcopter's altitude hold was steady. After an engineer doubled the proportional gain, altitude oscillates with growing swings. What is going on?

69.A telescope mount jerks sharply every time an operator enters a new target angle, then tracks smoothly. Its PID computes the derivative of the error. What is the usual fix?

70.A brushless motor on a gimbal starts buzzing loudly as soon as a small derivative gain is added. The encoder has coarse resolution. What is the most likely cause, and fix?

71.A lawn mower robot climbs a steep slope with its drive motors at full output for 10 seconds, still below the target speed. At the top it surges well past the target speed. What is the most likely cause?

72.Which change most directly prevents integral windup?

73.You are tuning a new wheel velocity loop by hand. What is a sensible first step?

74.A PID loop has Kp = 2, Ki = 0.5 and Kd = 0.1. Right now the error is 0.4, the accumulated integral of error is 1.2, and the error is changing at -0.5 per second. What is the controller output?

75.A team doubles a PID loop from 100 Hz to 200 Hz. The code adds Ki times the error to the integral every tick without multiplying by the time step. What happens?

76.A pipe-crawling robot's speed controller removed its steady error after an integral term was added, but now speed swings slowly above and below the target with a long period. What do you adjust first?

77.Why does added latency in a feedback loop tend to cause oscillation?

78.A camera gimbal uses a cascade: an outer angle loop feeds a setpoint to an inner rate loop. How should their speeds compare?

79.A camera dolly robot lags behind its planned position during constant-speed moves. It uses only a position PID. What change reduces the lag most directly?

80.A welding positioner arm holds heavy fixtures at different angles. Its joint PIDs work, but errors spike as the arm moves through poses where gravity loads change. What helps most?

81.A tracked inspection robot cannot follow an aggressive trajectory. Logs show the motor commands pinned at their maximum. Raising Kp does not help. Why, and what is the fix?

82.A wheel motor's feedforward model is: voltage = 0.4 V static term + 0.12 V per rad/s of speed. What feedforward voltage should be sent for a target of 50 rad/s?

83.Why is feedforward alone usually not enough for a robot joint?

84.A control loop runs at 50 Hz. Sensor latency is 30 ms, computation takes 10 ms, and the actuator responds after 20 ms. How many control periods of delay is that in total?

85.A position loop needs a closed-loop bandwidth of about 5 Hz. What loop rate is a sensible minimum?

86.A drive controller on a general-purpose operating system logs loop periods that vary between 5 and 25 ms, though it assumes a fixed 10 ms. The derivative term looks noisy. What is the first fix?

87.A field robot running pure pursuit weaves side to side. Its pose estimate reaches the controller about 150 ms late. What is a good fix?

88.A joint encoder has 1000 counts per revolution, and the velocity loop runs at 1 kHz. At 6 rpm, how many counts arrive per control cycle on average?

89.How does model predictive control (MPC) produce its command at each step?

90.A rover must keep steering rate, speed and distance to a drop-off edge within limits while tracking a path. Why is MPC often chosen over PID here?

91.A car-like delivery robot runs MPC with a 0.5 s horizon. At 3 m/s it overshoots sharp corners and brakes too late. What is the most likely cause?

92.A rover's MPC solver takes about 30 ms per solve, but the controller is meant to run at 50 Hz. What should you try first?

93.MPC plans an entire control sequence from a model. Why is it still considered feedback control?

94.In pure pursuit, the lookahead point is 2 m away and sits 0.5 m to the left of the robot in its own frame. What curvature does pure pursuit command?

95.A vineyard sprayer using pure pursuit weaves back and forth across straight rows. What change most likely fixes it?

96.A pure pursuit follower uses a fixed 3 m lookahead. On tight turns in a parking lot it cuts corners badly. What usually helps?

97.Why do path tracking controllers usually express errors in the path frame rather than the world frame?

98.A path runs straight along the +y axis from the origin. Headings are measured counterclockwise from +x. A robot is at (0.3, 2.0) with heading 80 degrees. Which describes its tracking error?

99.A theme park food cart robot tracks a time-stamped trajectory. It sits exactly on the path but is 0.5 m behind where it should be at this time. What kind of error is this?

100.Which statement about forward and inverse kinematics of a serial arm is correct?

101.A planar two-link arm has link lengths 0.4 m and 0.3 m. Joint 1 is at 90 degrees from the x-axis and joint 2 is at -90 degrees relative to link 1. Where is the tool?

102.A planar two-link arm on a seed-sorting table has links of 0.5 m and 0.3 m. Which target, measured as distance from the base joint, can it not reach?

103.A dishwashing arm's IK solver sometimes flips from elbow-up to elbow-down halfway through a move, swinging the forearm wildly. What is the best fix?

104.A bridge inspection arm moves the tool in a straight line, and joint speeds spike as the arm nears full extension. What is happening?

105.On a six-joint arm with a spherical wrist, joints 4 and 6 suddenly spin quickly in opposite directions while the tool barely moves. Joint 5 is near zero. What is the cause?

106.What does damped least squares inverse kinematics trade off near a singularity?

107.An IK solver returns 200 degrees for a joint whose range is -180 to +180 degrees and which can rotate freely. What value should be commanded?

108.What does the manipulator Jacobian relate?

109.For a planar two-link arm, the Jacobian determinant is L1 x L2 x sin(theta2), where theta2 is the elbow angle. At which elbow angles is the arm singular?