-- Lua "motor driver" for a four legged (aka quadruped) walking robot -- -- This script consumes controller outputs (i.e. roll, pitch, yaw/steering, throttle, lateral) from -- the vehicle code and then calculates the outputs for 12 servos controlling four legs -- -- AutoPilot servo connections: -- Output1: front right coxa (hip) servo -- Output2: front right femur (thigh) servo -- Output3: front right tibia (shin) servo -- Output4: front left coxa (hip) servo -- Output5: front left femur (thigh) servo -- Output6: front left tibia (shin) servo -- Output7: back left coxa (hip) servo -- Output8: back left femur (thigh) servo -- Output9: back left tibia (shin) servo -- Output10: back right coxa (hip) servo -- Output11: back right femur (thigh) servo -- Output12: back right tibia (shin) servo -- -- CAUTION: This script should only be used with ArduPilot Rover's firmware -- luacheck: only 0 local FRAME_LEN = 80 -- frame length in mm local FRAME_WIDTH = 150 -- frame width in mm local COXA_LEN = 30 -- distance (in mm) from coxa (aka hip) servo to femur servo local FEMUR_LEN = 85 -- distance (in mm) from femur servo to tibia servo local TIBIA_LEN = 125 -- distance (in mm) from tibia servo to foot --body position and rotation parameters local body_rot_max = 10 -- body rotation maximum for any individual axis local body_rot_x = 0 -- body rotation about the X axis (i.e. roll rotation) local body_rot_y = 0 -- body rotation about the Y axis (i.e. pitch rotation) local body_rot_z = 0 -- body rotation about the Z axis (i.e. yaw rotation) local body_pos_x = 0 -- body position in the X axis (i.e. forward, back). should be -40mm to +40mm local body_pos_y = 0 -- body position in the Y axis (i.e. right, left). should be -40mm to +40mm local body_pos_z = 0 -- body position in the Z axis (i.e. up, down). should be -40mm to +40mm -- starting positions of the legs local endpoint_LB = {math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN} local endpoint_LF = {math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(-45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN} local endpoint_RF = {-math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(-45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN} local endpoint_RB = {-math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN} -- control input enum local control_input_roll = 1 local control_input_pitch = 2 local control_input_throttle = 3 local control_input_yaw = 4 local control_input_height = 8 local xy_travel_max = 80 -- x and y axis travel max (used to convert control input) in mm local yaw_travel_max = 10 -- yaw travel maximum (used to convert control input) local height_max = 40 -- height maximum (used to convert control input) local travel_dz = 5 -- travel deadzone. x, y and yaw travel requests are ignored if their absolute value is less than this number local x_travel = 0 -- target lenght of gait along x local y_travel = 0 -- target travel of gait along y local yaw_travel = 0 -- yaw rotation travel target local leg_lift_height = 50 -- leg lift height (in mm) while walking -- gait definition parameters local gait_type = 0 -- gait pattern. 0 = alternating gait, 1 = wave gait. local gait_step = 0 -- gait step in execution local gait_step_total = 0 -- number of steps in gait local gait_step_leg_start = {0,0,0,0} -- leg starts moving on this gait step (front-right, front-left, back-left, back-right) local gait_lifted_steps = 0 -- number of steps that a leg is lifted for local gait_down_steps = 0 -- number of steps that the leg lifted needs to be put down for local gait_lift_divisor = 0 -- when a leg is lifted and brought back down the action is divided into 2 or multiple steps, so the travel distance also need to be split in between the steps to make the transition natural local gait_half_lift_height = 0 -- used to split lift across two steps local gait_travel_divisor = 0 -- number of steps in the gait the leg is touching the floor, this is used as a factor to split the travel distance between the steps local gait_pos_x = {0,0,0,0} -- X-axis position for each leg (back-right, front-right, back-left, front-left) local gait_pos_y = {0,0,0,0} -- Y-axis position for each leg (back-right, front-right, back-left, front-left) local gait_pos_z = {0,0,0,0} -- Z-axis position for each leg (back-right, front-right, back-left, front-left) local gait_rot_z = {0,0,0,0} -- Z-axis rotation for each leg (back-right, front-right, back-left, front-left) local last_angle = {0,0,0,0,0,0,0,0,0,0,0,0} local start_time = 0 local curr_target = 0 function Gaitselect() if (gait_type == 0) then -- alternating gait gait_step_total = 6 gait_step_leg_start = {1,4,4,1} gait_lifted_steps = 2 gait_down_steps = 1 gait_lift_divisor = 2 gait_half_lift_height = 1 gait_travel_divisor = 4 elseif (gait_type == 1) then -- wave gait with 28 steps gait_step_total = 28 gait_step_leg_start = {8,15,1,22} gait_lifted_steps = 3 gait_down_steps = 2 gait_lift_divisor = 2 gait_half_lift_height = 3 gait_travel_divisor = 24 end end -- Calculate Gait sequence function calc_gait_sequence() local move_requested = (math.abs(x_travel) > travel_dz) or (math.abs(y_travel) > travel_dz) or (math.abs(yaw_travel) > travel_dz) if move_requested then for leg_index=1, 4 do update_leg(leg_index,move_requested) end gait_step = gait_step + 1 if (gait_step>gait_step_total) then gait_step = 1 end else gait_pos_x = {0,0,0,0} gait_pos_y = {0,0,0,0} gait_pos_z = {0,0,0,0} gait_rot_z = {0,0,0,0} end end -- in order for the robot to move forward it needs to move its legs in a -- specific order and this is repeated over and over to attain linear motion. when a -- specific leg number is passed the update_leg() produces the set of values for the -- given leg at that step, for each cycle of the gait each leg will move to a set -- distance which is decided by the x_travel, yaw_travel, y_travel function update_leg(moving_leg,move_requested) local leg_step = gait_step - gait_step_leg_start[moving_leg] if ((move_requested and (gait_lifted_steps > 0) and leg_step==0) or (not move_requested and leg_step==0 and ((gait_pos_x[moving_leg]>2) or (gait_pos_y[moving_leg]>2) or (gait_rot_z[moving_leg] >2)))) then gait_pos_x[moving_leg] = 0 gait_pos_z[moving_leg] = -leg_lift_height gait_pos_y[moving_leg] = 0 gait_rot_z[moving_leg] = 0 elseif (((gait_lifted_steps==2 and leg_step==0) or (gait_lifted_steps>=3 and (leg_step==-1 or leg_step==(gait_step_total-1)))) and move_requested) then gait_pos_x[moving_leg] = -x_travel/gait_lift_divisor gait_pos_z[moving_leg] = -3*leg_lift_height/(3+gait_half_lift_height) gait_pos_y[moving_leg] = -y_travel/gait_lift_divisor gait_rot_z[moving_leg] = -yaw_travel/gait_lift_divisor elseif ((gait_lifted_steps>=2) and (leg_step==1 or leg_step==-(gait_step_total-1)) and move_requested) then gait_pos_x[moving_leg] = x_travel/gait_lift_divisor gait_pos_z[moving_leg] = -3*leg_lift_height/(3+gait_half_lift_height) gait_pos_y[moving_leg] = y_travel/gait_lift_divisor gait_rot_z[moving_leg] = yaw_travel/gait_lift_divisor elseif (((gait_lifted_steps==5 and (leg_step==-2 ))) and move_requested) then gait_pos_x[moving_leg] = -x_travel * 0.5 gait_pos_z[moving_leg] = -leg_lift_height * 0.5 gait_pos_y[moving_leg] = -y_travel * 0.5 gait_rot_z[moving_leg] = -yaw_travel * 0.5 elseif ((gait_lifted_steps==5) and (leg_step==2 or leg_step==-(gait_step_total-2)) and move_requested) then gait_pos_x[moving_leg] = x_travel * 0.5 gait_pos_z[moving_leg] = -leg_lift_height * 0.5 gait_pos_y[moving_leg] = y_travel * 0.5 gait_rot_z[moving_leg] = yaw_travel * 0.5 elseif ((leg_step==gait_down_steps or leg_step==-(gait_step_total-gait_down_steps)) and gait_pos_y[moving_leg]<0) then gait_pos_x[moving_leg] = x_travel * 0.5 gait_pos_z[moving_leg] = 0 gait_pos_y[moving_leg] = y_travel * 0.5 gait_rot_z[moving_leg] = yaw_travel * 0.5 else gait_pos_x[moving_leg] = gait_pos_x[moving_leg] - (x_travel/gait_travel_divisor) gait_pos_z[moving_leg] = 0 gait_pos_y[moving_leg] = gait_pos_y[moving_leg] - (y_travel/gait_travel_divisor) gait_rot_z[moving_leg] = gait_rot_z[moving_leg] - (yaw_travel/gait_travel_divisor) end end -- Body Forward Kinematics calculates where each leg should be. -- inputs are -- a) body rotations: body_rot_x, body_rot_y, body_rot_z -- b) body position: body_pos_x, body_pos_y, body_pos_z -- c) offset of the center of body function body_forward_kinematics(X, Y, Z, Xdist, Ydist, Zrot) local totaldist_x = X + Xdist + body_pos_x local totaldist_y = Y + Ydist + body_pos_y local distBodyCenterFeet = math.sqrt(totaldist_x^2 + totaldist_y^2) local AngleBodyCenter = math.atan(totaldist_y, totaldist_x) local rolly = math.tan(math.rad(body_rot_y)) * totaldist_x local pitchy = math.tan(math.rad(body_rot_x)) * totaldist_y local ansx = math.cos(AngleBodyCenter + math.rad(body_rot_z+Zrot)) * distBodyCenterFeet - totaldist_x + body_pos_x local ansy = math.sin(AngleBodyCenter + math.rad(body_rot_z+Zrot)) * distBodyCenterFeet - totaldist_y + body_pos_y local ansz = rolly + pitchy + body_pos_z return {ansx, ansy, ansz} end -- Leg Inverse Kinematics calculates the angles for each servo of each joint using the output of the -- body_forward_kinematics() function which gives the origin of each leg on the body frame function leg_inverse_kinematics(x, y, z) local coxa = math.deg(math.atan(x, y)) local trueX = math.sqrt(x^2 + y^2) - COXA_LEN local im = math.sqrt(trueX^2 + z^2) local q1 = -math.atan(z, trueX) local d1 = FEMUR_LEN^2 - TIBIA_LEN^2 + im^2 local d2 = 2*FEMUR_LEN*im local q2 = math.acos(d1/d2) local femur = math.deg(q1+q2) d1 = FEMUR_LEN^2 - im^2 + TIBIA_LEN^2 d2 = 2*TIBIA_LEN*FEMUR_LEN local tibia = math.deg(math.acos(d1/d2)-math.rad(90)) return {coxa, -femur, -tibia} end -- checks if the servo has moved to its expected position function servo_estimate(current_angle) local target = 0 for j = 1, 12 do curr_target = math.abs(current_angle[j] - last_angle[j]) if curr_target > target then target = curr_target end end local target_time = target * (0.24/60) * 1000 return (millis() - start_time) > target_time end -- main_inverse_kinematics produces the inverse kinematic solution for each -- leg joint servo by taking into consideration the initial_pos, gait offset and the body inverse kinematic values. function main_inverse_kinematics() local ans_RB = body_forward_kinematics(endpoint_RB[1]+gait_pos_x[1], endpoint_RB[2]+gait_pos_y[1], endpoint_RB[3]+gait_pos_z[1], -FRAME_LEN*0.5, FRAME_WIDTH*0.5, gait_rot_z[1]) local angles_RB = leg_inverse_kinematics(endpoint_RB[1]+ans_RB[1]+gait_pos_x[1], endpoint_RB[2]+ans_RB[2]+gait_pos_y[1], endpoint_RB[3]+ans_RB[3]+gait_pos_z[1]) angles_RB[1] = 45 + angles_RB[1] local ans_RF = body_forward_kinematics(endpoint_RF[1]+gait_pos_x[2], endpoint_RF[2]+gait_pos_y[2], endpoint_RF[3]+gait_pos_z[2], -FRAME_LEN*0.5, -FRAME_WIDTH*0.5, gait_rot_z[2]) local angles_RF = leg_inverse_kinematics(endpoint_RF[1]-ans_RF[1]+gait_pos_x[2], endpoint_RF[2]-ans_RF[2]-gait_pos_y[2], endpoint_RF[3]+ans_RF[3]+gait_pos_z[2]) angles_RF[1] = 135 + angles_RF[1] local ans_LB = body_forward_kinematics(endpoint_LB[1]+gait_pos_x[3], endpoint_LB[2]+gait_pos_y[3], endpoint_LB[3]+gait_pos_z[3], FRAME_LEN*0.5, FRAME_WIDTH*0.5, gait_rot_z[3]) local angles_LB = leg_inverse_kinematics(endpoint_LB[1]+ans_LB[1]+gait_pos_x[3], endpoint_LB[2]+ans_LB[2]+gait_pos_y[3], endpoint_LB[3]+ans_LB[3]+gait_pos_z[3]) angles_LB[1] = -45 + angles_LB[1] local ans_LF = body_forward_kinematics(endpoint_LF[1]+gait_pos_x[4], endpoint_LF[2]+gait_pos_y[4], endpoint_LF[3]+gait_pos_z[4], FRAME_LEN*0.5, -FRAME_WIDTH*0.5, gait_rot_z[4]) local angles_LF = leg_inverse_kinematics(endpoint_LF[1]-ans_LF[1]+gait_pos_x[4], endpoint_LF[2]-ans_LF[2]-gait_pos_y[4], endpoint_LF[3]+ans_LF[3]+gait_pos_z[4]) angles_LF[1] = -135 + angles_LF[1] Gaitselect() local current_angle = {angles_RF[1],angles_RF[2],angles_RF[3], angles_LF[1],angles_LF[2],angles_LF[3], angles_LB[1],angles_LB[2],angles_LB[3], angles_RB[1],angles_RB[2],angles_RB[3]} if servo_estimate(current_angle) then start_time = millis() calc_gait_sequence() last_angle = current_angle end return current_angle end -- servo angles when robot is disarmed and resting body on the ground local rest_angles = { 45, -90, 40, -- front right leg (coxa, femur, tibia) -45, -90, 40, -- front left leg (coxa, femur, tibia) -45, -90, 40, -- back left leg (coxa, femur, tibia) 45, -90, 40} -- back right leg (coxa, femur, tibia) function update() local throttle = vehicle:get_control_output(control_input_throttle) * xy_travel_max local gait_direction if throttle > 0 then gait_direction = -1 y_travel = throttle elseif throttle < 0 then gait_direction = 1 y_travel = -throttle elseif throttle == 0 then gait_direction = 1 y_travel = 0 end yaw_travel = -vehicle:get_control_output(control_input_yaw) * yaw_travel_max body_rot_x = -vehicle:get_control_output(control_input_roll) * body_rot_max body_rot_y = -vehicle:get_control_output(control_input_pitch) * body_rot_max body_pos_z = vehicle:get_control_output(control_input_height) * height_max local servo_direction = { gait_direction * 1, -1, 1, -- front right leg (coxa, femur, tibia) gait_direction * 1, 1, -1, -- front left leg (coxa, femur, tibia) gait_direction * -1, -1, 1, -- back left leg (coxa, femur, tibia) gait_direction * -1, 1, -1} -- back right leg (coxa, femur, tibia) local angles if arming:is_armed() then angles = main_inverse_kinematics() else angles = rest_angles end for i = 1, 12 do SRV_Channels:set_output_pwm_chan_timeout(i-1, math.floor(((angles[i] * servo_direction[i] * 1000)/90) + 1500), 1000) end return update,10 end -- turn off rudder based arming/disarming param:set_and_save('ARMING_RUDDER', 0) gcs:send_text(0, "quadruped simulation") return update()