Cost of Transport

• Also called: CoT, COT, specific resistance
• Category: Actuation & drivetrain › Ratings
• Tags: legged-locomotion, energy-efficiency, metrics, reinforcement-learning, actuation

A dimensionless measure of locomotion efficiency: the energy used to move a body a given distance, divided by its weight times that distance.

Definition

Cost of transport (CoT) measures how much energy a robot, animal or vehicle spends to move itself. It is defined as energy divided by weight times distance, E / (m g d), or equivalently power divided by weight times speed, P / (m g v). Dividing by weight and distance makes the quantity dimensionless, so a small quadruped, a humanoid, a car and a running animal can be compared on the same scale. The idea goes back to Gabrielli and von Kármán's 1950 comparison of vehicles, where the same ratio was called specific resistance.

The value depends heavily on what energy is counted. Total or electrical CoT uses all the power drawn from the battery, including motor losses, electronics and computers. Mechanical CoT uses only the mechanical power delivered at the joints, usually the sum over actuators of joint torque times joint velocity. A common convention counts only positive mechanical work, because energy absorbed by braking is generally lost as heat rather than returned to the battery; summing signed power would let negative work cancel positive work and understate the true cost. Papers therefore need to state which definition they use, and numbers from different definitions should not be compared directly.

Cost of transport changes with speed, gait and terrain. For animals and for many robots, each gait has a speed range in which CoT is lowest, and switching gait can lower it again at higher speeds. In learned locomotion, CoT is used both as an evaluation metric and as a reward or penalty term that encourages efficient, natural-looking motion; it is also a common way to show that a policy trained with motion priors uses less energy than one trained with hand-tuned rewards.

Why it matters

Battery capacity limits how long and how far mobile robots can operate, and actuator heating limits how hard they can work. Cost of transport turns efficiency into a single number that can be compared across designs, controllers and speeds, which helps decide between gaits, actuators and control strategies.

Key applications

• Comparing energy efficiency of legged robot designs and controllers
• Reward and penalty terms for learned locomotion policies
• Choosing gaits and speeds for long-range missions
• Evaluating actuators, transmissions and regenerative drives
• Comparing robots with animals and vehicles on a common scale

In practice

A team compares two locomotion policies for the same quadruped. They log joint torques and velocities at the controller rate while the robot walks at several fixed speeds on a treadmill, compute mechanical power as the sum of positive torque-velocity products, and divide by the robot's weight and speed to get mechanical CoT at each speed. They also log battery current and voltage to compute total CoT. One policy has a lower mechanical CoT but draws similar battery power, which they trace to high-frequency torque oscillation that heats the motors. They add a torque-rate penalty to the reward and repeat the comparison.

Common misconceptions

• A single CoT number describes a robot — CoT varies with speed, gait, payload and terrain, so comparisons must state the conditions
• Mechanical and total cost of transport are interchangeable — mechanical CoT ignores motor losses and electronics, and the two can differ by a large factor
• Summing signed joint power gives the energy used — negative work is usually not recovered, so many definitions count positive power only
• Cost of transport has units — it is dimensionless when computed with weight (m g) rather than mass

Who should know this

• Legged locomotion engineers
• Reinforcement learning practitioners designing locomotion rewards
• Actuator and power system designers
• Researchers comparing robot and animal locomotion

Related technologies

• Specific Resistance
• Adversarial Motion Priors
• Regenerative Motor Drives
• Quasi-Direct-Drive Actuators
• Passive Dynamic Walking

Related terms

• Locomotion
• Gait
• Quadruped
• Humanoid Robot
• Reinforcement Learning
• Quasi Direct Drive

Related projects

• LeRobot: HuggingFace ML library for real-world robotics in PyTorch
• MuJoCo: DeepMind physics engine for robotics and ML research
• PyBullet: Python physics simulator for robotics and RL research with fast CPU-based simulation
• Microduck: Pollen Robotics' $399 walking duck robot: open-source software, closed hardware
• Isaac Lab: NVIDIA robot learning framework: one task API across Newton, PhysX and Isaac Sim
• RLinf: Scalable infrastructure for post-training foundation models via RL