The team has assessed the new technology by racing, sliding, and jumping one-fifth-scale, fully autonomous auto-rally cars at the equivalent of 90 mph. The work, tested at the Georgia Tech Autonomous Racing Facility, is sponsored by the US Army Research Office.

Traditional robotic-vehicle techniques use the same control approach whether a vehicle is driving normally or at the edge of roadway adhesion, explained Professor Panagiotis Tsiotras (AE).

Aggressive driving in a robotic vehicle—maneuvering at the edge—is a unique control problem involving a highly complex system. However, by merging statistical physics with control theory, and utilizing leading-edge computation, we can create a new perspective, a new framework, for control of autonomous systems.

—Evangelos Theodorou, an AE assistant professor and project leader

Path integral optimal control frameworks provide a methodology for developing optimal control algorithms based on stochastic sampling of trajectories. However, the researchers noted in a 2015 paper on their work, a major issue with this approach is the handling of uncontrolled dynamics of the target system.

This is problematic since the probability of sampling a low cost trajectory using the uncontrolled dynamics is typically very low. This problem becomes more drastic when the underlying dynamics are nonlinear and sampled trajectories can become trapped in undesirable parts of the state space. … Although in some simple simulated scenarios changing the variance is not necessary, in many cases the natural variance of a system will be too low to produce useful deviations from the current trajectory. Previous methods have either dealt with this problem by artificially adding noise into the system and then optimizing the noisy system. Or they have simply ignored the problem entirely and sampled from whatever distribution worked best.

Although these approaches can be successful, both are problematic in that the optimization either takes place with respect to the wrong system or the resulting algorithm ignores the theoretical basis of path integral control. The approach we take here generalizes these approaches in that it enables for both the mean and variance of the sampling distribution to be changed by the control designer, without violating the underlying assumptions made in the path integral derivation. This enables the algorithm to converge fast enough that it can be applied in a model predictive control setting.

—Williams et al. (2015)

The Georgia Tech researchers used a stochastic trajectory-optimization capability, based on a path-integral approach, to create their MPPI control algorithm. Using statistical methods, the team integrated large amounts of handling-related information, together with data on the dynamics of the vehicular system, to compute the most stable trajectories from myriad possibilities.

Processed by the high-power graphics processing unit (GPU) that the vehicle carries, the MPPI control algorithm continuously samples data coming from global positioning system (GPS) hardware, inertial motion sensors, and other sensors. The onboard hardware-software system performs real-time analysis of a vast number of possible trajectories and relays optimal handling decisions to the vehicle moment by moment.

In essence, the MPPI approach combines both the planning and execution of optimized handling decisions into a single highly efficient phase. It’s regarded as the first technology to carry out this computationally demanding task; in the past, optimal-control data inputs could not be processed in real time.

The researchers’s two auto-rally vehicles—custom built by the team—utilize special electric motors to achieve the right balance between weight and power. The cars carry a motherboard with a quad-core processor, a potent GPU, and a battery.

Each vehicle also has two forward-facing cameras, an inertial measurement unit, and a GPS receiver, along with sophisticated wheel-speed sensors. The power, navigation, and computation equipment is housed in a rugged aluminum enclosure able to withstand violent rollovers. Each vehicle weighs about 48 pounds (21.8 kg) and is about three feet long.

These vehicles are able to test the team’s control algorithms without any need for off-vehicle devices or computation, except for a nearby GPS receiver. The onboard GPU lets the MPPI algorithm sample more than 2,500, 2.5-second-long trajectories in less than 1/60 of a second.

An important aspect in the team’s autonomous-control approach centers on the concept of costs—key elements of system functionality. Several cost components must be carefully matched to achieve optimal performance.

In the case of the Georgia Tech vehicles, the costs consist of three main areas:

• the cost for staying on the track;
• the cost for achieving a desired velocity; and
• the cost of the control system.

A sideslip-angle cost was also added to improve vehicle stability.

The cost approach is important to enabling a robotic vehicle to maximize speed while staying under control, explained James Rehg, a professor in the Georgia Tech School of Interactive Computing who is collaborating with Theodorou and Tsiotras.

It’s a complex balancing act, Rehg said. For example, when the researchers reduced one cost term to try to prevent vehicle sliding, they found they got increased drifting behavior.

What we’re talking about here is using the MPPI algorithm to achieve relative entropy minimization—and adjusting costs in the most effective way is a big part of that. To achieve the optimal combination of control and performance in an autonomous vehicle is definitely a non-trivial problem.

—James Rehg

Resources

• Grady Williams, Andrew Aldrich, Evangelos Theodorou (2015) “Model Predictive Path Integral Control using Covariance Variable Importance Sampling”