packages = ['numpy']


x = [-np.pi/4, np.pi/2, np.pi/4] # Initial robot state def controlCommand(x, param): f = fkin(x, param) J = Jkin(x, param) u = np.linalg.pinv(J) @ logmap(param.Mu, f) # Position & orientation tracking # u = np.linalg.pinv(J[:2,:]) @ (param.Mu[:2] - f[:2]) # Position tracking # u = np.linalg.pinv(J[2:,:]) @ (param.Mu[2:] - f[2:]) # Orientation tracking # u = J.T @ logmap(param.Mu, f) * 1E-4 # Gradient-based tracking # u = np.zeros(param.nbVarX) # Zero control commands return u
x = [-np.pi/4, np.pi/2, np.pi/4] # Initial robot state def controlCommand(x, param): f = fkin(x, param) J = Jkin(x, param) pinvJ = np.linalg.inv(J.T @ J + np.eye(param.nbVarX) * 1E2) @ J.T # Damped pseudoinverse u = pinvJ @ logmap(param.Mu, f) # Position & orientation tracking return u
x = [-np.pi/4, np.pi/2, np.pi/4] # Initial robot state def controlCommand(x, param): f = fkin(x, param) J = Jkin(x, param) # Weights in task space Wf = np.diag([1, 1, 0]) pinvWJ = np.linalg.inv(J.T @ Wf @ J + np.eye(param.nbVarX) * 1E-2) @ J.T @ Wf # Weighted pseudoinverse u = pinvWJ @ logmap(param.Mu, f) # Position & orientation tracking # # Weights in configuration space # Wx = np.diag([0.01, 1, 1]) # pinvWJ = Wx @ J[:2,:].T @ np.linalg.inv(J[:2,:] @ Wx @ J[:2,:].T + np.eye(2) * 1E-2) # Weighted pseudoinverse # u = pinvWJ @ (param.Mu[:2] - f[:2]) # Position tracking return u
x = np.array([-np.pi/4, np.pi/2, np.pi/4]) # Initial robot pose xh = np.array([-np.pi/4, np.pi/2, np.pi/4]) # Preferred robot pose def controlCommand(x, param): f = fkin(x, param) J = Jkin(x, param) # Prioritized tracking with motion of first joint as secondary task u1 = np.linalg.pinv(J[:2,:]) @ (param.Mu[:2] - f[:2]) # Position tracking N = np.eye(param.nbVarX) - np.linalg.pinv(J[:2,:]) @ J[:2,:] # Nullspace projection matrix u = u1 + N @ [1, 0, 0] # Control commands # # Prioritized tracking with preferred pose maintenance as secondary task # u1 = np.linalg.pinv(J[:2,:]) @ (param.Mu[:2] - f[:2]) # Position tracking # N = np.eye(param.nbVarX) - np.linalg.pinv(J[:2,:]) @ J[:2,:] # Nullspace projection matrix # u = u1 + N @ (xh - x) # Control commands # # Prioritized control (position tracking prioritized over orientation tracking) # dfp = (param.Mu[:2] - f[:2]) * 10 # Position correction # dfo = (param.Mu[2:] - f[2:]) * 10 # Orientation correction # Jp = J[:2,:] # Jacobian for position # Jo = J[2:,:] # Jacobian for orientation # pinvJp = np.linalg.inv(Jp.T @ Jp + np.eye(param.nbVarX) * 1e-2) @ Jp.T # Damped pseudoinverse # Np = np.eye(param.nbVarX) - pinvJp @ Jp # Nullspace projection operator # up = pinvJp @ dfp # Command for position tracking # JoNp = Jo @ Np # pinvJoNp = JoNp.T @ np.linalg.inv(JoNp @ JoNp.T + np.eye(1) * 1e1) # Damped pseudoinverse # uo = pinvJoNp @ (dfo - Jo @ up) # Command for orientation tracking (with position tracking prioritized) # u = up + Np @ uo # Control commands return u

(click on the green run button to run the code; objects and joints can be moved with the mouse)

from pyodide.ffi import create_proxy from js import Path2D, document, console import numpy as np import asyncio object_angle = document.getElementById('object_angle') # Objects angle ######################################################################################### base1_svg = Path2D.new('m -40.741975,77.319831 c -0.47247,-4.03869 7.32825,-20.1653 10.1171,-22.57617 4.71807,-4.07862 14.00201,-4.3722 15.87822,-6.89366 1.16821,-1.06725 1.19306,-2.45846 1.19136,-4.984461 -0.005,-6.836939 0.0375,-38.9164375 -0.0588,-42.62054746 C -13.757555,-5.2728275 -9.8130348,-13.34661 -0.02248483,-13.67734 7.5903552,-13.93451 13.741895,-7.1292375 13.608255,-0.84839739 13.474625,5.4324325 13.073715,50.200081 13.741895,54.075491 c 0.66817,3.8754 3.0736,26.72695 3.0736,26.72695 l -53.47684,-0.23624 c -3.68777,-0.0163 -4.0806,-3.24637 -4.0806,-3.24637 z') base2_svg = Path2D.new('m -13.653647,45.770986 27.119789,-0.07088') seg11_svg = Path2D.new('M 1.1085815,-48.64595 C 2.8616565,-42.037584 12.141047,-7.3721658 13.181308,-3.8158258 14.730923,1.4818692 12.982058,10.29588 3.6015646,13.1191 -3.6924249,15.31437 -11.379603,10.30832 -12.856452,4.2020952 c -1.476846,-6.106188 -11.012844,-42.5297362 -12.082149,-45.6580692 -1.43181,-5.329295 -2.652606,-11.707828 -2.961653,-18.313541 -0.264086,-5.644652 2.111069,-7.347919 2.111069,-7.347919 2.624567,-3.183184 8.150604,-3.203987 10.333578,-6.275591 1.769697,-2.490098 1.823736,-5.627976 1.959877,-8.208118 0.347278,-6.581603 7.8818877,-11.888333 13.83865325,-11.31331 11.26196775,1.087146 13.17554475,9.678077 12.89920975,14.363762 -0.465778,7.897881 -5.8447437,11.223081 -10.8257944,12.5317 -4.0229212,1.0569 -4.0522977,5.558527 -3.6062254,8.077811 0.53206435,3.004955 1.69902315,6.035714 2.2984683,9.29523 z') seg12_svg = Path2D.new('m 0.05406256,-11.597507 c -6.39589386,0 -11.58398456,5.1988245 -11.58398456,11.60742169 0,6.40859681 5.1880907,11.60742231 11.58398456,11.60742231 6.39589414,0 11.58398444,-5.1988255 11.58398444,-11.60742231 0,-6.40859719 -5.1880903,-11.60742169 -11.58398444,-11.60742169 z') seg13_svg = Path2D.new('m 0.89874154,-90.983149 c -6.37570324,-0.50777 -11.96015354,4.262759 -12.46893054,10.651135 -0.508778,6.388373 4.2502031,11.982666 10.62590635,12.490434 6.37571205,0.507768 11.96015765,-4.262758 12.46893565,-10.65113 0.50878,-6.388376 -4.2501988,-11.982669 -10.62591146,-12.490439 z') seg14_svg = Path2D.new('M -24.784795,-41.659214 1.1085815,-48.64595') seg15_svg = Path2D.new('m -20.037453,-23.361462 c 0,0 0.150891,-2.736177 2.859936,-3.928038 2.698441,-1.058633 15.064238,-4.832856 18.5649072,-5.023273 3.4151981,-0.800461 4.5404475,1.903276 4.5404475,1.903276') seg21_svg = Path2D.new('m 1.0846146,-63.378335 c 0.2455591,-2.834423 3.4523451,-16.559449 4.0431711,-18.415736 1.4726648,-4.271726 5.7043363,-7.554682 6.9088533,-12.676592 0.896166,-8.180737 -5.5218419,-14.075707 -11.67006058,-13.690757 -5.14680322,0.32229 -11.25729142,3.07163 -11.71005642,12.988353 -0.245696,5.381384 2.1556935,6.934579 1.261502,10.892576 -1.067995,4.72731 -3.306673,16.43352 -4.123841,19.092346 -1.013352,3.297141 -2.321128,5.411066 -6.454795,11.635385 -4.133667,6.224321 -5.394419,14.031661 -6.200979,18.250843 -0.80656,4.219183 -2.639059,14.959257 -1.769749,20.046047 0.662189,3.874813 5.317911,7.0872532 8.194376,7.8656925 2.799342,0.6504765 3.517742,0.6405013 5.007603,2.5337107 1.489861,1.8932084 1.467073,4.13299795 2.141633,7.605938 0.4829,3.1674976 4.2207359,9.9421608 11.3304401,10.8558018 C 5.1524174,14.518915 14.875984,8.7881742 13.263942,-1.6038057 11.604726,-12.299883 3.6744317,-12.710682 0.92067775,-13.632854 -1.5420631,-15.114186 -2.6268693,-19.519275 -1.8747035,-22.72879 -1.1225409,-25.938308 1.196278,-37.889572 1.3340625,-40.676542 1.8762966,-51.644393 -0.30239687,-54.622686 1.0846146,-63.378335 Z') seg22_svg = Path2D.new('M -11.586565,0.93074939 C -11.083534,7.3068272 -5.4927791,12.069965 0.89597241,11.565935 7.284721,11.061904 12.059397,5.4810033 11.556367,-0.89507457 11.053335,-7.2711624 5.4625836,-12.034299 -0.92616504,-11.530269 -7.3149165,-11.02624 -12.089595,-5.4453385 -11.586565,0.93074939 Z') seg23_svg = Path2D.new('m -26.640574,-36.592971 c 5.304398,1.031726 26.42204728,5.61535 26.42204728,5.61535') seg24_svg = Path2D.new('m -18.97242,-7.0296766 c 0,0 5.357638,0.9161489 6.790283,-0.3224518 0,0 1.645529,-2.0773004 2.9224726,-3.1740806 1.2245317,-1.051764 3.0335173,-2.07985 3.0335173,-2.07985 1.9028326,-1.212528 2.2666634,-4.627153 3.1812597,-7.476594 1.7216337,-5.363774 1.9197573,-6.250728 1.9197573,-6.250728') seg31_svg = Path2D.new('m -28.6797,-26.841855 c -1.2675,3.57197 -1.218858,4.557009 -1.595581,8.234518 -0.376722,3.677509 -0.09415,6.442577 -0.0095,8.568278 -0.253944,2.7250156 1.116106,5.225167 1.12849,7.9985227 -0.113818,2.61245518 -0.732443,4.5287742 -1.461378,6.6813667 -0.049,4.0362406 -0.269163,8.1196006 0.283769,12.1263916 0.524743,2.889586 3.777418,3.398207 6.006756,4.487809 3.000431,1.151299 5.962802,2.459036 9.011639,3.446545 2.908512,0.626882 4.197412,-2.375507 4.231736,-4.87884 0.0854,-2.479073 0.335025,-4.760767 2.8765686,-5.44487 3.9560009,-1.216619 8.05245912,-1.946456 12.0010307,-2.99019 5.703849,-2.0129894 9.4239807,-8.5502843 7.7887937,-14.4529723 -1.270267,-5.5243102 -6.867591,-9.6714567 -12.54557065,-9.0219797 -3.01008665,0.221201 -5.63894195,1.895241 -8.24502045,3.5658663 -2.0818469,1.3351245 -1.6868669,-3.2534803 -1.7460679,-4.8326393 -0.0013,-3.276304 0.21006,-3.084655 0.0062,-4.979716 -0.203891,-1.895062 -0.264478,-4.611901 -1.494343,-8.479035 -5.412496,-0.0097 -15.221678,-0.05267 -15.221678,-0.05267 z') seg32_svg = Path2D.new('m -14.015345,-33.566241 c -1.232867,-1.390966 -2.465733,-2.781932 -3.698599,-4.172898 0.0038,-3.646334 0.02928,-7.293353 0.01923,-10.939249 -0.02501,-0.949144 -0.522837,-2.078703 -1.513796,-2.119205 -0.942425,0.01577 -1.897362,-0.08159 -2.832194,0.04493 -0.950302,0.333999 -1.133628,1.580185 -1.115778,2.522511 -0.04848,3.474219 -0.09695,6.948437 -0.145432,10.422655 -1.213181,1.407781 -2.426362,2.815561 -3.639543,4.223342 4.308705,0.006 8.617409,0.01194 12.926114,0.01791 z') seg33_svg = Path2D.new('m -12.412129,-26.867866 v -4.799995 c 0,-1.919999 -0.435344,-1.878396 -0.888867,-1.876655 -3.030562,0.01164 -14.262729,-0.07064 -14.523962,-0.04334 -0.467055,0 -0.934111,0 -0.883228,1.904343 0.01098,0.410814 0.0013,4.808677 0.0013,4.808677') seg34_svg = Path2D.new('M -10.345869,0.79321884 C -9.8879044,6.4881727 -4.8873495,10.735439 0.81892316,10.276563 6.5251942,9.8176865 10.782785,4.8259161 10.324819,-0.86903645 9.8668498,-6.5639995 4.8662942,-10.811265 -0.8399769,-10.35239 -6.5462504,-9.8935134 -10.803835,-4.901743 -10.345869,0.79321884 Z') seg35_svg = Path2D.new('m -10.926083,-10.640947 c -12.932836,-0.04585 -19.378158,-0.0931 -19.378158,-0.0931') seg36_svg = Path2D.new('M -9.9187154,15.300602 C -29.124234,15.272545 -30.475824,15.251842 -30.475824,15.251842') seg37_svg = Path2D.new('m -23.186087,-46.845579 h 5.542233 v 0') # Logarithmic map for R^2 x S^1 manifold def logmap(f, f0): diff = np.zeros(3) diff[:2] = f[:2] - f0[:2] diff[2] = np.imag(np.log(np.exp(f0[-1]*1j).conj().T * np.exp(f[-1]*1j).T)).conj() return diff # Apply angle offsets to match robot kinematic chain def emulate_DH_params(x): xt = np.copy(x) xt[0] = xt[0] - np.pi/2 orient = np.mod(np.sum(xt,0)+np.pi, 2*np.pi) - np.pi xt[2] = xt[2] - np.arctan(20.5/51) return xt, orient # Forward kinematics for end-effector (in robot coordinate system) def fkin(x, param): xt, orient = emulate_DH_params(x) L = np.tril(np.ones([param.nbVarX, param.nbVarX])) f = np.vstack([ param.l @ np.cos(L @ xt), param.l @ np.sin(L @ xt), orient ]) # f1,f2,f3, where f3 is the orientation (single Euler angle for planar robot) f[1] += 81 return f.flatten() # Forward kinematics for all joints (in robot coordinate system) def fkin0(x, param): xt, _ = emulate_DH_params(x) L = np.tril(np.ones([param.nbVarX, param.nbVarX])) f = np.vstack([ L @ np.diag(param.l) @ np.cos(L @ xt), L @ np.diag(param.l) @ np.sin(L @ xt) ]) f = np.hstack([np.zeros([2,1]), f]) f[1] += 81 return f # Jacobian with analytical computation (for single time step) def Jkin(xt, param): xt, _ = emulate_DH_params(xt) L = np.tril(np.ones([param.nbVarX, param.nbVarX])) J = np.vstack([ -np.sin(L @ xt).T @ np.diag(param.l) @ L, np.cos(L @ xt).T @ np.diag(param.l) @ L, np.ones([1,param.nbVarX]) ]) return J ## Parameters # =============================== param = lambda: None # Lazy way to define an empty class in python param.dt = 1e-1 # Time step length param.nbVarX = 3 # State space dimension (x1,x2,x3) param.nbVarF = 3 # Task space dimension (position and orientation) param.l = [79, 96, 55] # Robot links lengths param.sz = [50, 30] # Size of objects param.Mu = [90, 0, 0] # Object position and orientation ######################################################################################### # GUI scaling_factor = 2 # General scaling factor for rendering # Mouse events mouse0 = np.zeros(2) mouse = np.zeros(2) mousedown = 0 selected_obj = -1 hover_obj = -1 hover_joint = -1 move_joint= -1 hover0 = np.zeros(2) def onMouseMove(event): global mouse, mouse0, hover0, x offset = canvas.getBoundingClientRect() mouse0[0] = (event.clientX - offset.x) * canvas.width / canvas.clientWidth mouse0[1] = (event.clientY - offset.y) * canvas.height / canvas.clientHeight mouse[0] = (mouse0[0] - canvas.width * 0.5) / scaling_factor mouse[1] = (mouse0[1] - canvas.height * 0.5) / scaling_factor if move_joint >= 0: x[move_joint] -= 1E-2 * np.sum(hover0 - mouse0) hover0 = np.copy(mouse0) def onTouchMove(event): global mouse, mouse0, hover0, x offset = event.target.getBoundingClientRect() mouse0[0] = (event.touches.item(0).clientX - offset.x) * canvas.width / canvas.clientWidth mouse0[1] = (event.touches.item(0).clientY - offset.y) * canvas.height / canvas.clientHeight mouse[0] = (mouse0[0] - canvas.width * 0.5) / scaling_factor mouse[1] = (mouse0[1] - canvas.height * 0.5) / scaling_factor if move_joint >= 0: x[move_joint] -= 1E-2 * np.sum(hover0 - mouse0) hover0 = np.copy(mouse0) def onMouseDown(event): global mousedown, move_joint, hover0 mousedown = 1 if hover_joint >= 0: move_joint = hover_joint hover0 = np.copy(mouse0) def onMouseUp(event): global mousedown, selected_obj, move_joint mousedown = 0 selected_obj = -1 move_joint = -1 def onWheel(event): global hover_joint, hover_obj, x, object_angle if hover_obj == 0: #param.Mu[2] += 0.2 * (event.deltaY/106) object_angle.value = (float)(object_angle.value) + 0.2 * (event.deltaY/106) if hover_joint >= 0: x[hover_joint] -= 0.2 * (event.deltaY/106) document.addEventListener('mousemove', create_proxy(onMouseMove)) #for standard mouse document.addEventListener('touchmove', create_proxy(onTouchMove)) #for mobile interfaces document.addEventListener('mousedown', create_proxy(onMouseDown)) #for standard mouse #document.addEventListener('pointerdown', create_proxy(onMouseDown)) #for mobile interfaces document.addEventListener('touchstart', create_proxy(onMouseDown)) #for mobile interfaces document.addEventListener('mouseup', create_proxy(onMouseUp)) #for standard mouse #document.addEventListener('pointerup', create_proxy(onMouseUp)) #for mobile interfaces document.addEventListener('touchend', create_proxy(onMouseUp)) #for mobile interfaces document.addEventListener('wheel', create_proxy(onWheel)) #for standard mouse ######################################################################################### canvas = document.getElementById('canvas') ctx = canvas.getContext('2d') def clear_screen(): ctx.setTransform(1, 0, 0, 1, 0, 0) # Reset transformation to identity ctx.fillStyle = 'white' ctx.fillRect(0, 0, canvas.width, canvas.height) def draw_ground(): ctx.setTransform(scaling_factor, 0, 0, scaling_factor, canvas.width*0.5, canvas.height*0.5) # Reset transformation ctx.beginPath() ctx.lineCap = 'round' ctx.lineJoin = 'round' ctx.lineWidth = '5' ctx.strokeStyle = '#CCCCCC' ctx.moveTo(-200, 164) ctx.lineTo(200, 164) ctx.stroke() def draw_robot(xt, color1, color2, color3, color4, selectable): global hover_joint ctx.setTransform(scaling_factor, 0, 0, scaling_factor, canvas.width*0.5, canvas.height*0.5) # Reset transformation # Draw base ctx.translate(0, 81) ctx.lineWidth = '1' ctx.strokeStyle = color3 ctx.fillStyle = color1 ctx.fill(base1_svg) ctx.stroke(base1_svg) # Outline ctx.stroke(base2_svg) # Draw seg1 ctx.rotate(xt[0]) ctx.fillStyle = color1 ctx.fill(seg11_svg) ctx.stroke(seg11_svg) # Outline ctx.fillStyle = color2 if selectable and ctx.isPointInPath(seg12_svg, mouse0[0], mouse0[1]): ctx.fillStyle = '#3399FF' hover_joint = 0 ctx.fill(seg12_svg) ctx.stroke(seg12_svg) ctx.stroke(seg13_svg) ctx.stroke(seg14_svg) ctx.stroke(seg15_svg) # Draw seg2 ctx.translate(0, -79) ctx.rotate(xt[1]) ctx.fillStyle = color1 ctx.fill(seg21_svg) ctx.stroke(seg21_svg) # Outline ctx.fillStyle = color2 if selectable and ctx.isPointInPath(seg22_svg, mouse0[0], mouse0[1]): ctx.fillStyle = '#FF9933' hover_joint = 1 ctx.fill(seg22_svg) ctx.stroke(seg22_svg) ctx.stroke(seg23_svg) ctx.stroke(seg24_svg) # Draw seg3 ctx.translate(0, -96) ctx.rotate(xt[2]) ctx.fillStyle = color1 ctx.fill(seg31_svg) ctx.stroke(seg31_svg) # Outline ctx.fill(seg32_svg) ctx.stroke(seg32_svg) # Outline ctx.fill(seg33_svg) ctx.stroke(seg33_svg) # Outline ctx.fillStyle = color2 if selectable and ctx.isPointInPath(seg34_svg, mouse0[0], mouse0[1]): ctx.fillStyle = '#99FF33' hover_joint = 2 ctx.fill(seg34_svg) ctx.stroke(seg34_svg) ctx.stroke(seg35_svg) ctx.stroke(seg36_svg) ctx.stroke(seg37_svg) # Draw end-effector point ctx.translate(-20.5, -51) ctx.beginPath() ctx.arc(0, 0, 2, 0, 2 * np.pi) ctx.fillStyle = color4 ctx.fill() # # Draw skeleton of the kinematic chain # ctx.setTransform(scaling_factor, 0, 0, scaling_factor, canvas.width*0.5, canvas.height*0.5) # Reset transformation # ctx.lineCap = 'round' # ctx.lineJoin = 'round' # ctx.lineWidth = '2' # ctx.strokeStyle = '#FF8888' # f = fkin0(x, param) # ctx.beginPath() # ctx.moveTo(0, 81) # for i in range(param.nbVarX+1): # ctx.lineTo(f[0,i], f[1,i]) # ctx.stroke() def draw_obj(param, color, colortxt): global selected_obj, hover_obj ctx.setTransform(scaling_factor, 0, 0, scaling_factor, canvas.width*0.5, canvas.height*0.5) # Reset transformation ctx.translate(param.Mu[0], param.Mu[1]) ctx.rotate(param.Mu[2]) # Draw object ctx.fillStyle = color obj = Path2D.new() obj.rect(-param.sz[0]/2, -param.sz[1]/2, param.sz[0], param.sz[1]) ctx.fill(obj) if ctx.isPointInPath(obj, mouse0[0], mouse0[1]): hover_obj = 0 if ctx.isPointInPath(obj, mouse0[0], mouse0[1]) and mousedown==1: selected_obj = 0 #ctx.fillRect(-param.sz[0]/2, -param.sz[1]/2, param.sz[0], param.sz[1]) if param.sz[0] > 39 and param.sz[1] > 19: ctx.textAlign = 'center' ctx.textBaseline = 'middle' ctx.font = '10px Permanent Marker' ctx.fillStyle = colortxt ctx.fillText('Move me!', 0, 0) def controlCommand(x, param): #f_ee = fkin(x, param) #J = Jkin(x, param) #u = np.linalg.pinv(J) @ logmap(fh, f_ee) u = np.zeros(param.nbVarX) return u ######################################################################################### def errorHandler(e): msg = 'Error: ' + str(e) console.error(msg) el = document.getElementById('repl-err') el.innerText = msg #el.textContent = msg ######################################################################################### x = [-np.pi/4, np.pi/2, np.pi/4] # Initial robot state #u = np.zeros(param.nbVarX) async def main(): global hover_joint, hover_obj, param, x while True: try: u = controlCommand(x, param) except Exception as e: errorHandler(e) u = np.zeros(param.nbVarX) x += u * param.dt # Reinit hovering variables hover_joint = -1 hover_obj = -1 # Rendering clear_screen() draw_ground() draw_obj(param, '#FF3399', '#DD1177') draw_robot(x, '#CCCCCC', '#AAAAAA', '#222222', '#000000', True) # Object selection if selected_obj==0: param.Mu[:2] = mouse param.Mu[0] = max(min(param.Mu[0],225), -225) param.Mu[1] = max(min(param.Mu[1],175), -175) param.Mu[2] = (float)(object_angle.value) await asyncio.sleep(0.0001) pyscript.run_until_complete(main())