This paper presents a novel design approach for a two-DOF foot force sensor for a high speed running quadruped. The adopted approach harnesses the deformation property of an elastomeric material to relate applied force to measurable deformation. A lightweight, robust and compact magnetic-ﬁeld based sensing system, consisting of an assembly of miniature halleffect sensors, is employed to infer the positional information of a magnet embedded in the elastomeric material. Instead of solving two non-linear models (magnetic ﬁeld and elastomeric) sequentially, a direct approach of using artiﬁcial neural networks (ANN) is utilized to relate magnetic ﬂux density (MFD) measurements to applied forces. The force sensor, which weighs only 24.5 grams, provides a measurement range of 0 – 1000 N normal to the ground and up to ± 125N parallel to the ground. The mean force measurement accuracy was found to be within 7% of the applied forces. The sensor designed as part of this work ﬁnds direct applications in ground reaction force sensing for a running quadrupedal robot.
So what’s the deal here?
To achieve high speed locomotion in quadrupled (legged) robots, force detection and sensing at the feet are required to achieve stable motion. Imagine trying to walk or run without sensation at your bottom of your feet! While there are all kinds of force sensors available, they are either too bulky, heavy, fragile and/or unable to measure and withstand the large impact forces associated with running.
Hence there are two motivating factors for the development of this novel force sensor:
What’s a Force Sensor?
A force sensor is a device that measures an applied force. One can think of a bathroom weighing scale as a force sensor. In this case, when you step onto the scale, it measures the force you are applying on the scale. (And by Newton’s 3rd Law, vice versa). If you walk on and off a bathroom scale, you will observe the scale increasing to a maximum and then decreasing as you walk off it. Such information is crucial for control of the legs of the quadruped to achieve walking and running motion. In fact, the human body does this so effortlessly that you don’t even notice it. The Cheetah is the fastest mammal in the world and it uses its nerves at its paws to detect contact and forces to achieve speeds over 100 km/h!
How does a Force Sensor work?
In order to measure forces, it needs to be transformed into a quantity that can be readily measured. In many cases, forces are transformed into displacement (which is easily measured with say a ruler). One common method is to use a spring to convert forces to extension (via Hooke’s Law). The common bathroom scale uses this mechanism to display your weight. The force applied on a lever in the scale that is connected to a spring system. As the extensions of springs are a linear function of applied forces, the spring will extend to different lengths depending on the applied force. The end of this spring is connected to a dial via a rack and pinion system that rotates to show the current applied weight (This is why you see the numbers rotating across the scale in older non-electronic versions).
Oh ok. So what’s so interesting about this Force Sensor?
Industrial force sensors are readily available and majority of them use a beam cantilever system rather than an actual spring to transform applied force to displacement and thereafter use strain gauges (a device that uses the property of electrical conductance to reflect changes in elasticity with varying resistance) to measure this extension accurately. Unfortunately, strain gauges are susceptible to temperature and creep effects as well as not being able to handle high impact forces. Hence use of strain-gauge based force sensors is infeasible for a running quadruped. Hence to overcome the limitations of such force sensors, a novel Magneto-Elasteromic approach was devised.
Wow! Tell me more about this Magneto-Elastomeric methodology!
The approach undertaken here converts the applied force into compression and shearing of an elastomeric material under large strain and its resultant deformation is inferred from positional and angular displacement of an embedded magnet on the elastomeric material. A network of magnetic sensors is employed to provide a robust and non-contact means of detecting motion of the magnet through active monitoring of its attached magnetic field (MFD). In contemporary literature, there are two theoretical models that govern this force-deformation-magnetic field relationship. There are:
So how does it work?
So in actual operation all we need to do is to measure the magnetic field. This will allow us extract the deformation of the elastomeric material and thereafter allow us to extract the applied force. However, in practice this requires cascaded inverse solutions to two highly coupled and non-linear elastomeric and magnetic field models. Issues relating to this model-based cascaded approach are:
To mitigate these issues, we bypass both models and directly relate empirical MFD measurements to applied force using Artificial Neural Networks (ANN). ANNs are a biologically inspired mathematical tool employed to perform multi-dimensional non-linear mapping for precise function approximation. In addition, principal component analysis (PCA) is used as a pseudo linear filter to optimally reduce the dimension of the input mapping space for efficiency.
Can you show me what it looks like?
The sensing system consists of 5 elastomeric RTV (Room Temperature Vulcanization) silicone cylindrical posts placed between two aluminium plates, with the bottom plate attached to the paw and the upper plate connected to the metacarpal. We machined the aluminum plates on a HAAS 3 axis CNC milling machine. Subsequently we bonded the RTV silicone posts to the aluminum plates. This bonding process ensured high shear capability of the sensor without any risk of peeling between the RTV silicone and the aluminum plates. We then affixed a customized printed circuit board (PCB) containing 5 magnetic hall-effect sensors to the upper plate. A small cylindrical magnet with uniform magnetization is embedded in the middle of the lower plate. The choice of a small magnet and close proximity between sensors and magnet creates a compact system as well as minimizing possible ferromagnetic disturbances.
Great! Can I see the performance of the sensing system?
The data below compares the trained-ANN force estimation with the actual forces as measured by an industrial grade force-torque sensor (FTS). A spatial window was selected to magnify the differences between actual and estimated forces. The experimental results reveal that the average force sensing error in normal direction is 6.49% and 2.07% in the transverse direction. Most importantly, The weight of the force sensor was measured to be 24.5 grams, which is substantially lighter than most multi DOF, high force sensing range sensors currently available.