Wheeled Robotic Mobility Dimi Apostolopoulos
Significance of Mobility Move Position Transport Employ instruments and tools React to work loads in a controllable fashion ROBOTIC MOBILITY Dimi Apostolopoulos Page 2
Classification by Locomotion Type Wheels Legs Tracks Hybrids Special limbs Special joints ESA ExoMars Rover JAXA Rover NASA JSC Chariot NASA JPL ATHLETE ROBOTIC MOBILITY Dimi Apostolopoulos Page 3
Selecting Locomotion Type Wheels for Faster movement Generally fewer actuated DOFs Better packaging & survivability Hybrids for multi-mission tasks Legged for very rough terrain Reconfigurable, hopping systems for extreme terrain Undulatory for confined spaces Scaling considerations are critical ROBOTIC MOBILITY Dimi Apostolopoulos Page 4
This Lecture Wheeled Mobility 400 kg 200 kg 20 kg 600 kg CMU Systems 1200 kg 6000 kg ROBOTIC MOBILITY Dimi Apostolopoulos Page 5
Elements of Robotic Mobility ROBOTIC MOBILITY Dimi Apostolopoulos Page 6
Elements of Robotic Mobility Critical Dimensions Suspension 3-D Geometry Wheel (number, geometry, disposition) Actuation Inherent features for controllability C.G. & Ground Clearance Drive (type, actuation Requirements) Optimized FOV Steering (scheme, geometry, kinematics) Sensor Placement ROBOTIC MOBILITY Dimi Apostolopoulos Page 7
Robotic Mobility Locomotion elements (geometry, elastic vs. rigid) Wheel disposition and chassis geometry Drive scheme (independent vs. coordinated) Steering scheme (explicit vs. induced) Suspension (from passive to active, 2D vs. 3D) Articulation (passive vs. active, # & type of axis) Control (speed, traction, slip) Actuation (electric/hydraulic, etc.) Sensing (direct vs. inferred) Inherent features for higher terrainability and ease of control ROBOTIC MOBILITY Dimi Apostolopoulos Page 8
Synthesizing Novel Robotic Mobility Requirements Analysis Conceptual Design Preliminary Design Configuration Design Critical Design Development ROBOTIC MOBILITY Dimi Apostolopoulos Page 9
Physics-based Analysis of Mobility Requirements Analysis Quasi-static mechanics of robot-terrain interaction (force, torque, power, energy) Kinematics & dynamics Conceptual Design Stability analysis Controllability analysis Preliminary Design Physics of sensing Configuration Design Critical Design Development ROBOTIC MOBILITY Dimi Apostolopoulos Page 10
In-soil Performance Terramechanics Wheel-soil interaction models Wheel sinkage Motion resistance and traction Force, torque, power, energy Sizing wheels, drive actuation, drive electronics, drive mechanisms ROBOTIC MOBILITY Dimi Apostolopoulos Page 11
Wheel-ground Contact Contact patch A AbL (, ) W A This stress is called ground pressure. Tracks -- rectangular patch. But ground pressure is not always uniform. Sometimes get more sinkage than expected. p p ROBOTIC MOBILITY Dimi Apostolopoulos Page 12
Basic Physics of Wheel-Soil Interaction F A Normal Stress (pressure) p F A F F A Relates to ground pressure and sinkage. Shear Stress F A F Relates to traction, slip, and skid. ROBOTIC MOBILITY Dimi Apostolopoulos Page 13
Traction and Force W F 1 F 2 R 1 R 2 F R What are drive forces to overcome soil resistances? Will soil support the loads? F: Traction, R: Resistance, F > soil s capacity to react to loads ROBOTIC MOBILITY Dimi Apostolopoulos Page 14
Motion Resistance R c W Tandem W 2 W 1 σ F --Resistance by compacting soil (sinkage) under the wheel k b c Rc b k n1 z0 n1 The wider the wheel and greater the sinkage, the greater the resistance. R c2 F 2 R c1 ROBOTIC MOBILITY Dimi Apostolopoulos Page 15 F 1 Equal to work/length of pressing a block of width b to depth z.
Wheel Slip, Soil Thrust & Traction Not all rotational velocity is translated into linear velocity. ω v Rate of slip: i o r v v H Cannot be easily predicted, but can be measured and used for feedback control. Soil thrust actually takes slip into account: F K H AcW tan 1 1e io Ideal Soil Thrust i o K Slip Term ROBOTIC MOBILITY Dimi Apostolopoulos Page 16
Physics-Based Modeling & Analysis CMU s LocSyn Tool Example: Required Drive Torque T drws R c + R b + R r + R g d w = ----- 2 Compaction Resistance Drive Torque vs. Drive Torque Wheel Loading vs. Slope 2 b w sin + R b -------------------------- 2 sin cos 2cKc z K z 2 l r 90 2 cl r 2 = + + ------------------------- + -------- + cl w w 540 180 tan r 45 + -- 2 2 K c N c tan K 2N --------- + 1 2 2z w 2 = cos = cos = acos 1 -------- tan l d r = z w tan 45 - w 2 R cr w = 2 n + 2 -------------- 3W w cos 2n + 1 -------------------- -------------------------------------------------------------------------------------- d w 2n + 2 1 ----------- ----------- 2n + 1 2n + 1 3 n n + 1 k c + b w k n + 1 d w k c + b w k = 3W w cos 2n + 2 -------------------------------------------------------------------------- 2n + 1 2n + 2 2n + 1 R crw 3 n n + 1 Drive Torque vs. Rolling Radius Drive Torque vs. Tire Width Number of wheels: 6 Wheelbase: 2.5 m x 1.5 m Roll Radius: 0.25 m Tire width: 0.20 m Parametric analysis: Select wheel & mobility chassis key dimensions, and size actuators ROBOTIC MOBILITY Dimi Apostolopoulos Page 17
Significance of All-Wheel Drive R c2 W 2 F2 Rc1 W 1 F 1 Positive traction Greater pull Better slope climbing Better obstacle climbing Smoother control W 2 W 1 W F2 F 1 Drawbar Pull R c2 Rc1 θ θ N ROBOTIC MOBILITY Dimi Apostolopoulos Page 18
All-Wheel Drive for Obstacle Climbing Wheel dimension Chassis dimension ROBOTIC MOBILITY Dimi Apostolopoulos Page 19
Wheel Size vs. Number of Wheels Estimated ~2.2 W per wheel 150 kg 3-wheeled rover / ~50 kg/wheel 0.75 m rolling radius SILVRCLAW Martian soil: c= 1 kpa, = 18 deg ROBOTIC MOBILITY Dimi Apostolopoulos Page 20
Drawbar Pull (DP) Difference between soil thrust (max traction) and rolling resistance. c Max DP: 550 N Max slope: 22 deg Key metric of mobility; how much the vehicle can pull arctan(dp/w) is approximately equal to max gradeability as imposed by wheel-terrain interaction a b d e Analytical estimates within 3% of actual measured DP Direction of travel a. Robot driving normally b. Cable tension rapidly increases c. Wheels slipping d. Motion controller fault, at least one wheel stops servoing e. Robot reverses, cable goes slack Load cell Steel cable Wall ROBOTIC MOBILITY Dimi Apostolopoulos Page 21
Inclined Terrain Mobility Downhill gradeability Cross-hill gradeability Static stability vs. soil stability vs. actuator limitations ROBOTIC MOBILITY Dimi Apostolopoulos Page 22
Static Stability Limits *nomin al *low *high (values from tilt-table testing) ROBOTIC MOBILITY Dimi Apostolopoulos Page 23
Gradeability Static vs. Terrain Stability Tip-over Rollover The robot static stability limits to be greater than the terrain stability limits Analysis to help optimize vehicle geometry (center of gravity C.G. location, wheel base, wheel size) ROBOTIC MOBILITY Dimi Apostolopoulos Page 24
Gradeability Dynamic Limitations Analysis to help optimize vehicle geometry (C.G. location) and dynamic characteristics (deceleration performance) d 2 x/dt Robot Braking This analysis can be used to set max deceleration limits that the motion control imposes ROBOTIC MOBILITY Dimi Apostolopoulos Page 25
Improving Gradeability through Active Posturing Leaning posture at 20 ROBOTIC MOBILITY Dimi Apostolopoulos Page 26
Improving Path Tracking with Active Posturing Level posture Leaning posture ROBOTIC MOBILITY Dimi Apostolopoulos Page 27
Maneuverability Optimal steering geometry Turning radius Force, torque, power, energy Sizing wheels, drive/steering actuation, drive/steering electronics, steering mechanisms ROBOTIC MOBILITY Dimi Apostolopoulos Page 28
Steering Geometries Knuckle steering Single-axis (Ackermann) Four-wheel steering (double Ackermann, independent) Crab steering Articulated frame steering Skid steering Combined steering ROBOTIC MOBILITY Dimi Apostolopoulos Page 29
Steering Quasi-static Mechanics Overcome a moment resistance (M R ) in addition to compaction and bulldozing resistance. Moment resistance caused by lateral Coulomb friction. R i i 0 To minimize moment resistance, widen the body (increase B) and shorten the wheel base (decrease L) F F o i M R B M R R B x R M pbxdx Q x ROBOTIC MOBILITY Dimi Apostolopoulos Page 30
Skid Steering Power Draw L/2 L/2 F y4 All Intermittent Torques F y3 F Y1 F Y3 L L/2 F y1 M r Pivot Turn About Center Axle o F y2 Operational Condition Pivot turn about center axle Hard Surface No Obstruction = 0.7, R r = 1.5% RR = 1.5% Pivot turn about center axle Soft Surface No Obstruction = 0.4, R r = 25% f RR = 25% Power 3 x drive 3 x drive F Y2 F Y4 Pivot turn around obstacle Hard Surface Frt Wheel Obstructed = 0.7 f RR = 1.5% 3.5 x drive o Pivot Turn Around Obstacle ROBOTIC MOBILITY Dimi Apostolopoulos Page 31
Evaluation of Steering Geometries Ackerman (AS) Articulated (RS) Explicit (ES) ROBOTIC MOBILITY Dimi Apostolopoulos Page 32
Significance of Explicit Wheel Steering Ackerman (AS) Better terrainability Finer maneuverability More control flexibility Better tracking Articulated (RS) Explicit (ES) ROBOTIC MOBILITY Dimi Apostolopoulos Page 33
Steering Limitations Analysis to help optimize vehicle geometry (C.G. location, track width) and control parameters (max allowable steering speed) mv 2 /r ROBOTIC MOBILITY Dimi Apostolopoulos Page 34
Terrain Adaptation & Motion Smoothing Optimal suspension geometry Passive Dynamic (spring/damper type) Geometric Passive with active adjustability Active Elastic mobility elements ROBOTIC MOBILITY Dimi Apostolopoulos Page 35
Geometric Suspensions Averaging Pivoted Arm Body leveled Rocker arms at opposite angles ROBOTIC MOBILITY Dimi Apostolopoulos Page 36
Passive Geometric Suspensions - 6x6 Chasses JPL MER JPL Pathfinder JPL Rocky Series ESA ExoMars Rover EPFL SOLERO EPFLCRAB ROBOTIC MOBILITY Dimi Apostolopoulos Page 37
Passive Geometric Suspension 4x4 Chasses CMU Hyperion NASA Ames K10 Pitch CMU Zoe Roll ESA Lunar Robotic Mockup ROBOTIC MOBILITY Dimi Apostolopoulos Page 38
Semi-active Suspensions NASA JSC Chariot CMU Scarab Active DOF in series or parallel (e.g. Chariot) to passive suspension Discrete or continuous use of active DOF (e.g. Scarab s CG shifting) ROBOTIC MOBILITY Dimi Apostolopoulos Page 39
Suspension Configuration 6x6 w/ Pivoted Arms All Leading Arm All Trailing Arm Leading/Trailing/Trailing Leading/Leading/Trailing ROBOTIC MOBILITY Dimi Apostolopoulos Page 40
Step Climbing (1) How will this suspension layout perform during a step climb? Vehicle nose will rise first Hence Glacis plate will assist in step climb (Rem:- not all obstacles will be a step: Rugged boulders, tree stumps, etc.) ROBOTIC MOBILITY Dimi Apostolopoulos Page 41
Step Climbing Performance (2) Front Wheel Climbing Direction of Travel A Increased Reaction Force (Gives better Traction) e d F Z F X F Z F X e d Reaction Decreases ROBOTIC MOBILITY Dimi Apostolopoulos Page 42
Step Climbing Performance (3) Centre Wheel Climbing Centre-axle trailing arm will easily lift over step corner ROBOTIC MOBILITY Dimi Apostolopoulos Page 43
Analytical Configuration Drive, Suspension, Chassis PHASE 1 PHASE 3 PHASE 2 Middle wheel loses contact Both front and rear wheels lose contact during this phase ROBOTIC MOBILITY Dimi Apostolopoulos Page 44
Combine Force Equilibrium with (see next) i : angle between suspension arm and line hull-line : hull pitch angle 0.5W GR 11 o 1 39.8 o 11 o 2 39.8 o 11 o 3 39.8 o F 1 1 2 3 N 1 F 2 N 2 and N 3 are computed from the spring curve N 2 F 3 N 3 ROBOTIC MOBILITY Dimi Apostolopoulos Page 45
geometrically feasible configurations 0.5m H i 1.0m L L 12 = 0.375m 12 L 23 L 23 = 1.670m L A = 0.780m A B 1 L A 2 3 L A L A R w = 0.5m H i R w LH i + L A sin 1 = L 12 sin + L A sin 2 + + L A sin 2 + = L A sin 3 + + L 23 sin R w ROBOTIC MOBILITY Dimi Apostolopoulos Page 46
Derivation of Torque & Power for Drive System ROBOTIC MOBILITY Dimi Apostolopoulos Page 47
Tires/Wheels as Traction & Suspension Elements Lunokhod Wire-Mesh Wheel LRV Wire-Mesh Wheel MER & MSL Wheels Mitigate sinkage Increase contact area Minimize motion resistance Maximize traction W F R c σ ROBOTIC MOBILITY Dimi Apostolopoulos Page 48
Transmissibility 2.5 Unsprung Mass Sprung Mass 2 26 psi 20 psi Transmissibility 1.5 1 14 psi Significant consideration in that it affects dynamic-induced motions to sensors, payloads, and computing 0.5 Realistic shock duration 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Shock Duration / (s) ROBOTIC MOBILITY Dimi Apostolopoulos Page 49
Posture Changing for Terrain Adaptation JPL Gofor JPL All-Terrain Explorer Russian Wheel-Walking Rover ROBOTIC MOBILITY Dimi Apostolopoulos Page 50
Posture Changing for Science and Work JPL Nanorover CMU Scarab ROBOTIC MOBILITY Dimi Apostolopoulos Page 51
Dual-Use Locomotion Mechanisms CMU Nomad Suspension reconfiguration ROBOTIC MOBILITY Dimi Apostolopoulos Page 52
Mobility for Teleoperation & Safeguarding Significant inherent mobility features All-wheel drive In-plane, long-travel suspensions Progressive-spring behavior passive suspensions Geometric suspensions excellent too Maximum wheel diameter (fewer could be better) Skid-steered or explicitly steered Velocity control adequate (for high-speed teleoperation) Multiple wheels coupled to a single drivetrain (not always) Sensing (absolute speed & vector, inclination, traction) ROBOTIC MOBILITY Dimi Apostolopoulos Page 53
Closing Points Well-designed mobility key to robotic performance Use mechanics, geometry, analysis to design better robots Rationalize subsystem selections Blend methodological engineering and innovation to create high-performance systems Test, test, test Gladiator ROBOTIC MOBILITY Dimi Apostolopoulos Page 54